Package 'ade4'

Title: Analysis of Ecological Data: Exploratory and Euclidean Methods in Environmental Sciences
Description: Tools for multivariate data analysis. Several methods are provided for the analysis (i.e., ordination) of one-table (e.g., principal component analysis, correspondence analysis), two-table (e.g., coinertia analysis, redundancy analysis), three-table (e.g., RLQ analysis) and K-table (e.g., STATIS, multiple coinertia analysis). The philosophy of the package is described in Dray and Dufour (2007) <doi:10.18637/jss.v022.i04>.
Authors: Stéphane Dray <[email protected]>, Anne-Béatrice Dufour <[email protected]>, and Jean Thioulouse <[email protected]>, with contributions from Thibaut Jombart, Sandrine Pavoine, Jean R. Lobry, Sébastien Ollier, Daniel Borcard, Pierre Legendre, Stéphanie Bougeard and Aurélie Siberchicot. Based on earlier work by Daniel Chessel.
Maintainer: Aurélie Siberchicot <[email protected]>
License: GPL (>= 2)
Version: 1.7-22
Built: 2024-11-02 06:40:20 UTC
Source: CRAN

Help Index

The ade4 package

Description

This package is developed in the Biometry and Evolutionary Biology Lab (UMR CNRS 5558) - University Lyon 1. It contains Data Analysis functions to analyse Ecological and Environmental data in the framework of Euclidean Exploratory methods, hence the name ade4.

ade4 is characterized by (1) the implementation of graphical and statistical functions, (2) the availability of numerical data, (3) the redaction of technical and thematic documentation and (4) the inclusion of bibliographic references.

To cite ade4, please use citation("ade4").

Author(s)

Stéphane Dray, Anne-Béatrice Dufour, and Jean Thioulouse. Contributions from Daniel Borcard, Stéphanie Bougeard, Thibaut Jombart, Pierre Legendre, Jean R. Lobry, Sébastien Ollier, Sandrine Pavoine and Aurélie Siberchicot. Based on earlier work by Daniel Chessel.

References

Dray S and Dufour A (2007). “The ade4 Package: Implementing the Duality Diagram for Ecologists.” _Journal of Statistical Software_, *22*(4), pp. 1-20. doi: 10.18637/jss.v022.i04 (URL: http://doi.org/10.18637/jss.v022.i04).

See ade4 website: http://pbil.univ-lyon1.fr/ADE-4/

See Also

ade4TkGUI, adegenet, adehabitat, adegraphics

Phylogenies and quantitative traits from Abouheif

Description

This data set gathers three phylogenies with three sets of traits as reported by Abouheif (1999).

Usage

data(abouheif.eg)

Format

abouheif.eg is a list containing the 6 following objects :

tre1

is a character string giving the first phylogenetic tree made up of 8 leaves.

vec1

is a numeric vector with 8 values.

tre2

is a character string giving the second phylogenetic tree made up of 7 leaves.

vec2

is a numeric vector with 7 values.

tre3

is a character string giving the third phylogenetic tree made up of 15 leaves.

vec3

is a numeric vector with 15 values.

Source

Data taken from the phylogenetic independence program developped by Ehab Abouheif

References

Abouheif, E. (1999) A method for testing the assumption of phylogenetic independence in comparative data. Evolutionary Ecology Research, 1, 895–909.

Examples

data(abouheif.eg)
par(mfrow=c(2,2))
symbols.phylog(newick2phylog(abouheif.eg$tre1), abouheif.eg$vec1,
 sub = "Body Mass (kg)", csi = 2, csub = 2)
symbols.phylog(newick2phylog(abouheif.eg$tre2), abouheif.eg$vec2,
 sub = "Body Mass (kg)", csi = 2, csub = 2)
dotchart.phylog(newick2phylog(abouheif.eg$tre1), abouheif.eg$vec1,
 sub = "Body Mass (kg)", cdot = 2, cnod = 1, possub = "topleft",
  csub = 2, ceti = 1.5)
dotchart.phylog(newick2phylog(abouheif.eg$tre2), abouheif.eg$vec2,
 sub = "Body Mass (kg)", cdot = 2, cnod = 1, possub = "topleft",
  csub = 2, ceti = 1.5)
par(mfrow = c(1,1))

w.phy=newick2phylog(abouheif.eg$tre3)
dotchart.phylog(w.phy,abouheif.eg$vec3, clabel.n = 1)

Spatial pattern analysis in plant communities

Description

Counts of individuals of Acacia ehrenbergiana from five parallel transects of 32 quadrats.

Usage

data(acacia)

Format

acacia is a data frame with 15 variables :
se.T1, se.T2, se.T3, se.T4, se.T5 are five numeric vectors containing quadrats counts of seedlings from transects 1 to 5 respectively;
sm.T1, sm.T2, sm.T3, sm.T4, sm.T5 are five numeric vectors containing quadrats counts of small trees (crown < 1 m2m^{2} in canopy) of transects 1 to 5 respectively;
la.T1, la.T2, la.T3, la.T4, la.T5 are five numeric vectors containing quadrats counts of trees with large crown (crown > 1 m2m^{2} in canopy) of transects 1 to 5 respectively.

Source

Greig-Smith, P. and Chadwick, M.J. (1965) Data on pattern within plant communities. III. Acacia-Capparis semi-desert scrub in the Sudan. Journal of Ecology, 53, 465–474.

References

Hill, M.O. (1973) The intensity of spatial pattern in plant communities. Journal of Ecology, 61, 225–235.

Examples

data(acacia)
if(adegraphicsLoaded()) {
  gg <- s1d.barchart(acacia, p1d.horizontal = FALSE, psub.position = "topleft", 
    plabels.cex = 0, ylim = c(0,20))
} else {
  par(mfcol = c(5, 3))
  par(mar = c(2, 2, 2, 2))
  for(k in 1:15) {
    barplot(acacia[, k], ylim = c(0, 20), col = grey(0.8))
    ade4:::scatterutil.sub(names(acacia)[k], 1.5, "topleft")
  }
  par(mfcol = c(1, 1))
}

Add graphics to an existing plot

Description

add.scatter is a function which defines a new plot area within an existing plot and displays an additional graphic inside this area. The additional graphic is determined by a function which is the first argument taken by add.scatter. It can be used in various ways, for instance to add a screeplot to an ordination scatterplot (add.scatter.eig).
The function add.scatter.eig uses the following colors: black (represented axes), grey(axes retained in the analysis) and white (others).

Usage

add.scatter(func,posi = c("bottomleft","bottomright","topleft","topright"),
ratio = 0.2, inset = 0.01, bg.col = 'white')
add.scatter.eig(w, nf = NULL, xax, yax, posi = "bottomleft", ratio =
.25, inset = 0.01, sub = "Eigenvalues", csub = 2 * ratio)

Arguments

func

an - evaluated - function producing a graphic
posi

a character vector (only its first element being considered) giving the position of the added graph. Possible values are "bottomleft" (="bottom"),"bottomright","topleft" (="top"),"topright", and "none" (no plot).
ratio

the size of the added graph in proportion of the current plot region
inset

the inset from which the graph is drawn, in proportion of the whole plot region. Can be a vector of length 2, giving the inset in x and y. If atomic, same inset is used in x and y
bg.col

the color of the background of the added graph
w

numeric vector of eigenvalues
nf

the number of retained factors, NULL if not provided
xax

first represented axis
yax

second represented axis
sub

title of the screeplot
csub

size of the screeplot title

Details

add.scatter uses par("plt") to redefine the new plot region. As stated in par documentation, this produces to (sometimes surprising) interactions with other parameters such as "mar". In particular, such interactions are likely to reset the plot region by default which would cause the additional graphic to take the whole plot region. To avoid such inconvenient, add par([other options], plt=par("plt")) when using par in your graphical function (argument func).

Value

The matched call (invisible).

Author(s)

Thibaut Jombart [email protected]

See Also

scatter

Examples

data(microsatt)
  w <- dudi.coa(data.frame(t(microsatt$tab)), scann = FALSE, nf = 3)
    
  if(adegraphicsLoaded()) {
    a1 <- rnorm(100)
    b1 <- s1d.barchart(sort(a1), p1d.horizontal = FALSE, plot = FALSE)
    h1 <- s1d.hist(a1, pgrid.draw = FALSE, porigin.draw = FALSE, pbackground.col = "grey", 
      plot = FALSE, ppoly.col = "white", ppoly.alpha = 1)
    g1 <- insert(h1, b1, posi = "topleft", plot = FALSE)
  
    a2 <- rnorm(100)
    b2 <- s1d.barchart(sort(a2), p1d.horizontal = FALSE, plot = FALSE)
    h2 <- s1d.hist(a2, pgrid.draw = FALSE, porigin.draw = FALSE, pbackground.col = "grey", 
      plot = FALSE, ppoly.col = "white", ppoly.alpha = 1)
    g2 <- insert(h2, b2, posi = "topleft", inset = c(0.25, 0.01), plot = FALSE)
  
    a3 <- rnorm(100)
    b3 <- s1d.barchart(sort(a3), p1d.horizontal = FALSE, plot = FALSE)
    h3 <- s1d.hist(a3, pgrid.draw = FALSE, porigin.draw = FALSE, pbackground.col = "grey", 
      plot = FALSE, ppoly.col = "white", ppoly.alpha = 1)
    g3 <- insert(h3, b3, posi = "bottomleft", inset = 0.4, ratio = 0.2, plot = FALSE)
  
    a4 <- rnorm(100)
    b4 <- s1d.barchart(sort(a4), p1d.horizontal = FALSE, plot = FALSE)
    h4 <- s1d.hist(a4, pgrid.draw = FALSE, porigin.draw = FALSE, pbackground.col = "grey", 
      plot = FALSE, ppoly.col = "white", ppoly.alpha = 1)
    g4 <- insert(h3, b3, posi = "bottomright", ratio = 0.3, plot = FALSE)
    
    G1 <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2), plot = TRUE)
    
    g5 <- s.label(w$co, plot = FALSE)
    g6 <- plotEig(w$eig, w$nf, psub = list(text = "Eigenvalues"), 
      pbackground = list(box = TRUE), plot = FALSE)
    G2 <- insert(g6, g5, posi = "bottomright", ratio = 0.25)

  } else {
    par(mfrow=c(2,2))
    f1 <- function(a){
      opar=par("mar","xaxt","yaxt","plt")
      on.exit(par(opar))
      par(mar=rep(.1,4),xaxt="n",yaxt="n",plt=par("plt"))
    
      hist(a,xlab="",ylab="",main="",col="white",proba=TRUE)
      lines(seq(-4,4,le=50),dnorm(seq(-4,4,le=50)),col="red")
    }
    
    a <- rnorm(100)
    barplot(sort(a))
    add.scatter(f1(a),posi="topleft",bg.col="grey")
    
    a <- rnorm(100)
    barplot(sort(a))
    add.scatter(f1(a),posi="topleft",bg.col="grey",inset=c(.25,.01))
    
    a <- rnorm(100)
    barplot(sort(a))
    add.scatter(f1(a),posi="topleft",bg.col="grey",inset=.25,ratio=.1)
    
    a <- rnorm(100)
    barplot(sort(a))
    add.scatter(f1(a),posi="bottomright",bg.col="grey",ratio=.3)
    par(mfrow=c(1,1))
    
    s.label(w$co)
    add.scatter.eig(w$eig,w$nf,posi="bottomright",1,2)
  }

Codon usage

Description

aminoacyl is a list containing the codon counts of 36 genes encoding yeast aminoacyl-tRNA-synthetase(S.Cerevisiae).

Usage

data(aminoacyl)

Format

aminoacyl is a list containing the 5 following objects:

genes

is a vector giving the gene names.

localisation

is a vector giving the cellular localisation of the proteins (M = mitochondrial, C = cytoplasmic, I = indetermined, CI = cyto and mito).

codon

is a vector containing the 64 triplets.

AA

is a factor giving the amino acid names for each codon.

usage.codon

is a dataframe containing the codon counts for each gene.

Source

Data prepared by D. Charif [email protected] starting from:
http://www.expasy.org/sprot/

References

Chiapello H., Olivier E., Landes-Devauchelle C., Nitschké P. and Risler J.L (1999) Codon usage as a tool to predict the cellular localisation of eukariotic ribosomal proteins and aminoacyl-tRNA synthetases. Nucleic Acids Res., 27, 14, 2848–2851.

Examples

data(aminoacyl)
aminoacyl$genes
aminoacyl$usage.codon
dudi.coa(aminoacyl$usage.codon, scannf = FALSE)

Analysis of molecular variance

Description

The analysis of molecular variance tests the differences among population and/or groups of populations in a way similar to ANOVA. It includes evolutionary distances among alleles.

Usage

amova(samples, distances, structures)
## S3 method for class 'amova'
print(x, full = FALSE, ...)

Arguments

samples

a data frame with haplotypes (or genotypes) as rows, populations as columns and abundance as entries
distances

an object of class dist computed from Euclidean distance. If distances is null, equidistances are used.
structures

a data frame containing, in the jth row and the kth column, the name of the group of level k to which the jth population belongs
x

an object of class amova
full

a logical value indicating whether the original data ('distances', 'samples', 'structures') should be printed
...

further arguments passed to or from other methods

Value

Returns a list of class amova

call

call
results

a data frame with the degrees of freedom, the sums of squares, and the mean squares. Rows represent levels of variability.
componentsofcovariance

a data frame containing the components of covariance and their contribution to the total covariance
statphi

a data frame containing the phi-statistics

Author(s)

Sandrine Pavoine [email protected]

References

Excoffier, L., Smouse, P.E. and Quattro, J.M. (1992) Analysis of molecular variance inferred from metric distances among DNA haplotypes: application to human mitochondrial DNA restriction data. Genetics, 131, 479–491.

See Also

randtest.amova

Examples

data(humDNAm)
amovahum <- amova(humDNAm$samples, sqrt(humDNAm$distances), humDNAm$structures)
amovahum

Allelic frequencies in ten honeybees populations at eight microsatellites loci

Description

This data set gives the occurences for the allelic form on 8 loci in 10 populations of honeybees.

Usage

data(apis108)

Format

A data frame containing 180 rows (allelic forms on 8 loci) and 10 columns (populations of honeybees : El.Hermel, Al.Hoceima, Nimba, Celinda, Pretoria, Chalkidiki, Forli, Valenciennes, Umea and Seville).

Source

http://www1.montpellier.inra.fr/URLB/apis/libanfreq.pdf

Franck P., Garnery L., Solignac M. and Cornuet J.M. (2000) Molecular confirmation of a fourth lineage in honeybees from the Near-East. Apidologie, 31, 167–180.

Examples

data(apis108)
str(apis108)
names(apis108)

Apportionment of Quadratic Entropy

Description

The hierarchical apportionment of quadratic entropy defined by Rao (1982).

Usage

apqe(samples, dis = NULL, structures)
## S3 method for class 'apqe'
print(x, full = FALSE, ...)

Arguments

samples

a data frame with haplotypes (or genotypes) as rows, populations as columns and abundance or presence-absence as entries
dis

an object of class dist computed from Euclidean distance. If dis is null, equidistances are used.
structures

a data frame that contains, in the jth row and the kth column, the name of the group of level k to which the jth population belongs
x

an object of class apqe
full

a logical value that indicates whether the original data ('distances', 'samples', 'structures') should be printed
...

... further arguments passed to or from other methods

Value

Returns a list of class apqe

call

call
results

a data frame that contains the components of diversity.

Author(s)

Sandrine Pavoine [email protected]

References

Rao, C.R. (1982) Diversity: its measurement, decomposition, apportionment and analysis. Sankhya: The Indian Journal of Statistics, A44, 1–22.

Pavoine S. and Dolédec S. (2005) The apportionment of quadratic entropy: a useful alternative for partitioning diversity in ecological data. Environmental and Ecological Statistics, 12, 125–138.

Examples

data(ecomor)
ecomor.phylog <- taxo2phylog(ecomor$taxo)
apqe(ecomor$habitat, ecomor.phylog$Wdist)

Distribution of Alpine plants in Aravo (Valloire, France)

Description

This dataset describe the distribution of 82 species of Alpine plants in 75 sites. Species traits and environmental variables are also measured.

Usage

data(aravo)

Format

aravo is a list containing the following objects :

spe

is a data.frame with the abundance values of 82 species (columns) in 75 sites (rows).

env

is a data.frame with the measurements of 6 environmental variables for the sites.

traits

is data.frame with the measurements of 8 traits for the species.

spe.names

is a vector with full species names.

Details

The environmental variables are:

Aspect Relative south aspect (opposite of the sine of aspect with flat coded 0)
Slope Slope inclination (degrees)
Form Microtopographic landform index: 1 (convexity); 2 (convex slope); 3 (right slope); 4 (concave slope); 5 (concavity)
Snow Mean snowmelt date (Julian day) averaged over 1997-1999
PhysD Physical disturbance, i.e., percentage of unvegetated soil due to physical processes
ZoogD Zoogenic disturbance, i.e., quantity of unvegetated soil due to marmot activity: no; some; high

The species traits for the plants are:

Height Vegetative height (cm)
Spread Maximum lateral spread of clonal plants (cm)
Angle Leaf elevation angle estimated at the middle of the lamina
Area Area of a single leaf
Thick Maximum thickness of a leaf cross section (avoiding the midrib)
SLA Specific leaf area
Nmass Mass-based leaf nitrogen content
Seed Seed mass

Source

Choler, P. (2005) Consistent shifts in Alpine plant traits along a mesotopographical gradient. Arctic, Antarctic, and Alpine Research, 37,444–453.

Examples

data(aravo)
coa1 <- dudi.coa(aravo$spe, scannf = FALSE, nf = 2)
dudienv <- dudi.hillsmith(aravo$env, scannf = FALSE, nf = 2, row.w = coa1$lw)
duditrait <- dudi.pca(aravo$traits, scannf = FALSE, nf = 2, row.w = coa1$cw)
rlq1 <- rlq(dudienv, coa1, duditrait, scannf = FALSE, nf = 2)
plot(rlq1)

Fauna Table with double (row and column) partitioning

Description

This data set gives information about species of benthic macroinvertebrates in different sites and dates.

Usage

data(ardeche)

Format

ardeche is a list with 6 components.

tab

is a data frame containing fauna table with 43 species (rows) and 35 samples (columns).

col.blocks

is a vector containing the repartition of samples for the 6 dates : july 1982, august 1982, november 1982, february 1983, april 1983 and july 1983.

row.blocks

is a vector containing the repartition of species in the 4 groups defining the species order.

dat.fac

is a date factor for samples (6 dates).

sta.fac

is a site factor for samples (6 sites).

esp.fac

is a species order factor (Ephemeroptera, Plecoptera, Coleoptera, Trichoptera).

Details

The columns of the data frame ardeche$tab define the samples by a number between 1 and 6 (the date) and a letter between A and F (the site).

Source

Cazes, P., Chessel, D., and Dolédec, S. (1988) L'analyse des correspondances internes d'un tableau partitionné : son usage en hydrobiologie. Revue de Statistique Appliquée, 36, 39–54.

Examples

data(ardeche)
dudi1 <- dudi.coa(ardeche$tab, scan = FALSE)
s.class(dudi1$co, ardeche$dat.fac)
if(adegraphicsLoaded()) {
  s.label(dudi1$co, plab.cex = 0.5, add = TRUE)
} else {
  s.label(dudi1$co, clab = 0.5, add.p = TRUE)
}

Graphical Display of Areas

Description

'area' is a data frame with three variables.
The first variable is a factor defining the polygons.
The second and third variables are the xy coordinates of the polygon vertices in the order where they are found.

area.plot : grey levels areas mapping

poly2area takes an object of class 'polylist' (maptools package) and returns a data frame of type area.
area2poly takes an object of type 'area' and returns a list of class 'polylist'
area2link takes an object of type 'area' and returns a proximity matrix which terms are given by the length of the frontier between two polygons.
area.util.contour,area.util.xy and area.util.class are three utility functions.

Usage

area.plot(x, center = NULL, values = NULL, graph = NULL, lwdgraph = 2,
nclasslegend = 8, clegend = 0.75, sub = "", csub = 1, 
possub = "topleft", cpoint = 0, label = NULL, clabel = 0, ...)

area2poly(area)
poly2area(polys)
area2link(area)
area.util.contour(area)
area.util.xy(area)

Arguments

x

a data frame with three variables
center

a matrix with the same row number as x and two columns, the coordinates of polygone centers. If NULL, it is computed with area.util.xy
values

if not NULL, a vector which values will be mapped to grey levels. The values must be in the same order as the values in unique(x.area[,1])
graph

if not NULL, graph is a neighbouring graph (object of class "neig") between polygons
lwdgraph

a line width to draw the neighbouring graph
nclasslegend

if value not NULL, a number of classes for the legend
clegend

if not NULL, a character size for the legend, used with par("cex")*clegend
sub

a string of characters to be inserted as sub-title
csub

a character size for the sub-titles, used with par("cex")*csub
possub

a string of characters indicating the sub-titles position ("topleft", "topright", "bottomleft", "bottomright")
cpoint

if positive, a character size for drawing the polygons vertices (check up), used with par("cex")*cpoint
label

if not NULL, by default the levels of the factor that define the polygons are used as labels. To change this value, use label. These labels must be in the same order than unique(x.area[,1])
clabel

if not NULL, a character size for the polygon labels,
used with par("cex")*clabel
polys

a list belonging to the 'polylist' class in the spdep package
area

a data frame of class 'area'
...

further arguments passed to or from other methods

Value

poly2area returns a data frame 'factor,x,y'.
area2poly returns a list of class polylist.

Author(s)

Daniel Chessel

Examples

data(elec88)
par(mfrow = c(2, 2))
area.plot(elec88$area, cpoint = 1)
area.plot(elec88$area, lab = elec88$lab$dep, clab = 0.75)
area.plot(elec88$area, clab = 0.75)
# elec88$neig <- neig(area = elec88$area)
area.plot(elec88$area, graph = elec88$neig, sub = "Neighbourhood graph", possub = "topright")
par(mfrow = c(1, 1))

## Not run: 
    par(mfrow = c(3, 3))
    for(i in 1:9) {
      x <- elec88$tab[,i]
      area.plot(elec88$area, val = x, sub = names(elec88$tab)[i], csub = 3, cleg = 1.5)
    }
    par(mfrow = c(1, 1))
    
    if(adegraphicsLoaded()) {
      if(requireNamespace("sp", quietly = TRUE)) {
        s.value(elec88$xy, elec88$tab, Sp = elec88$Spatial,
          method = "color", psub.text = names(elec88$tab), psub.cex = 3, 
          pSp.col = "white", pgrid.draw = FALSE, porigin.include = FALSE)
      }
    } else {
      par(mfrow = c(3, 3))
      for(i in 1:9) {
        x <- elec88$tab[, i]
        s.value(elec88$xy, elec88$tab[, i], contour = elec88$contour,
         meth = "greylevel", sub = names(elec88$tab)[i], csub = 3, 
         cleg = 1.5, incl = FALSE)
        }
      par(mfrow = c(1, 1))
    }
    
    if(!adegraphicsLoaded()) {
      data(irishdata)
      par(mfrow = c(2, 2))
      w <- ade4:::area.util.contour(irishdata$area)
      xy <- ade4:::area.util.xy(irishdata$area)
      area.plot(irishdata$area, cpoint = 1)
      apply(w, 1, function(x) segments(x[1], x[2], x[3], x[4], lwd = 3))
      area.plot(irishdata$area, clabel = 1)
      s.label(xy, area = irishdata$area, incl = FALSE, clab = 0, 
        cpoi = 3, addax = FALSE, contour = w)
      s.label(xy, area = irishdata$area, incl = FALSE, 
        addax = FALSE, contour = w)
      par(mfrow = c(1, 1))

    }

## End(Not run)

data(irishdata)
w <- irishdata$area[c(42:53, 18:25), ]
w
w$poly <- as.factor(as.character(w$poly))
area.plot(w, clab = 2)
 
points(68, 59, pch = 20, col = "red", cex = 3)
points(68, 35, pch = 20, col = "red", cex = 3)
points(45, 12, pch = 20, col = "red", cex = 3)
sqrt((59 - 35) ^ 2) + sqrt((68 - 45) ^ 2 + (35 - 12) ^ 2)
area2link(w)

Arrivals at an intensive care unit

Description

This data set gives arrival times of 254 patients at an intensive care unit during one day.

Usage

data(arrival)

Format

arrival is a list containing the 2 following objects :

times

is a vector giving the arrival times in the form HH:MM

hours

is a vector giving the number of arrivals per hour for the day considered

Source

Data taken from the Oriana software developped by Warren L. Kovach [email protected] starting from https://www.kovcomp.co.uk/oriana/index.html.

References

Fisher, N. I. (1993) Statistical Analysis of Circular Data. Cambridge University Press.

Examples

data(arrival)
dotcircle(arrival$hours, pi/2 + pi/12)

Taxonomy

Description

The function as.taxo creates an object of class taxo that is a sub-class of data.frame. Each column of the data frame must be a factor corresponding to a level j of the taxonomy (genus, family, ...). The levels of factor j define some classes that must be completly included in classes of factor j+1.
A factor with exactly one level is not allowed. A factor with exactly one individual in each level is not allowed. The function dist.taxo compute taxonomic distances.

Usage

as.taxo(df)
dist.taxo(taxo)

Arguments

df

a data frame
taxo

a data frame of class taxo

Value

as.taxo returns a data frame of class taxo. dist.taxo returns a numeric of class dist.

Author(s)

Daniel Chessel
Sébastien Ollier [email protected]

See Also

taxo2phylog to transform an object of class taxo into an object of class phylog

Examples

data(taxo.eg)
tax <- as.taxo(taxo.eg[[1]])
tax.phy <- taxo2phylog(as.taxo(taxo.eg[[1]]),add.tools=TRUE)
par(mfrow = c(1,2))
plot(tax.phy, clabel.l = 1.25, clabel.n = 1.25, f = 0.75)
plot(taxo2phylog(as.taxo(taxo.eg[[1]][sample(15),])),
 clabel.l = 1.25, clabel.n = 1.25, f = 0.75)
par(mfrow = c(1,1))
all(dist.taxo(tax)==tax.phy$Wdist)

Small Ecological Dataset

Description

atlas is a list containing three kinds of information about 23 regions (The French Alps) :
geographical coordinates, meteorology and bird presences.

Usage

data(atlas)

Format

atlas is a list of 9 components:

area

is a convex hull of 23 geographical regions.

xy

are the coordinates of the region centers and altitude (in meters).

names.district

is a vector of region names.

meteo

is a data frame with 7 variables: min and max temperature in january; min and max temperature in july; january, july and total rainfalls.

birds

is a data frame with 15 variables (species).

contour

is a data frame with 4 variables (x1, y1, x2, y2) for the contour display of The French Alps.

alti

is a data frame with 3 variables altitude in percentage [0,800], ]800,1500] and ]1500,5000].

Spatial

is the map of the 23 regions of The French Alps (an object of the class SpatialPolygons of sp).

Spatial.contour

is the contour of the map of the 23 regions of the French Alps (an object of the class SpatialPolygons of sp).

Source

Extract from:
Lebreton, Ph. (1977) Les oiseaux nicheurs rhonalpins. Atlas ornithologique Rhone-Alpes. Centre Ornithologique Rhone-Alpes, Universite Lyon 1, 69621 Villeurbanne. Direction de la Protection de la Nature, Ministere de la Qualite de la Vie. 1–354.

Examples

data(atlas)
if(adegraphicsLoaded()) {
  if(requireNamespace("sp", quietly = TRUE)) {
    g11 <- s.Spatial(atlas$Spatial, pSp.col = "white", plot = FALSE)
    g12 <- s.label(atlas$area[, 2:3], plabels.cex = 0, plot = FALSE)
    g1 <- superpose(g11, g12, plot = FALSE)
    g2 <- s.label(atlas$xy, lab = atlas$names.district, Sp = atlas$Spatial, 
      pgrid.dra = FALSE, pSp.col = "white", plot = FALSE)
    obj3 <- sp::SpatialPolygonsDataFrame(Sr = atlas$Spatial, data = atlas$meteo)
    g3 <- s.Spatial(obj3[, 1], nclass = 12, psub = list(position = "topleft", 
      text = "Temp Mini January", cex = 2), plot = FALSE)
    g4 <- s.corcircle((dudi.pca(atlas$meteo, scann = FALSE)$co), plabels.cex = 1, plot = FALSE)
    G1 <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))
  
    obj5 <- sp::SpatialPolygonsDataFrame(Sr = atlas$Spatial, 
      data = dudi.pca(atlas$meteo, scann = FALSE)$li)
    g5 <- s.Spatial(obj5[, 1], nclass = 12, psub = list(position = "topleft", 
      text = "Principal Component Analysis analysis", cex = 1.5), plot = FALSE)
    coa1 <- dudi.coa(atlas$birds, scann = FALSE, nf = 1)
    obj6 <- sp::SpatialPolygonsDataFrame(Sr = atlas$Spatial, data = coa1$li)
    g6 <- s.Spatial(obj6[, 1], nclass = 12, psub = list(position = "topleft", 
      text = "Correspondence analysis", cex = 1.5), plot = FALSE)
    g7 <- s.value(atlas$xy, coa1$li$Axis1, Sp = atlas$Spatial.contour, ppoints.cex = 2, 
      porigin.include = FALSE, paxes.draw = FALSE, pSp.col = "white", plot = FALSE)
    g8 <- triangle.label(atlas$alti, plabels.cex = 0, plot = FALSE)
    G2 <- ADEgS(list(g5, g6, g7, g8), layout = c(2, 2))
  
  }
} else {
  op <- par(no.readonly = TRUE) 
  par(mfrow = c(2, 2))
  area.plot(atlas$area, cpoin = 1.5)
  area.plot(atlas$area, lab = atlas$names.district, clab = 1)
  x <- atlas$meteo$mini.jan
  
  names(x) <- row.names(atlas$meteo)
  area.plot(atlas$area, val = x, ncl = 12, sub = "Temp Mini January", csub = 2, cleg = 1)
  s.corcircle((dudi.pca(atlas$meteo, scann = FALSE)$co), clab = 1)
  
  area.plot(atlas$area, val = dudi.pca(atlas$meteo,scann=FALSE)$li[, 1], ncl = 12, 
    sub = "Principal Component Analysis analysis", csub = 1.5, cleg = 1)
  birds.coa <- dudi.coa(atlas$birds, sca = FALSE, nf = 1)
  x <- birds.coa$li$Axis1
  area.plot(atlas$area, val = x, ncl = 12, sub = "Correspondence analysis", csub = 1.5, cleg = 1)
  
  s.value(atlas$xy, x, contour = atlas$contour, csi = 2, incl = FALSE, addax = FALSE)
  triangle.plot(atlas$alti)
  par(op)
  par(mfrow = c(1, 1))}

Genetic variability of Cacadors

Description

This data set contains information about genetic variability of Atya innocous and Atya scabra in Guadeloupe (France).

Usage

data(atya)

Format

atya is a list with the following components:

xy

a data frame with the coordinates of the 31 sites

gen

a data frame with 22 variables collected on 31 sites

neig

an object of class neig

nb

a neighborhood object (class nb defined in package spdep)

Source

Fievet, E., Eppe, F. and Dolédec, S. (2001) Etude de la variabilité morphométrique et génétique des populations de Cacadors (Atya innocous et Atya scabra) de l'île de Basse-Terre. Direction Régionale de L'Environnement Guadeloupe, Laboratoire des hydrosystèmes fluviaux, Université Lyon 1.

Examples

## Not run: 
data(atya)
if(requireNamespace("pixmap", quietly = TRUE)) {
  atya.digi <- pixmap::read.pnm(system.file("pictures/atyadigi.pnm",
      package = "ade4"))
  atya.carto <- pixmap::read.pnm(system.file("pictures/atyacarto.pnm",
      package = "ade4"))
  par(mfrow = c(1, 2))
  pixmap:::plot(atya.digi)
  pixmap:::plot(atya.carto)
  points(atya$xy, pch = 20, cex = 2)
}
if(requireNamespace("spdep", quietly = TRUE)) {
  plot(neig2nb(atya$neig), atya$xy, col = "red", add = TRUE, lwd = 2)
  par(mfrow = c(1,1))
}

## End(Not run)

Bird species distribution

Description

This data set contains information about spatial distribution of bird species in a zone surrounding the river Rhône near Lyon (France).

Usage

data(avijons)

Format

avijons is a list with the following components:

xy

a data frame with the coordinates of the sites

area

an object of class area

fau

a data frame with the abundance of 64 bird species in 91 sites

spe.names.fr

a vector of strings of character with the species names in french

Spatial

an object of the class SpatialPolygons of sp, containing the map

Source

Bournaud, M., Amoros, C., Chessel, D., Coulet, M., Doledec, S., Michelot, J.L., Pautou, G., Rostan, J.C., Tachet, H. and Thioulouse, J. (1990). Peuplements d'oiseaux et propriétés des écocomplexes de la plaine du Rhône : descripteurs de fonctionnement global et gestion des berges. Rapport programme S.R.E.T.I.E., Ministère de l'Environnement CORA et URA CNRS 367, Univ. Lyon I.

References

Thioulouse, J., Chessel, D. and Champely, S. (1995) Multivariate analysis of spatial patterns: a unified approach to local and global structures. Environmental and Ecological Statistics, 2, 1–14.

See a data description at http://pbil.univ-lyon1.fr/R/pdf/pps051.pdf (in French).

Examples

data(avijons)
w1 <- dudi.coa(avijons$fau, scannf = FALSE)$li
area.plot(avijons$area, center = avijons$xy, val = w1[, 1], clab = 0.75, 
  sub = "CA Axis 1", csub = 3)
  
## Not run: 
data(avijons)
if(!adegraphicsLoaded()) {
  if(requireNamespace("pixmap", quietly = TRUE)) {
    pnm.eau <- pixmap::read.pnm(system.file("pictures/avijonseau.pnm", package = "ade4"))
    pnm.rou <- pixmap::read.pnm(system.file("pictures/avijonsrou.pnm", package = "ade4"))
    pnm.veg <- pixmap::read.pnm(system.file("pictures/avijonsveg.pnm", package = "ade4"))
    pnm.vil <- pixmap::read.pnm(system.file("pictures/avijonsvil.pnm", package = "ade4"))
    jons.coa <- dudi.coa(avijons$fau, scan = FALSE, nf = 4)
    
    par(mfcol = c(3, 2))
    s.value(avijons$xy, jons.coa$li[, 1], pixmap = pnm.rou, inclu = FALSE,
      grid = FALSE, addax = FALSE, cleg = 0, sub = "F1+ROADS", csub = 3)
    s.value(avijons$xy, jons.coa$li[, 1], pixmap = pnm.veg, inclu = FALSE,
      grid = FALSE, addax = FALSE, cleg = 0, sub = "F1+TREES", csub = 3)
    s.value(avijons$xy, jons.coa$li[, 1], pixmap = pnm.eau, inclu = FALSE,
      grid = FALSE, addax = FALSE, cleg = 0, sub = "F1+WATER", csub = 3)
    s.value(avijons$xy, jons.coa$li[, 2], pixmap = pnm.rou, inclu = FALSE,
      grid = FALSE, addax = FALSE, cleg = 0, sub = "F2+ROADS", csub = 3)
    s.value(avijons$xy, jons.coa$li[, 2], pixmap = pnm.veg, inclu = FALSE,
      grid = FALSE, addax = FALSE, cleg = 0, sub = "F2+TREES", csub = 3)
    s.value(avijons$xy, jons.coa$li[, 2], pixmap = pnm.eau, inclu = FALSE,
      grid = FALSE, addax = FALSE, cleg = 0, sub = "F2+WATER", csub = 3)
    par(mfrow = c(1, 1))
  }

  if(requireNamespace("spdep", quietly = TRUE) & 
    requireNamespace("pixmap", quietly = TRUE)) {
    
    link1 <- area2link(avijons$area)
    lw1 <- apply(link1, 1, function(x) x[x > 0])
    neig1 <- neig(mat01 = 1*(link1 > 0))
    nb1 <- neig2nb(neig1)
    listw1 <- spdep::nb2listw(nb1,lw1)
    jons.ms <- multispati(jons.coa, listw1, scan = FALSE, nfp = 3, nfn = 2)
    summary(jons.ms)
    par(mfrow = c(2, 2))
    barplot(jons.coa$eig)
    barplot(jons.ms$eig)
    s.corcircle(jons.ms$as)
    plot(jons.coa$li[, 1], jons.ms$li[, 1])
    par(mfrow = c(1, 1))

    par(mfcol = c(3, 2))
    s.value(avijons$xy, jons.ms$li[, 1], pixmap = pnm.rou, inclu = FALSE,
      grid = FALSE, addax = FALSE, cleg = 0, sub = "F1+ROADS", csub = 3)
    s.value(avijons$xy, jons.ms$li[, 1], pixmap = pnm.veg, inclu = FALSE,
      grid = FALSE, addax = FALSE, cleg = 0, sub = "F1+TREES", csub = 3)
    s.value(avijons$xy, jons.ms$li[, 1], pixmap = pnm.eau, inclu = FALSE,
      grid = FALSE, addax = FALSE, cleg = 0, sub = "F1+WATER", csub = 3)
    s.value(avijons$xy, jons.ms$li[, 2], pixmap = pnm.rou, inclu = FALSE,
      grid = FALSE, addax = FALSE, cleg = 0, sub = "F2+ROADS", csub = 3)
    s.value(avijons$xy, jons.ms$li[, 2], pixmap = pnm.veg, inclu = FALSE,
      grid = FALSE, addax = FALSE, cleg = 0, sub = "F2+TREES", csub = 3)
    s.value(avijons$xy, jons.ms$li[, 2], pixmap = pnm.eau, inclu = FALSE,
      grid = FALSE, addax = FALSE, cleg = 0, sub = "F2+WATER", csub = 3)
    par(mfrow = c(1, 1))
}}
## End(Not run)

Fauna Table for Constrained Ordinations

Description

avimedi is a list containing the information about 302 sites :
frequencies of 51 bird species ; two factors (habitats and Mediterranean origin).

Usage

data(avimedi)

Format

This list contains the following objects:

fau

is a data frame 302 sites - 51 bird species.

plan

is a data frame 302 sites - 2 factors : reg with two levels Provence (Pr, South of France) and Corsica (Co) ; str with six levels describing the vegetation from a very low matorral (1) up to a mature forest of holm oaks (6).

nomesp

is a vector 51 latin names.

Source

Blondel, J., Chessel, D., & Frochot, B. (1988) Bird species impoverishment, niche expansion, and density inflation in mediterranean island habitats. Ecology, 69, 1899–1917.

Examples

## Not run: 
data(avimedi)
coa1 <- dudi.coa(avimedi$fau, scan = FALSE, nf = 3)
bet1 <- bca(coa1, avimedi$plan$str, scan = FALSE)
wit1 <- wca(coa1, avimedi$plan$reg, scan=FALSE)
pcaiv1 <- pcaiv(coa1, avimedi$plan, scan = FALSE)
    
if(adegraphicsLoaded()) {
  g1 <- s.class(coa1$li, avimedi$plan$str:avimedi$plan$reg, 
    psub.text = "Correspondences Analysis", plot = FALSE)
  g2 <- s.class(bet1$ls, avimedi$plan$str, psub.text = "Between Analysis", plot = FALSE)
  g3 <- s.class(wit1$li, avimedi$plan$str, psub.text = "Within Analysis", plot = FALSE)

  g41 <- s.match(pcaiv1$li, pcaiv1$ls, plabels.cex = 0, 
    psub.text = "Canonical Correspondences Analysis", plot = FALSE)
  g42 <- s.class(pcaiv1$li, avimedi$plan$str:avimedi$plan$reg, plot = FALSE)
  g4 <- superpose(g41, g42, plot = FALSE)
  
  G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))

} else {
  par(mfrow = c(2,2))
  s.class(coa1$li,avimedi$plan$str:avimedi$plan$reg,
      sub = "Correspondences Analysis")
  s.class(bet1$ls, avimedi$plan$str,
      sub = "Between Analysis")
  s.class(wit1$li, avimedi$plan$str,
      sub = "Within Analysis")
  s.match(pcaiv1$li, pcaiv1$ls, clab = 0,
      sub = "Canonical Correspondences Analysis")
  s.class(pcaiv1$li, avimedi$plan$str:avimedi$plan$reg, 
      add.plot = TRUE)
  par(mfrow=c(1,1))
}

## End(Not run)

Ecological Tables Triplet

Description

This data set is a list of information about 51 sites : bird species and environmental variables.
A data frame contains biological traits for each species.

Usage

data(aviurba)

Format

This list contains the following objects:

fau

is a data frame 51 sites 40 bird species.

mil

is a data frame 51 sites 11 environmental variables (see details).

traits

is a data frame 40 species 4 biological traits (see details).

species.names.fr

is a vector of the species names in french.

species.names.la

is a vector of the species names in latin.

species.family

is a factor : the species families.

Details

aviurba$mil contains for each site, 11 habitat attributes describing the degree of urbanization. The presence or absence of farms or villages, small buildings, high buildings, industry, fields, grassland, scrubby areas, deciduous woods, coniferous woods, noisy area are noticed. At least, the vegetation cover (variable 11) is a factor with 8 levels from a minimum cover (R5) up to a maximum (R100).

aviurba$traits contains four factors : feeding habit (insectivor, granivore, omnivore), feeding stratum (ground, aerial, foliage and scrub), breeding stratum (ground, building, scrub, foliage) and migration strategy (resident, migrant).

Source

Dolédec, S., Chessel, D., Ter Braak,C. J. F. and Champely S. (1996) Matching species traits to environmental variables: a new three-table ordination method. Environmental and Ecological Statistics, 3, 143–166.

Examples

data(aviurba)
a1 <- dudi.coa(aviurba$fau, scan = FALSE, nf=4)
a2 <- dudi.acm(aviurba$mil, row.w = a1$lw, scan = FALSE, nf = 4)
plot(coinertia(a1, a2, scan = FALSE))

Genomes of 43 Bacteria

Description

bacteria is a list containing 43 species and genomic informations : codons, amino acid and bases.

Usage

data(bacteria)

Format

This list contains the following objects:

code

is a factor with the amino acid names for each codon.

espcodon

is a data frame 43 species 64 codons.

espaa

is a data frame 43 species 21 amino acid.

espbase

is a data frame 43 species 4 bases.

Source

Data prepared by J. Lobry [email protected] starting from https://www.jcvi.org/.

Examples

data(bacteria)
names(bacteria$espcodon)
names(bacteria$espaa)
names(bacteria$espbase)
sum(bacteria$espcodon) # 22,619,749 codons

if(adegraphicsLoaded()) {
  g <- scatter(dudi.coa(bacteria$espcodon, scann = FALSE), 
    posi = "bottomleft")
} else {
  scatter(dudi.coa(bacteria$espcodon, scann = FALSE), 
    posi = "bottom")
}

Table of Factors

Description

banque gives the results of a bank survey onto 810 customers.

Usage

data(banque)

Format

This data frame contains the following columns:

  1. csp: "Socio-professional categories" a factor with levels

    • agric Farmers

    • artis Craftsmen, Shopkeepers, Company directors

    • cadsu Executives and higher intellectual professions

    • inter Intermediate professions

    • emplo Other white-collar workers

    • ouvri Manual workers

    • retra Pensionners

    • inact Non working population

    • etudi Students

  2. duree: "Time relations with the customer" a factor with levels

    • dm2 <2 years

    • d24 [2 years, 4 years[

    • d48 [4 years, 8 years[

    • d812 [8 years, 12 years[

    • dp12 >= 12 years

  3. oppo: "Stopped a check?" a factor with levels

    • non no

    • oui yes

  4. age: "Customer's age" a factor with levels

    • ai25 [18 years, 25 years[

    • ai35 [25 years, 35 years[

    • ai45 [35 years, 45 years[

    • ai55 [45 years, 55 years[

    • ai75 [55 years, 75 years[

  5. sexe: "Customer's gender" a factor with levels

    • hom Male

    • fem Female

  6. interdit: "No checkbook allowed" a factor with levels

    • non no

    • oui yes

  7. cableue: "Possess a bank card?" a factor with levels

    • non no

    • oui yes

  8. assurvi: "Contrat of life insurance?" a factor with levels

    • non no

    • oui yes

  9. soldevu: "Balance of the current accounts" a factor with levels

    • p4 credit balance > 20000

    • p3 credit balance 12000-20000

    • p2 credit balance 4000-120000

    • p1 credit balance >0-4000

    • n1 debit balance 0-4000

    • n2 debit balance >4000

  10. eparlog: "Savings and loan association account amount" a factor with levels

    • for > 20000

    • fai >0 and <20000

    • nul nulle

  11. eparliv: "Savings bank amount" a factor with levels

    • for > 20000

    • fai >0 and <20000

    • nul nulle

  12. credhab: "Home loan owner" a factor with levels

    • non no

    • oui yes

  13. credcon: "Consumer credit amount" a factor with levels

    • nul none

    • fai >0 and <20000

    • for > 20000

  14. versesp: "Check deposits" a factor with levels

    • oui yes

    • non no

  15. retresp: "Cash withdrawals" a factor with levels

    • fai < 2000

    • moy 2000-5000

    • for > 5000

  16. remiche: "Endorsed checks amount" a factor with levels

    • for >10000

    • moy 10000-5000

    • fai 1-5000

    • nul none

  17. preltre: "Treasury Department tax deductions" a factor with levels

    • nul none

    • fai <1000

    • moy >1000

  18. prelfin: "Financial institution deductions" a factor with levels

    • nul none

    • fai <1000

    • moy >1000

  19. viredeb: "Debit transfer amount" a factor with levels

    • nul none

    • fai <2500

    • moy 2500-5000

    • for >5000

  20. virecre: "Credit transfer amount" a factor with levels

    • for >10000

    • moy 10000-5000

    • fai <5000

    • nul aucun

  21. porttit: "Securities portfolio estimations" a factor with levels

    • nul none

    • fai < 20000

    • moy 20000-100000

    • for >100000

Source

anonymous

Examples

data(banque)
banque.acm <- dudi.acm(banque, scannf = FALSE, nf = 3)
apply(banque.acm$cr, 2, mean)
banque.acm$eig[1:banque.acm$nf] # the same thing

if(adegraphicsLoaded()) {
  g <- s.arrow(banque.acm$c1, plabels.cex = 0.75)
} else {
  s.arrow(banque.acm$c1, clab = 0.75)
}

African Estuary Fishes

Description

This data set is a list containing relations between sites and fish species linked to dates.

Usage

data(baran95)

Format

This list contains the following objects:

fau

is a data frame 95 seinings and 33 fish species.

plan

is a data frame 2 factors : date and site. The date has 6 levels (april 1993, june 1993, august 1993, october 1993, december 1993 and february 1994) and the sites are defined by 4 distances to the Atlantic Ocean (km03, km17, km33 and km46).

species.names

is a vector of species latin names.

Source

Baran, E. (1995) Dynamique spatio-temporelle des peuplements de Poissons estuariens en Guinée (Afrique de l'Ouest). Thèse de Doctorat, Université de Bretagne Occidentale. Data collected by net fishing sampling in the Fatala river estuary.

References

See a data description at http://pbil.univ-lyon1.fr/R/pdf/pps027.pdf (in French).

Examples

data(baran95)
w <- dudi.pca(log(baran95$fau + 1), scal = FALSE, scann = FALSE, 
    nf = 3)
w1 <- wca(w, baran95$plan$date, scann = FALSE)
fatala <- ktab.within(w1)
stat1 <- statis(fatala, scan = FALSE, nf = 3)
mfa1 <- mfa(fatala, scan = FALSE, nf = 3)

if(adegraphicsLoaded()) {
  g1 <- s.class(stat1$C.Co, baran95$plan$site, facets = baran95$plan$date, 
    pellipses.axes.draw = FALSE, ppoints.cex = 0.5, plot = FALSE)
  n1 <- length(g1@ADEglist)
  g2 <- ADEgS(lapply(1:n1, function(i) s.label(stat1$C.Co, plabels.cex = 0, 
    ppoints.cex = 0.5, plot = FALSE)), positions = g1@positions, plot = FALSE)
  G1 <- superpose(g2, g1, plot = TRUE)
    
  G2 <- kplot(stat1, arrow = FALSE, traject = FALSE, class = baran95$plan$site, 
    col.plabels.cex = 0, ppoints.cex = 0.5)
  
  g3 <- s.class(mfa1$co, baran95$plan$site, facets = baran95$plan$date, 
    pellipses.axes.draw = FALSE, ppoints.cex = 0.5, plot = FALSE)
  n2 <- length(g3@ADEglist)
  g4 <- ADEgS(lapply(1:n2, function(i) s.label(mfa1$co, plabels.cex = 0, 
    ppoints.cex = 0.5, plot = FALSE)), positions = g3@positions, plot = FALSE)
  G3 <- superpose(g4, g3, plot = TRUE)
    
} else {
  par(mfrow = c(3, 2))
  w2 <- split(stat1$C.Co, baran95$plan$date)
  w3 <- split(baran95$plan$site, baran95$plan$date)
  for (j in 1:6) {
    s.label(stat1$C.Co[,1:2], clab = 0, sub = tab.names(fatala)[j], csub = 3)
    s.class(w2[[j]][, 1:2], w3[[j]], clab = 2, axese = FALSE, add.plot = TRUE)
  }
  par(mfrow = c(1, 1))
  
  kplot(stat1, arrow = FALSE, traj = FALSE, clab = 2, uni = TRUE, 
    class = baran95$plan$site) #simpler
    
  par(mfrow = c(3, 2))
  w4 <- split(mfa1$co, baran95$plan$date)
  for (j in 1:6) {
    s.label(mfa1$co[, 1:2], clab = 0, sub = tab.names(fatala)[j], csub = 3)
    s.class(w4[[j]][, 1:2], w3[[j]], clab = 2, axese = FALSE, add.plot = TRUE)
  }
  par(mfrow = c(1, 1))
}

Between-Class Analysis

Description

Performs a particular case of a Principal Component Analysis with respect to Instrumental Variables (pcaiv), in which there is only a single factor as explanatory variable.

Usage

## S3 method for class 'dudi'
bca(x, fac, scannf = TRUE, nf = 2, ...)

Arguments

x

a duality diagram, object of class dudi from one of the functions dudi.coa, dudi.pca,...
fac

a factor partitioning the rows of dudi$tab in classes
scannf

a logical value indicating whether the eigenvalues barplot should be displayed
nf

if scannf FALSE, a numeric value indicating the number of kept axes
...

further arguments passed to or from other methods

Value

Returns a list of class dudi, subclass 'between' containing

tab

a data frame class-variables containing the means per class for each variable
cw

a numeric vector of the column weigths
lw

a numeric vector of the class weigths
eig

a numeric vector with all the eigenvalues
rank

the rank of the analysis
nf

an integer value indicating the number of kept axes
c1

a data frame with the column normed scores
l1

a data frame with the class normed scores
co

a data frame with the column coordinates
li

a data frame with the class coordinates
call

the matching call
ratio

the bewteen-class inertia percentage
ls

a data frame with the row coordinates
as

a data frame containing the projection of inertia axes onto between axes

Note

To avoid conflict names with the base:::within function, the function within is now deprecated and removed. To be consistent, the between function is also deprecated and is replaced by the method bca.dudi of the new generic bca function.

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

References

Dolédec, S. and Chessel, D. (1987) Rythmes saisonniers et composantes stationnelles en milieu aquatique I- Description d'un plan d'observations complet par projection de variables. Acta Oecologica, Oecologia Generalis, 8, 3, 403–426.

Examples

data(meaudret)
pca1 <- dudi.pca(meaudret$env, scan = FALSE, nf = 4)
pca2 <- dudi.pca(meaudret$spe, scal = FALSE, scan = FALSE, nf = 4)
bet1 <- bca(pca1, meaudret$design$site, scan = FALSE, nf = 2)
bet2 <- bca(pca2, meaudret$design$site, scan = FALSE, nf = 2)
  
if(adegraphicsLoaded()) {
  g1 <- s.class(pca1$li, meaudret$design$site, psub.text = "Principal Component Analysis (env)",
    plot = FALSE)
  g2 <- s.class(pca2$li, meaudret$design$site, psub.text = "Principal Component Analysis (spe)",
    plot = FALSE)
  g3 <- s.class(bet1$ls, meaudret$design$site, psub.text = "Between sites PCA (env)", plot = FALSE)
  g4 <- s.class(bet2$ls, meaudret$design$site, psub.text = "Between sites PCA (spe)", plot = FALSE)
  G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))
  
} else {
  par(mfrow = c(2, 2))
  s.class(pca1$li, meaudret$design$site, sub = "Principal Component Analysis (env)", csub = 1.75)
  s.class(pca2$li, meaudret$design$site, sub = "Principal Component Analysis (spe)", csub = 1.75)
  s.class(bet1$ls, meaudret$design$site, sub = "Between sites PCA (env)", csub = 1.75)
  s.class(bet2$ls, meaudret$design$site, sub = "Between sites PCA (spe)", csub = 1.75)
  par(mfrow = c(1, 1))
}

coib <- coinertia(bet1, bet2, scann = FALSE)
plot(coib)

Between-class coinertia analysis

Description

Performs a between-class analysis after a coinertia analysis

Usage

## S3 method for class 'coinertia'
bca(x, fac, scannf = TRUE, nf = 2, ...)

Arguments

x

a coinertia analysis (object of class coinertia) obtained by the function coinertia
fac

a factor partitioning the rows in classes
scannf

a logical value indicating whether the eigenvalues barplot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes
...

further arguments passed to or from other methods

Details

This analysis is equivalent to do a between-class analysis on each initial dudi, and a coinertia analysis on the two between analyses. This function returns additional outputs for the interpretation.

Value

An object of the class betcoi. Outputs are described by the print function

Note

To avoid conflict names with the base:::within function, the function within is now deprecated and removed. To be consistent, the betweencoinertia function is also deprecated and is replaced by the method bca.coinertia of the new generic bca function.

Author(s)

Stéphane Dray [email protected] and Jean Thioulouse [email protected]

References

Franquet E., Doledec S., and Chessel D. (1995) Using multivariate analyses for separating spatial and temporal effects within species-environment relationships. Hydrobiologia, 300, 425–431.

See Also

coinertia, bca

Examples

data(meaudret)
pca1 <- dudi.pca(meaudret$env, scan = FALSE, nf = 4)
pca2 <- dudi.pca(meaudret$spe, scal = FALSE, scan = FALSE, nf = 4)
   
bet1 <- bca(pca1, meaudret$design$site, scan = FALSE, nf = 2)
bet2 <- bca(pca2, meaudret$design$site, scan = FALSE, nf = 2)
coib <- coinertia(bet1, bet2, scannf = FALSE)

coi <- coinertia(pca1, pca2, scannf = FALSE, nf = 3)
coi.b <- bca(coi,meaudret$design$site, scannf = FALSE)
## coib and coi.b are equivalent

plot(coi.b)

Between-Class RLQ analysis

Description

Performs a particular RLQ analysis where a partition of sites (rows of R) is taken into account. The between-class RLQ analysis search for linear combinations of traits and environmental variables maximizing the covariances between the traits and the average environmental conditions of classes.

Usage

## S3 method for class 'rlq'
bca(x, fac, scannf = TRUE, nf = 2, ...)
## S3 method for class 'betrlq'
plot(x, xax = 1, yax = 2, ...)
## S3 method for class 'betrlq'
print(x, ...)

Arguments

x

an object of class rlq (created by the rlq function) for the bca.rlq function. An object of class betrlq for the print and plot functions
fac

a factor partitioning the rows of R
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes
xax

the column number for the x-axis
yax

the column number for the y-axis
...

further arguments passed to or from other methods

Value

The bca.rlq function returns an object of class 'betrlq' (sub-class of 'dudi'). See the outputs of the print function for more details.

Author(s)

Stéphane Dray [email protected]

References

Wesuls, D., Oldeland, J. and Dray, S. (2012) Disentangling plant trait responses to livestock grazing from spatio-temporal variation: the partial RLQ approach. Journal of Vegetation Science, 23, 98–113.

See Also

rlq, bca, wca.rlq

Examples

data(piosphere)
afcL <- dudi.coa(log(piosphere$veg + 1), scannf = FALSE)
acpR <- dudi.pca(piosphere$env, scannf = FALSE, row.w = afcL$lw)
acpQ <- dudi.hillsmith(piosphere$traits, scannf = FALSE, row.w =
  afcL$cw)
rlq1 <- rlq(acpR, afcL, acpQ, scannf = FALSE)

brlq1 <- bca(rlq1, fac = piosphere$habitat, scannf = FALSE)
brlq1
plot(brlq1)

Between-Class Analysis

Description

Outputs and graphical representations of the results of a between-class analysis.

Usage

## S3 method for class 'between'
plot(x, xax = 1, yax = 2, ...) 
## S3 method for class 'between'
print(x, ...)
## S3 method for class 'betcoi'
plot(x, xax = 1, yax = 2, ...)
## S3 method for class 'betcoi'
print(x, ...)
## S3 method for class 'between'
summary(object, ...)

Arguments

x, object

an object of class between or betcoi
xax, yax

the column index of the x-axis and the y-axis
...

further arguments passed to or from other methods

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]
Stéphane Dray [email protected]

References

Dolédec, S. and Chessel, D. (1987) Rythmes saisonniers et composantes stationnelles en milieu aquatique I- Description d'un plan d'observations complet par projection de variables. Acta Oecologica, Oecologia Generalis, 8, 3, 403–426.

See Also

bca.dudi, bca.coinertia

Examples

data(meaudret)

pca1 <- dudi.pca(meaudret$env, scan = FALSE, nf = 4)
pca2 <- dudi.pca(meaudret$spe, scal = FALSE, scan = FALSE, nf = 4)
bet1 <- bca(pca1, meaudret$design$site, scan = FALSE, nf = 2)
bet2 <- bca(pca2, meaudret$design$site, scan = FALSE, nf = 2)

if(adegraphicsLoaded()) {
  g1 <- s.class(pca1$li, meaudret$design$site, psub.text = "Principal Component Analysis (env)", 
    plot = FALSE)
  g2 <- s.class(pca2$li, meaudret$design$site, psub.text = "Principal Component Analysis (spe)", 
    plot = FALSE)
  g3 <- s.class(bet1$ls, meaudret$design$site, psub.text = "Between sites PCA (env)", 
    plot = FALSE)
  g4 <- s.class(bet2$ls, meaudret$design$site, psub.text = "Between sites PCA (spe)", 
    plot = FALSE)
  G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))
  
} else {
  par(mfrow = c(2, 2))
  s.class(pca1$li, meaudret$design$site, sub = "Principal Component Analysis (env)", csub = 1.75)
  s.class(pca2$li, meaudret$design$site, sub = "Principal Component Analysis (spe)", csub = 1.75)
  s.class(bet1$ls, meaudret$design$site, sub = "Between sites PCA (env)", csub = 1.75)
  s.class(bet2$ls, meaudret$design$site, sub = "Between sites PCA (spe)", csub = 1.75)
  par(mfrow = c(1,1))
}

coib <- coinertia(bet1, bet2, scann = FALSE)
plot(coib)

Cubic Ecological Data

Description

bf88 is a list of 6 data frames corresponding to 6 stages of vegetation.
Each data frame gives some bird species informations for 4 counties.

Usage

data(bf88)

Format

A list of six data frames with 79 rows (bird species) and 4 columns (counties).
The 6 arrays (S1 to S6) are the 6 stages of vegetation.
The attribut 'nomesp' of this list is a vector of species French names.

Source

Blondel, J. and Farre, H. (1988) The convergent trajectories of bird communities along ecological successions in european forests. Oecologia (Berlin), 75, 83–93.

Examples

data(bf88)
fou1 <- foucart(bf88, scann = FALSE, nf = 3)
fou1

if(adegraphicsLoaded()) {
  g1 <- scatter(fou1, plot = FALSE)
  g2 <- s.traject(fou1$Tco, fou1$TC[, 1], plines.lty = 1:length(levels(fou1$TC[, 1])), plot = FALSE)
  g3 <- s.traject(fou1$Tco, fou1$TC[, 2], plines.lty = 1:length(levels(fou1$TC[, 2])), plot = FALSE)
  g41 <- s.label(fou1$Tco, plot = FALSE)
  g42 <- s.label(fou1$co, plab.cex = 2, plot = FALSE)
  g4 <- superpose(g41, g42, plot = FALSE)
  G1 <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))
  
  G2 <- kplot(fou1, row.plab.cex = 0, psub.cex = 2)

} else {
  par(mfrow = c(2,2))
  scatter(fou1)
  s.traject(fou1$Tco, fou1$TC[, 1])
  s.traject(fou1$Tco, fou1$TC[, 2])
  s.label(fou1$Tco)
  s.label(fou1$co, add.p = TRUE, clab = 2)
  par(mfrow = c(1, 1))
  kplot(fou1, clab.c = 2, clab.r = 0, csub = 3)
}

Double Weighted Centring

Description

This function creates a doubly centred matrix.

Usage

bicenter.wt(X, row.wt = rep(1, nrow(X)), col.wt = rep(1, ncol(X)))

Arguments

X

a matrix with n rows and p columns
row.wt

a vector of positive or null weights of length n
col.wt

a vector of positive or null weights of length p

Value

returns a doubly centred matrix

Author(s)

Daniel Chessel

Examples

w <- matrix(1:6, 3, 2)
bicenter.wt(w, c(0.2,0.6,0.2), c(0.3,0.7))

w <- matrix(1:20, 5, 4)
sum(bicenter.wt(w, runif(5), runif(4))^2)

Wine Tasting

Description

The bordeaux data frame gives the opinions of 200 judges in a blind tasting of five different types of claret (red wine from the Bordeaux area in the south western parts of France).

Usage

data(bordeaux)

Format

This data frame has 5 rows (the wines) and 4 columns (the judgements) divided in excellent, good, mediocre and boring.

Source

van Rijckevorsel, J. (1987) The application of fuzzy coding and horseshoes in multiple correspondence analysis. DSWO Press, Leiden (p. 32)

Examples

data(bordeaux)
bordeaux
score(dudi.coa(bordeaux, scan = FALSE))

Ecological and Biological Traits

Description

This data set gives ecological and biological characteristics of 131 species of aquatic insects.

Usage

data(bsetal97)

Format

bsetal97 is a list of 8 components.

species.names

is a vector of the names of aquatic insects.

taxo

is a data frame containing the taxonomy of species: genus, family and order.

biol

is a data frame containing 10 biological traits for a total of 41 modalities.

biol.blo

is a vector of the numbers of items for each biological trait.

biol.blo.names

is a vector of the names of the biological traits.

ecol

is a data frame with 7 ecological traits for a total of 34 modalities.

ecol.blo

is a vector of the numbers of items for each ecological trait.

ecol.blo.names

is a vector of the names of the ecological traits.

Details

The 10 variables of the data frame bsetal97$biol are called in bsetal97$biol.blo.names and the number of modalities per variable given in bsetal97$biol.blo. The variables are: female size - the body length from the front of the head to the end of the abdomen (7 length modalities), egg length - the egg size (6 modalities), egg number - count of eggs actually oviposited, generations per year (3 modalities: ≤1\leq 1, 2, > 2), oviposition period - the length of time during which oviposition occurred (3 modalities: ≤2\leq 2 months, between 2 and 5 months, > 5 months), incubation time - the time between oviposition and hatching of the larvae (3 modalities: ≤4\leq 4 weeks, between 4 and 12 weeks, > 12 weeks), egg shape (1-spherical, 2-oval, 3-cylindrical), egg attachment - physiological feature of the egg and of the female (4 modalities), clutch structure (1-single eggs, 2-grouped eggs, 3-egg masses), clutch number (3 modalities : 1, 2, > 2).

The 7 variables of the data frame bsetal97$ecol are called in bsetal97$ecol.blo.names and the number of modalities per variable given in bsetal97$ecol.blo. The variables are: oviposition site - position relative to the water (7 modalities), substratum type for eggs - the substratum to which the eggs are definitely attached (6 modalities), egg deposition - the position of the eggs during the oviposition process (4 modalities), gross habitat - the general habitat use of the species such as temporary waters or estuaries (8 modalities), saturation variance - the exposure of eggs to the risk of dessication (2 modalities), time of day (1-morning, 2-day, 3-evening, 4-night), season - time of the year (1-Spring, 2-Summer, 3-Automn).

Source

Statzner, B., Hoppenhaus, K., Arens, M.-F. and Richoux, P. (1997) Reproductive traits, habitat use and templet theory: a synthesis of world-wide data on aquatic insects. Freshwater Biology, 38, 109–135.

References

See a data description at http://pbil.univ-lyon1.fr/R/pdf/pps029.pdf (in French).

Examples

data(bsetal97)
X <- prep.fuzzy.var(bsetal97$biol, bsetal97$biol.blo)
Y <- prep.fuzzy.var(bsetal97$ecol, bsetal97$ecol.blo)
plot(coinertia(dudi.fca(X, scan = FALSE), 
    dudi.fca(Y, scan = FALSE), scan = FALSE))

Buech basin

Description

This data set contains informations about Buech basin characteristics.

Usage

data(buech)

Format

buech is a list with the following components:

tab1

a data frame with 10 environmental variables collected on 31 sites in Juin (1984)

tab2

a data frame with 10 environmental variables collected on 31 sites in September (1984)

xy

a data frame with the coordinates of the sites

neig

an object of class neig

contour

a data frame for background map

nb

the neighbouring graph between sites, object of the class nb

Spatial

an object of the class SpatialPolygons of sp, containing the map

Details

Variables of buech$tab1 and buech$tab2 are the following ones:
pH ; Conductivity (μ\mu S/cm) ; Carbonate (water hardness (mg/l CaCO3)) ; hardness (total water hardness (mg/l CaCO3)) ; Bicarbonate (alcalinity (mg/l HCO3-)) ; Chloride (alcalinity (mg/l Cl-)) ; Suspens (particles in suspension (mg/l)) ; Organic (organic particles (mg/l)) ; Nitrate (nitrate rate (mg/l NO3-)) ; Ammonia (amoniac rate (mg/l NH4-))

Source

Vespini, F. (1985) Contribution à l'étude hydrobiologique du Buech, rivière non aménagée de Haute-Provence. Thèse de troisième cycle, Université de Provence.

Vespini, F., Légier, P. and Champeau, A. (1987) Ecologie d'une rivière non aménagée des Alpes du Sud : Le Buëch (France) I. Evolution longitudinale des descripteurs physiques et chimiques. Annales de Limnologie, 23, 151–164.

Examples

data(buech)
if(adegraphicsLoaded()) {
  if(requireNamespace("sp", quietly = TRUE)) {
    g1 <- s.label(buech$xy, Sp = buech$Spatial, nb = buech$nb, 
      pSp.col = "transparent", plot = FALSE)
    g2 <- s.value(buech$xy, buech$tab2$Suspens - buech$tab1$Suspens, 
      Sp = buech$Spatial, nb = buech$nb, pSp.col = "transparent", plot = FALSE)
    G <- cbindADEg(g1, g2, plot = TRUE)
  }
} else {
  par(mfrow = c(1,2))
  s.label(buech$xy, contour = buech$contour, neig = buech$neig)
  s.value(buech$xy, buech$tab2$Suspens - buech$tab1$Suspens,
    contour = buech$contour, neig = buech$neig, csi = 3)
  par(mfrow = c(1,1))
}

Genetics-Ecology-Environment Triple

Description

This data set contains environmental and genetics informations about 16 Euphydryas editha butterfly colonies studied in California and Oregon.

Usage

data(butterfly)

Format

butterfly is a list with the following components:

xy

a data frame with the two coordinates of the 16 Euphydryas editha butterfly colonies

envir

a environmental data frame of 16 sites - 4 variables

genet

a genetics data frame of 16 sites - 6 allele frequencies

contour

a data frame for background map (California map)

Spatial

an object of the class SpatialPolygons of sp, containing the map

Source

McKechnie, S.W., Ehrlich, P.R. and White, R.R. (1975). Population genetics of Euphydryas butterflies. I. Genetic variation and the neutrality hypothesis. Genetics, 81, 571–594.

References

Manly, B.F. (1994) Multivariate Statistical Methods. A primer. Second edition. Chapman & Hall, London. 1–215.

Examples

data(butterfly)

if(adegraphicsLoaded()) {
  if(requireNamespace("sp", quietly = TRUE)) {
    g1 <- s.label(butterfly$xy, Sp = butterfly$Spatial, pSp.col = "white", 
      porigin.include = FALSE, plot = FALSE)
    g2 <- table.value(dist(butterfly$xy), plot = FALSE)
    g3 <- s.value(butterfly$xy, dudi.pca(butterfly$envir, scan = FALSE)$li[, 1], 
      Sp = butterfly$Spatial, pori.inc = FALSE, pSp.col = "transparent", ppoints.cex = 2, 
        plot = FALSE)
    ## mt <- mantel.randtest(dist(butterfly$xy), dist(butterfly$gen), 99)
    G <- ADEgS(list(g1, g2, g3), layout = c(2, 2), plot = TRUE)
  }
} else {
  par(mfrow = c(2, 2))
  s.label(butterfly$xy, contour = butterfly$contour, inc = FALSE)
  table.dist(dist(butterfly$xy), labels = row.names(butterfly$xy)) # depends of mva
  s.value(butterfly$xy, dudi.pca(butterfly$envir, scan = FALSE)$li[,1], 
      contour = butterfly$contour, inc = FALSE, csi = 3)
  plot(mantel.randtest(dist(butterfly$xy), dist(butterfly$gen), 99),
      main = "genetic/spatial")
  par(mfrow = c(1,1))
}

Between- and within-class double principal coordinate analysis

Description

These functions allow to study the variations in diversity among communities (as in dpcoa) taking into account a partition in classes

Usage

bwca.dpcoa(x, fac, cofac, scannf = TRUE, nf = 2, ...)
## S3 method for class 'dpcoa'
bca(x, fac, scannf = TRUE, nf = 2, ...) 
## S3 method for class 'dpcoa'
wca(x, fac, scannf = TRUE, nf = 2, ...) 
## S3 method for class 'betwit'
randtest(xtest, nrepet = 999, ...)
## S3 method for class 'betwit'
summary(object, ...)
## S3 method for class 'witdpcoa'
print(x, ...)
## S3 method for class 'betdpcoa'
print(x, ...)

Arguments

x

an object of class dpcoa
fac

a factor partitioning the collections in classes
scannf

a logical value indicating whether the eigenvalues barplot should be displayed
nf

if scannf FALSE, a numeric value indicating the number of kept axes
...

further arguments passed to or from other methods
cofac

a cofactor partitioning the collections in classes used as a covariable
nrepet

the number of permutations
xtest, object

an object of class betwit created by a call to the function bwca.dpcoa

Value

Objects of class betdpcoa, witdpcoa or betwit

Author(s)

Stéphane Dray [email protected]

References

Dray, S., Pavoine, S. and Aguirre de Carcer, D. (2015) Considering external information to improve the phylogenetic comparison of microbial communities: a new approach based on constrained Double Principal Coordinates Analysis (cDPCoA). Molecular Ecology Resources, 15, 242–249. doi:10.1111/1755-0998.12300

See Also

dpcoa

Examples

## Not run: 

## First example of Dray et al (2015) paper

con <- url("https://pbil.univ-lyon1.fr/datasets/dray/MER2014/soilmicrob.rda")
load(con)
close(con)

## Partial CCA
coa <- dudi.coa(soilmicrob$OTU, scannf = FALSE)
wcoa <- wca(coa, soilmicrob$env$pH, scannf = FALSE)
wbcoa <- bca(wcoa,soilmicrob$env$VegType, scannf = FALSE)

## Classical DPCoA
dp <- dpcoa(soilmicrob$OTU, soilmicrob$dphy, RaoDecomp = FALSE, scannf = FALSE)

## Between DPCoA (focus on the effect of vegetation type)
bdp <- bca(dp, fac = soilmicrob$env$VegType , scannf = FALSE)
bdp$ratio ## 0.2148972
randtest(bdp) ## p = 0.001

## Within DPCoA (remove the effect of pH)
wdp <- wca(dp, fac = soilmicrob$env$pH, scannf = FALSE)
wdp$ratio ## 0.5684348

## Between Within-DPCoA (remove the effect of pH and focus on vegetation type)
wbdp <- bwca.dpcoa(dp, fac = soilmicrob$env$VegType, cofac =  soilmicrob$env$pH, scannf = FALSE)
wbdp$ratio ## 0.05452813
randtest(wbdp) ## p = 0.001

## End(Not run)

Transformation to make Euclidean a distance matrix

Description

This function computes the smallest positive constant that makes Euclidean a distance matrix and applies it.

Usage

cailliez(distmat, print = FALSE, tol = 1e-07, cor.zero = TRUE)

Arguments

distmat

an object of class dist
print

if TRUE, prints the eigenvalues of the matrix
tol

a tolerance threshold for zero
cor.zero

if TRUE, zero distances are not modified

Value

an object of class dist containing a Euclidean distance matrix.

Author(s)

Daniel Chessel
Stéphane Dray [email protected]

References

Cailliez, F. (1983) The analytical solution of the additive constant problem. Psychometrika, 48, 305–310.

Legendre, P. and Anderson, M.J. (1999) Distance-based redundancy analysis: testing multispecies responses in multifactorial ecological experiments. Ecological Monographs, 69, 1–24.

Legendre, P., and Legendre, L. (1998) Numerical ecology, 2nd English edition edition. Elsevier Science BV, Amsterdam.

Examples

data(capitales)
d0 <- capitales$dist
is.euclid(d0) # FALSE
d1 <- cailliez(d0, TRUE)
# Cailliez constant = 2429.87867 
is.euclid(d1) # TRUE
plot(d0, d1)
abline(lm(unclass(d1)~unclass(d0)))
print(coefficients(lm(unclass(d1)~unclass(d0))), dig = 8) # d1 = d + Cte
is.euclid(d0 + 2428) # FALSE
is.euclid(d0 + 2430) # TRUE the smallest constant

Road Distances

Description

This data set gives the road distances between 15 European capitals and their coordinates.

Usage

data(capitales)

Format

capitales is a list with the following components:

xy

a data frame containing the coordinates of capitals

area

a data frame containing three variables, designed to be used in area.plot function

logo

a list of pixmap objects, each one symbolizing a capital

Spatial

an object of the class SpatialPolygons of sp, containing the map

dist

a dist object the road distances between 15 European capitals

Examples

data(capitales)
attr(capitales$dist, "Labels")
index <- pmatch(tolower(attr(capitales$dist, "Labels")), names(capitales$logo))
w1 <- capitales$area

if(adegraphicsLoaded()) {
  if(requireNamespace("sp", quietly = TRUE)) {
    g1 <- s.label(capitales$xy, lab = rownames(capitales$xy), porigin.include = FALSE, 
      plot = FALSE)
    g2 <- s.logo(capitales$xy[sort(rownames(capitales$xy)), ], capitales$logo, 
      Sp = capitales$Spatial, pbackground.col = "lightblue", pSp.col = "white", pgrid.draw = FALSE, 
      plot = FALSE)
    g3 <- table.value(capitales$dist, ptable.margin = list(b = 5, l = 5, t = 15, r = 15), 
      ptable.x.tck = 3, ptable.y.tck = 3, plot = FALSE)
    g4 <- s.logo(pcoscaled(lingoes(capitales$dist)), capitales$logo[index], plot = FALSE) 
    
    G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))
  }
  
} else {
  if(requireNamespace("pixmap", quietly = TRUE)) {
    par(mfrow = c(2, 2))
    s.label(capitales$xy, lab = attr(capitales$dist, "Labels"), include.origin = FALSE)
    area.plot(w1)
  	rect(min(w1$x), min(w1$y), max(w1$x), max(w1$y), col = "lightblue")
  	invisible(lapply(split(w1, w1$id), function(x) polygon(x[, -1], col = "white")))
  	s.logo(capitales$xy, capitales$logo, klogo = index, add.plot = TRUE, 
  	 include.origin = FALSE, clogo = 0.5) # depends on pixmap
    table.dist(capitales$dist, lab = attr(capitales$dist, "Labels")) # depends on mva
    s.logo(pcoscaled(lingoes(capitales$dist)), capitales$logo, klogo = index, clogo = 0.5) 
      # depends on pixmap
    par(mfrow = c(1, 1))
  }
  }

Phylogeny and quantative trait of carnivora

Description

This data set describes the phylogeny of carnivora as reported by Diniz-Filho et al. (1998). It also gives the body mass of these 19 species.

Usage

data(carni19)

Format

carni19 is a list containing the 2 following objects :

tre

is a character string giving the phylogenetic tree in Newick format.

bm

is a numeric vector which values correspond to the body mass of the 19 species (log scale).

Source

Diniz-Filho, J. A. F., de Sant'Ana, C.E.R. and Bini, L.M. (1998) An eigenvector method for estimating phylogenetic inertia. Evolution, 52, 1247–1262.

Examples

data(carni19)
carni19.phy <- newick2phylog(carni19$tre)
par(mfrow = c(1,2))
symbols.phylog(carni19.phy,carni19$bm-mean(carni19$bm))
dotchart.phylog(carni19.phy, carni19$bm, clabel.l=0.75)
par(mfrow = c(1,1))

Phylogeny and quantitative traits of carnivora

Description

This data set describes the phylogeny of 70 carnivora as reported by Diniz-Filho and Torres (2002). It also gives the geographic range size and body size corresponding to these 70 species.

Usage

data(carni70)

Format

carni70 is a list containing the 2 following objects:

tre

is a character string giving the phylogenetic tree in Newick format. Branch lengths are expressed as divergence times (millions of years)

tab

is a data frame with 70 species and two traits: size (body size (kg)) ; range (geographic range size (km)).

Source

Diniz-Filho, J. A. F., and N. M. Tôrres. (2002) Phylogenetic comparative methods and the geographic range size-body size relationship in new world terrestrial carnivora. Evolutionary Ecology, 16, 351–367.

Examples

## Not run: 
if (requireNamespace("adephylo", quietly = TRUE) & requireNamespace("ape", quietly = TRUE)) {
  data(carni70)
  carni70.phy <- newick2phylog(carni70$tre)
  plot(carni70.phy)
  
  size <- scalewt(log(carni70$tab))[,1]
  names(size) <- row.names(carni70$tab)
  symbols.phylog(carni70.phy,size)
  
  tre <- ape::read.tree(text = carni70$tre)
  adephylo::orthogram(size, tre = tre)
  
  yrange <- scalewt(carni70$tab[,2])
  names(yrange) <- row.names(carni70$tab)
  symbols.phylog(carni70.phy,yrange)
  adephylo::orthogram(as.vector(yrange), tre = tre)
  
  if(adegraphicsLoaded()) {
    g1 <- s.label(cbind.data.frame(size, yrange), plabel.cex = 0)
    g2 <- addhist(g1)
  } else {
    s.hist(cbind.data.frame(size, yrange), clabel = 0)
  }
}
## End(Not run)

Taxonomy, phylogenies and quantitative traits of carnivora and herbivora

Description

This data set describes the taxonomic and phylogenetic relationships of 49 carnivora and herbivora species as reported by Garland and Janis (1993) and Garland et al. (1993). It also gives seven traits corresponding to these 49 species.

Usage

data(carniherbi49)

Format

carniherbi49 is a list containing the 5 following objects :

taxo

is a data frame with 49 species and 2 columns : 'fam', a factor family with 14 levels and 'ord', a factor order with 3 levels.

tre1

is a character string giving the phylogenetic tree in Newick format as reported by Garland et al. (1993).

tre2

is a character string giving the phylogenetic tree in Newick format as reported by Garland and Janis (1993).

tab1

is a data frame with 49 species and 2 traits: 'bodymass' (body mass (kg)) and 'homerange' (home range (km)).

tab2

is a data frame with 49 species and 5 traits: 'clade' (dietary with two levels Carnivore and Herbivore), 'runningspeed' (maximal sprint running speed (km/h)), 'bodymass' (body mass (kg)), 'hindlength' (hind limb length (cm)) and 'mtfratio' (metatarsal/femur ratio).

Source

Garland, T., Dickerman, A. W., Janis, C. M. and Jones, J. A. (1993) Phylogenetic analysis of covariance by computer simulation. Systematics Biology, 42, 265–292.

Garland, T. J. and Janis, C.M. (1993) Does metatarsal-femur ratio predict maximal running speed in cursorial mammals? Journal of Zoology, 229, 133–151.

Examples

## Not run: 
data(carniherbi49)
par(mfrow=c(1,3))
plot(newick2phylog(carniherbi49$tre1), clabel.leaves = 0,
 f.phylog = 2, sub ="article 1")
plot(newick2phylog(carniherbi49$tre2), clabel.leaves = 0,
 f.phylog = 2, sub = "article 2")
taxo <- as.taxo(carniherbi49$taxo)
plot(taxo2phylog(taxo), clabel.nodes = 1.2, clabel.leaves = 1.2)
par(mfrow = c(1,1))

## End(Not run)

Enzymatic polymorphism in Mus musculus

Description

This data set is a data frame with 74 rows (mice) and 15 columns (loci enzymatic polymorphism of the DNA mitochondrial). Each value contains 6 characters coding for two allelles. The missing values are coding by '000000'.

Usage

data(casitas)

Format

The 74 individuals of casitas belong to 4 groups:

1

24 mice of the sub-species Mus musculus domesticus

2

11 mice of the sub-species Mus musculus castaneus

3

9 mice of the sub-species Mus musculus musculus

4

30 mice from a population of the lake Casitas (California)

Source

Exemple du logiciel GENETIX. Belkhir k. et al. GENETIX, logiciel sous WindowsTM pour la génétique des populations. Laboratoire Génome, Populations, Interactions CNRS UMR 5000, Université de Montpellier II, Montpellier (France).
https://kimura.univ-montp2.fr/genetix/

References

Orth, A., T. Adama, W. Din and F. Bonhomme. (1998) Hybridation naturelle entre deux sous espèces de souris domestique Mus musculus domesticus et Mus musculus castaneus près de Lake Casitas (Californie). Genome, 41, 104–110.

Examples

data(casitas)
str(casitas)
names(casitas)

Qualitative Weighted Variables

Description

This data set gives the age, the fecundity and the number of litters for 26 groups of cats.

Usage

data(chatcat)

Format

chatcat is a list of two objects :

tab

is a data frame with 3 factors (age, feco, nport).

eff

is a vector of numbers.

Details

One row of tab corresponds to one group of cats.
The value in eff is the number of cats in this group.

Source

Pontier, D. (1984) Contribution à la biologie et à la génétique des populations de chats domestiques (Felis catus). Thèse de 3ème cycle. Université Lyon 1, p. 67.

Examples

data(chatcat)
summary(chatcat$tab)
w <- acm.disjonctif(chatcat$tab) #  Disjonctive table
names(w) <- c(paste("A", 1:5, sep = ""), paste("B", 1:5, sep = ""), 
    paste("C", 1:2, sep = ""))
w <- t(w*chatcat$num)
w <- data.frame(w)
w # BURT table

Pair of Variables

Description

This data set is a contingency table of age classes and fecundity classes of cats Felis catus.

Usage

data(chats)

Format

chats is a data frame with 8 rows and 8 columns.
The 8 rows are age classes (age1, ..., age8).
The 8 columns are fecundity classes (f0, f12, f34, ..., fcd).
The values are cats numbers (contingency table).

Source

Legay, J.M. and Pontier, D. (1985) Relation âge-fécondité dans les populations de Chats domestiques, Felis catus. Mammalia, 49, 395–402.

Examples

data(chats)
chatsw <- as.table(t(chats))
chatscoa <- dudi.coa(data.frame(t(chats)), scann = FALSE)

if(adegraphicsLoaded()) {
  g1 <- table.value(chatsw, ppoints.cex = 1.3, meanX = TRUE, ablineX = TRUE, plabel.cex = 1.5, 
    plot = FALSE)
  g2 <- table.value(chatsw, ppoints.cex = 1.3, meanY = TRUE, ablineY = TRUE, plabel.cex = 1.5, 
    plot = FALSE)
  g3 <- table.value(chatsw, ppoints.cex = 1.3, coordsx = chatscoa$c1[,
  1], coordsy = chatscoa$l1[, 1], meanX = TRUE, ablineX = TRUE, plot = FALSE)
  g4 <- table.value(chatsw, ppoints.cex = 1.3, meanY = TRUE, ablineY = TRUE, 
    coordsx = chatscoa$c1[, 1], coordsy = chatscoa$l1[, 1], plot = FALSE)
  G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))

} else {
  par(mfrow = c(2, 2))
  table.cont(chatsw, abmean.x = TRUE, csi = 2, abline.x = TRUE, clabel.r = 1.5, clabel.c = 1.5)
  table.cont(chatsw, abmean.y = TRUE, csi = 2, abline.y = TRUE, clabel.r = 1.5, clabel.c = 1.5)
  table.cont(chatsw, x = chatscoa$c1[, 1], y = chatscoa$l1[, 1], abmean.x = TRUE, csi = 2, 
    abline.x = TRUE, clabel.r = 1.5, clabel.c = 1.5)
  table.cont(chatsw, x = chatscoa$c1[, 1], y = chatscoa$l1[, 1], abmean.y = TRUE, csi = 2, 
    abline.y = TRUE, clabel.r = 1.5, clabel.c = 1.5)
  par(mfrow = c(1, 1))
}

Charolais-Zebus

Description

This data set gives six different weights of 23 charolais and zebu oxen.

Usage

data(chazeb)

Format

chazeb is a list of 2 components.

tab

is a data frame with 23 rows and 6 columns.

cla

is a factor with two levels "cha" and "zeb".

Source

Tomassone, R., Danzard, M., Daudin, J. J. and Masson J. P. (1988) Discrimination et classement, Masson, Paris. p. 43

Examples

data(chazeb)
if(!adegraphicsLoaded())
  plot(discrimin(dudi.pca(chazeb$tab, scan = FALSE), 
    chazeb$cla, scan = FALSE))

Enzymatic polymorphism in Leuciscus cephalus

Description

This data set contains a list of three components: spatial map, allellic profiles and sample sizes.

Usage

data(chevaine)

Format

This data set is a list of three components:

tab

a data frame with 27 populations and 9 allelic frequencies (4 locus)

coo

a list containing all the elements to build a spatial map

eff

a numeric containing the numbers of fish samples per station

References

Guinand B., Bouvet Y. and Brohon B. (1996) Spatial aspects of genetic differentiation of the European chub in the Rhone River basin. Journal of Fish Biology, 49, 714–726.

See a data description at http://pbil.univ-lyon1.fr/R/pdf/pps054.pdf (in French).

Examples

data(chevaine)
names(chevaine)
str(chevaine)

Veterinary epidemiological study to assess the risk factors for losses in broiler chickens

Description

This data set contains information about potential risk factors for losses in broiler chickens

Usage

data(chickenk)

Format

A list with 5 components:

mortality

a data frame with 351 observations and 4 variables which describe the losses (dependent dataset Y)

FarmStructure

a data frame with 351 observations and 5 variables which describe the farm structure (explanatory dataset)

OnFarmHistory

a data frame with 351 observations and 4 variables which describe the flock characteristics at placement (explanatory dataset)

FlockCharacteristics

a data frame with 351 observations and 6 variables which describe the flock characteristics during the rearing period (explanatory dataset)

CatchingTranspSlaught

a data frame with 351 observations and 5 variables which describe the transport, lairage conditions, slaughterhouse and inspection features (explanatory dataset)

Source

Lupo C., le Bouquin S., Balaine L., Michel V., Peraste J., Petetin I., Colin P. and Chauvin C. (2009) Feasibility of screening broiler chicken flocks for risk markers as an aid for meat inspection. Epidemiology and Infection, 137, 1086-1098

Examples

data(chickenk)
kta1 <- ktab.list.df(chickenk)

Fruit Production

Description

The clementines is a data set containing the fruit production of 20 clementine trees during 15 years.

Usage

data(clementines)

Format

A data frame with 15 rows and 20 columns

Source

Tisné-Agostini, D. (1988) Description par analyse en composantes principales de l'évolution de la production du clémentinier en association avec 12 types de porte-greffe. Rapport technique, DEA Analyse et modélisation des systèmes biologiques, Université Lyon 1.

Examples

data(clementines)

op <- par(no.readonly = TRUE) 
par(mfrow = c(5, 4))
par(mar = c(2, 2, 1, 1))
for(i in 1:20) {
  w0 <- 1:15
  plot(w0, clementines[, i], type = "b")
  abline(lm(clementines[, i] ~ w0))
}
par(op)

pca1 <- dudi.pca(clementines, scan = FALSE)
if(adegraphicsLoaded()) {
  g1 <- s.corcircle(pca1$co, plab.cex = 0.75)
  g2 <- s1d.barchart(pca1$li[, 1], p1d.hori = FALSE)
} else {
  s.corcircle(pca1$co, clab = 0.75)
  barplot(pca1$li[, 1])
}

op <- par(no.readonly = TRUE) 
par(mfrow = c(5, 4))
par(mar = c(2, 2, 1, 1))
clem0 <- pca1$tab
croi <- 1:15
alter <- c(rep(c(1, -1), 7), 1)
for(i in 1:20) {
  y <- clem0[,i]
  plot(w0, y, type = "b", ylim = c(-2, 2))
  z <- predict(lm(clem0[, i] ~ croi * alter))
  points(w0, z, pch = 20, cex = 2)
  for(j in 1:15)
    segments(j, y[j], j, z[j])
}
par(op)
par(mfrow = c(1, 1))

Frequenting movie theaters in France in 2003

Description

cnc2003 is a data frame with 94 rows (94 departments from continental Metropolitan France)and 12 variables.

Usage

data(cnc2003)

Format

This data frame contains the following variables:

popu

is the population department in million inhabitants.

entr

is the number of movie theater visitors in million.

rece

is the takings from ticket offices.

sean

is the number of proposed shows in thousands.

comm

is the number of equipped communes in movie theaters (units).

etab

is the number of active movie theaters (units).

salle

is the number of active screens.

faut

is the number of proposed seats.

artes

is the number of movie theaters offering "Art and Essay" movies.

multi

is the number of active multiplexes.

depart

is the name of the department.

reg

is the administrative region of the department.

Source

National Center of Cinematography (CNC), september 2003

See Also

This dataset is compatible with elec88 and presid2002

Examples

data(cnc2003)
sco.quant(cnc2003$popu, cnc2003[,2:10], abline = TRUE, csub = 3)

Coinertia Analysis

Description

The coinertia analysis performs a double inertia analysis of two tables.

Usage

coinertia(dudiX, dudiY, scannf = TRUE, nf = 2)
## S3 method for class 'coinertia'
 plot(x, xax = 1, yax = 2, ...) 
## S3 method for class 'coinertia'
 print(x, ...) 
## S3 method for class 'coinertia'
 summary(object, ...)

Arguments

dudiX

a duality diagram providing from one of the functions dudi.coa, dudi.pca, ...
dudiY

a duality diagram providing from one of the functions dudi.coa, dudi.pca, ...
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes


x, object

an object of class 'coinertia'
xax, yax

the numbers of the x-axis and the y-axis
...

further arguments passed to or from other methods

Value

Returns a list of class 'coinertia', sub-class 'dudi' containing:

call

call
rank

rank
nf

a numeric value indicating the number of kept axes
RV

a numeric value, the RV coefficient
eig

a numeric vector with all the eigenvalues
lw

a numeric vector with the rows weigths (crossed table)
cw

a numeric vector with the columns weigths (crossed table)
tab

a crossed table (CT)
li

CT row scores (cols of dudiY)
l1

Principal components (loadings for cols of dudiY)
co

CT col scores (cols of dudiX)
c1

Principal axes (cols of dudiX)
lX

Row scores (rows of dudiX)
mX

Normed row scores (rows of dudiX)
lY

Row scores (rows of dudiY)
mY

Normed row scores (rows of dudiY)
aX

Correlations between dudiX axes and coinertia axes
aY

Correlations between dudiY axes and coinertia axes

WARNING

IMPORTANT : dudi1 and dudi2 must have identical row weights.

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

References

Dolédec, S. and Chessel, D. (1994) Co-inertia analysis: an alternative method for studying species-environment relationships. Freshwater Biology, 31, 277–294.

Dray, S., Chessel, D. and J. Thioulouse (2003) Co-inertia analysis and the linking of the ecological data tables. Ecology, 84, 11, 3078–3089.

Examples

data(doubs)
dudi1 <- dudi.pca(doubs$env, scale = TRUE, scan = FALSE, nf = 3)
dudi2 <- dudi.pca(doubs$fish, scale = FALSE, scan = FALSE, nf = 2)
coin1 <- coinertia(dudi1,dudi2, scan = FALSE, nf = 2)
coin1
summary(coin1)

if(adegraphicsLoaded()) {
  g1 <- s.arrow(coin1$l1, plab.cex = 0.7)
  g2 <- s.arrow(coin1$c1, plab.cex = 0.7)
  g3 <- s.corcircle(coin1$aX, plot = FALSE)
  g4 <- s.corcircle(coin1$aY, plot = FALSE)
  cbindADEg(g3, g4, plot = TRUE)
  g5 <- plot(coin1)
    
} else {
s.arrow(coin1$l1, clab = 0.7)
s.arrow(coin1$c1, clab = 0.7)
par(mfrow = c(1,2))
s.corcircle(coin1$aX)
s.corcircle(coin1$aY)
par(mfrow = c(1,1))
plot(coin1)
}

Table of Fuzzy Biological Traits

Description

This data set coleo (coleoptera) is a a fuzzy biological traits table.

Usage

data(coleo)

Format

coleo is a list of 5 components.

tab

is a data frame with 110 rows (species) and 32 columns (categories).

species.names

is a vector of species names.

moda.names

is a vector of fuzzy variables names.

families

is a factor species family.

col.blocks

is a vector containing the number of categories of each trait.

Source

Bournaud, M., Richoux, P. and Usseglio-Polatera, P. (1992) An approach to the synthesis of qualitative ecological information from aquatic coleoptera communities. Regulated rivers: Research and Management, 7, 165–180.

Examples

data(coleo)
op <- par(no.readonly = TRUE) 
coleo.fuzzy <- prep.fuzzy.var(coleo$tab, coleo$col.blocks)
fca1 <- dudi.fca(coleo.fuzzy, sca = FALSE, nf = 3)
indica <- factor(rep(names(coleo$col), coleo$col))

if(adegraphicsLoaded()) {
  glist <- list()
  for(i in levels(indica)) {
    df <- coleo$tab[, which(indica == i)]
    names(df) <- coleo$moda.names[which(indica == i)]
    glist[i] <- s.distri(fca1$l1, df, psub.text = as.character(i), ellipseSize = 0, 
      starSize = 0.5, plot = FALSE, storeData = TRUE)
  }
  G <- ADEgS(glist, layout = c(3, 3))
  
} else {
  par(mfrow = c(3, 3))
  for(j in levels(indica)) 
    s.distri(fca1$l1, coleo$tab[, which(indica == j)], clab = 1.5, sub = as.character(j), 
      cell = 0, csta = 0.5, csub = 3, label = coleo$moda.names[which(indica == j)])
  par(op)
  par(mfrow = c(1, 1))
}

Functions to combine and adjust the outputs 3-table methods

Description

Functions to combine and adjust the outputs of the fourthcorner and randtest.rlq functions created using permutational models 2 and 4 (sequential approach).

Usage

combine.randtest.rlq(obj1, obj2, ...)
combine.4thcorner(four1,four2)
p.adjust.4thcorner(x, p.adjust.method.G = p.adjust.methods,
p.adjust.method.D = p.adjust.methods, p.adjust.D = c("global",
"levels"))

Arguments

four1

an object of the class 4thcorner created with modeltype = 2 (or 4)
four2

an object of the class 4thcorner created with modeltype = 4 (or 2)
obj1

an object created with randtest.rlq and modeltype = 2 (or 4)
obj2

an object created with randtest.rlq and modeltype = 4 (or 2)
x

an object of the class 4thcorner
p.adjust.method.G

a string indicating a method for multiple adjustment used for output tabG, see p.adjust.methods for possible choices
p.adjust.method.D

a string indicating a method for multiple adjustment used for output tabD/tabD2, see p.adjust.methods for possible choices
p.adjust.D

a string indicating if multiple adjustment for tabD/tabD2 should be done globally or only between levels of a factor ("levels", as in the original paper of Legendre et al. 1997)
...

further arguments passed to or from other methods

Details

The functions combines the outputs of two objects (created by fourthcorner and randtest.rlq functions) as described in Dray and Legendre (2008) and ter Braak et al (2012).

Value

The functions return objects of the same class than their argument. They simply create a new object where pvalues are equal to the maximum of pvalues of the two arguments.

Author(s)

Stéphane Dray [email protected]

References

Dray, S. and Legendre, P. (2008) Testing the species traits-environment relationships: the fourth-corner problem revisited. Ecology, 89, 3400–3412.

ter Braak, C., Cormont, A., and Dray, S. (2012) Improved testing of species traits-environment relationships in the fourth corner problem. Ecology, 93, 1525–1526.

See Also

rlq, fourthcorner, p.adjust.methods

Examples

data(aravo)
four2 <- fourthcorner(aravo$env, aravo$spe, aravo$traits, nrepet=99,modeltype=2)
four4 <- fourthcorner(aravo$env, aravo$spe, aravo$traits, nrepet=99,modeltype=4)
four.comb <- combine.4thcorner(four2,four4)
## or directly :
## four.comb <- fourthcorner(aravo$env, aravo$spe, aravo$traits, nrepet=99,modeltype=6)
summary(four.comb)
plot(four.comb, stat = "G")

Tests of randomization between distances applied to 'kdist' objetcs

Description

The mantelkdist and RVkdist functions apply to blocks of distance matrices the mantel.rtest and RV.rtest functions.

Usage

mantelkdist (kd, nrepet = 999, ...)
RVkdist (kd, nrepet = 999, ...)
## S3 method for class 'corkdist'
plot(x, whichinrow = NULL, whichincol = NULL, 
   gap = 4, nclass = 10,...)

Arguments

kd

a list of class kdist
nrepet

the number of permutations
x

an objet of class corkdist, coming from RVkdist or mantelkdist
whichinrow

a vector of integers to select the graphs in rows (if NULL all the graphs are computed)
whichincol

a vector of integers to select the graphs in columns (if NULL all the graphs are computed)
gap

an integer to determinate the space between two graphs
nclass

a number of intervals for the histogram
...

further arguments passed to or from other methods

Details

The corkdist class has some generic functions print, plot and summary. The plot shows bivariate scatterplots between semi-matrices of distances or histograms of simulated values with an error position.

Value

a list of class corkdist containing for each pair of distances an object of class randtest (permutation tests).

Author(s)

Daniel Chessel
Stéphane Dray [email protected]

Examples

data(friday87)
fri.w <- ktab.data.frame(friday87$fau, friday87$fau.blo, tabnames = friday87$tab.names)
fri.kc <- lapply(1:10, function(x) dist.binary(fri.w[[x]], 10))
names(fri.kc) <- substr(friday87$tab.names, 1, 4)
fri.kd <- kdist(fri.kc)
fri.mantel <- mantelkdist(kd = fri.kd, nrepet = 999)

plot(fri.mantel, 1:5, 1:5)
plot(fri.mantel, 1:5, 6:10)
plot(fri.mantel, 6:10, 1:5)
plot(fri.mantel, 6:10, 6:10)
s.corcircle(dudi.pca(as.data.frame(fri.kd), scan = FALSE)$co)
plot(RVkdist(fri.kd), 1:5, 1:5)

data(yanomama)
m1 <- mantelkdist(kdist(yanomama), 999)
m1
summary(m1)
plot(m1)

Corvus morphology

Description

This data set gives a morphological description of 28 species of the genus Corvus split in two habitat types and phylogeographic stocks.

Usage

data(corvus)

Format

corvus is data frame with 28 observations (the species) and 4 variables :

wing

: wing length (mm)

bill

: bill length (mm)

habitat

: habitat with two levels clos and open

phylog

: phylogeographic stock with three levels amer(America), orien(Oriental-Australian), pale(Paleoarctic-African)

References

Laiolo, P. and Rolando, A. (2003) The evolution of vocalisations in the genus Corvus: effects of phylogeny, morphology and habitat. Evolutionary Ecology, 17, 111–123.

Examples

data(corvus)

if(adegraphicsLoaded()) {
  g1 <- s.label(corvus[, 1:2], plab.cex = 0, porigin.include = FALSE, pgrid.draw = FALSE, 
    paxes.draw = TRUE, paxes.asp = "full", xlab = names(corvus)[2], 
    ylab = names(corvus)[2], plot = FALSE)
  g2 <- s.class(corvus[, 1:2], corvus[, 4]:corvus[, 3], plot = FALSE)
  G <- superpose(g1, g2, plot = TRUE)

} else {
  plot(corvus[, 1:2])
  s.class(corvus[, 1:2], corvus[, 4]:corvus[, 3], add.p = TRUE)
}

STATIS and Co-Inertia : Analysis of a series of paired ecological tables

Description

Analysis of a series of pairs of ecological tables. This function uses Partial Triadic Analysis (pta) and coinertia to do the computations.

Usage

costatis(KTX, KTY, scannf = TRUE)

Arguments

KTX

an objet of class ktab
KTY

an objet of class ktab
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed

Details

This function takes 2 ktabs. It does a PTA (partial triadic analysis: pta) on each ktab, and does a coinertia analysis (coinertia) on the compromises of the two PTAs.

Value

a list of class coinertia, subclass dudi. See coinertia

WARNING

IMPORTANT : KTX and KTY must have the same k-tables structure, the same number of columns, and the same column weights.

Author(s)

Jean Thioulouse [email protected]

References

Thioulouse J. (2011). Simultaneous analysis of a sequence of paired ecological tables: a comparison of several methods. Annals of Applied Statistics, 5, 2300-2325.

Examples

data(meau)
wit1 <- withinpca(meau$env, meau$design$season, scan = FALSE, scal = "total")
pcaspe <- dudi.pca(meau$spe, scale = FALSE, scan = FALSE, nf = 2)
wit2 <- wca(pcaspe, meau$design$season, scan = FALSE, nf = 2)
kta1 <- ktab.within(wit1, colnames = rep(c("S1","S2","S3","S4","S5","S6"), 4))
kta2 <- ktab.within(wit2, colnames = rep(c("S1","S2","S3","S4","S5","S6"), 4))
costatis1 <- costatis(kta1, kta2, scan = FALSE)
plot(costatis1)

Monte-Carlo test on a Costatis analysis (in C).

Description

Performs a Monte-Carlo test on a Costatis analysis.

Usage

costatis.randtest(KTX, KTY, nrepet = 999, ...)

Arguments

KTX

an objet of class ktab
KTY

an objet of class ktab
nrepet

the number of permutations
...

further arguments passed to or from other methods

Value

a list of the class randtest

Author(s)

Jean Thioulouse [email protected]

References

Thioulouse J. (2011). Simultaneous analysis of a sequence of paired ecological tables: a comparison of several methods. Annals of Applied Statistics, 5, 2300-2325.

Examples

data(meau)
wit1 <- withinpca(meau$env, meau$design$season, scan = FALSE, scal = "total")
pcaspe <- dudi.pca(meau$spe, scale = FALSE, scan = FALSE, nf = 2)
wit2 <- wca(pcaspe, meau$design$season, scan = FALSE, nf = 2)
kta1 <- ktab.within(wit1, colnames = rep(c("S1","S2","S3","S4","S5","S6"), 4))
kta2 <- ktab.within(wit2, colnames = rep(c("S1","S2","S3","S4","S5","S6"), 4))
costatis1 <- costatis(kta1, kta2, scan = FALSE)
costatis.randtest(kta1, kta2)

Dagnelie multinormality test

Description

Compute Dagnelie test of multivariate normality on a data table of n objects (rows) and p variables (columns), with n > (p+1).

Usage

dagnelie.test(x)

Arguments

x

Multivariate data table (matrix or data.frame).

Details

Dagnelie's goodness-of-fit test of multivariate normality is applicable to multivariate data. Mahalanobis generalized distances are computed between each object and the multivariate centroid of all objects. Dagnelie’s approach is that, for multinormal data, the generalized distances should be normally distributed. The function computes a Shapiro-Wilk test of normality of the Mahalanobis distances; this is our improvement of Dagnelie’s method. The null hypothesis (H0) is that the data are multinormal, a situation where the Mahalanobis distances should be normally distributed. In that case, the test should not reject H0, subject to type I error at the selected significance level.

Numerical simulations by D. Borcard have shown that the test had correct levels of type I error for values of n between 3p and 8p, where n is the number of objects and p is the number of variables in the data matrix (simulations with 1 <= p <= 100). Outside that range of n values, the results were too liberal, meaning that the test rejected too often the null hypothesis of normality. For p = 2, the simulations showed the test to be valid for 6 <= n <= 13 and too liberal outside that range. If H0 is not rejected in a situation where the test is too liberal, the result is trustworthy.

Calculation of the Mahalanobis distances requires that n > p+1 (actually, n > rank+1). With fewer objects (n), all points are at equal Mahalanobis distances from the centroid in the resulting space, which has min(rank,(n-1)) dimensions. For data matrices that happen to be collinear, the function uses ginv for inversion.

This test is not meant to be used with univariate data; in simulations, the type I error rate was higher than the 5% significance level for all values of n. Function shapiro.test should be used in that situation.

Value

A list containing the following results:

Shapiro.Wilk

W statistic and p-value
dim

dimensions of the data matrix, n and p
rank

the rank of the covariance matrix
D

Vector containing the Mahalanobis distances of the objects to the multivariate centroid

Author(s)

Daniel Borcard and Pierre Legendre

References

Dagnelie, P. 1975. L'analyse statistique a plusieurs variables. Les Presses agronomiques de Gembloux, Gembloux, Belgium.

Legendre, P. and L. Legendre. 2012. Numerical ecology, 3rd English edition. Elsevier Science BV, Amsterdam, The Netherlands.

Examples

# Example 1: 2 variables, n = 100
 n <- 100; p <- 2
 mat <- matrix(rnorm(n*p), n, p)
 (out <- dagnelie.test(mat))

 # Example 2: 10 variables, n = 50
 n <- 50; p <- 10
 mat <- matrix(rnorm(n*p), n, p)
 (out <- dagnelie.test(mat))

 # Example 3: 10 variables, n = 100
 n <- 100; p <- 10
 mat <- matrix(rnorm(n*p), n, p)
 (out <- dagnelie.test(mat))
 # Plot a histogram of the Mahalanobis distances
hist(out$D)

 # Example 4: 10 lognormal random variables, n = 50
 n <- 50; p <- 10
 mat <- matrix(round(exp(rnorm((n*p), mean = 0, sd = 2.5))), n, p)
 (out <- dagnelie.test(mat))
 # Plot a histogram of the Mahalanobis distances
 hist(out$D)

Deprecated functions in ade4

Description

The functions/data listed below are deprecated. The R code of the deprecated functions are stored for memory in the file ade4-deprecated.R.

- between: replaced by bca
- betweencoinertia: replaced by bca.coinertia
- char2genet: replaced by df2genind and genind2genpop in the adegenet package
- count2genet: replaced by df2genind and genind2genpop in the adegenet package
- dist.genet: replaced by dist.genpop in the adegenet package
- EH: replaced by EH in the adiv package
- freq2genet: replaced by df2genind and genind2genpop in the adegenet package
- fuzzygenet: replaced by df2genind in the adegenet package
- optimEH: replaced by optimEH in the adiv package
- orisaved: replaced by orisaved in the adiv package
- orthogram: replaced by orthogram in the adephylo package
- randEH: replaced by randEH in the adiv package
- within: replaced by wca
- withincoinertia: replaced by wca.coinertia

Exam marks for some students

Description

This data set gives the exam results of 104 students in the second year of a French University onto 9 subjects.

Usage

data(deug)

Format

deug is a list of three components.

tab

is a data frame with 104 students and 9 subjects : Algebra, Analysis, Proba, Informatic, Economy, Option1, Option2, English, Sport.

result

is a factor of 104 components giving the final exam levels (A+, A, B, B-, C-, D).

cent

is a vector of required marks by subject to get exactly 10/20 with a coefficient.

Source

University of Lyon 1

Examples

data(deug)
# decentred PCA
pca1 <- dudi.pca(deug$tab, scal = FALSE, center = deug$cent, scan = FALSE)
  
if(adegraphicsLoaded()) {
  g1 <- s.class(pca1$li, deug$result, plot = FALSE)
  g2 <- s.arrow(40 * pca1$c1, plot = FALSE)
  G <- superpose(g1, g2, plot = TRUE)
  
} else {
  s.class(pca1$li, deug$result)
  s.arrow(40 * pca1$c1, add.plot = TRUE)
}

Rao's dissimilarity coefficient

Description

Calculates the root square of Rao's dissimilarity coefficient between samples.

Usage

disc(samples, dis = NULL, structures = NULL)

Arguments

samples

a data frame with elements as rows, samples as columns, and abundance, presence-absence or frequencies as entries
dis

an object of class dist containing distances or dissimilarities among elements. If dis is NULL, equidistances are used.
structures

a data frame containing, in the jth row and the kth column, the name of the group of level k to which the jth population belongs.

Value

Returns a list of objects of class dist

Author(s)

Sandrine Pavoine [email protected]

References

Rao, C.R. (1982) Diversity and dissimilarity coefficients: a unified approach. Theoretical Population Biology, 21, 24–43.

Examples

data(humDNAm)
humDNA.dist <- disc(humDNAm$samples, sqrt(humDNAm$distances), humDNAm$structures)
humDNA.dist
is.euclid(humDNA.dist$samples)
is.euclid(humDNA.dist$regions)

## Not run: 
data(ecomor)
dtaxo <- dist.taxo(ecomor$taxo)
ecomor.dist <- disc(ecomor$habitat, dtaxo)
ecomor.dist
is.euclid(ecomor.dist)

## End(Not run)

Linear Discriminant Analysis (descriptive statistic)

Description

performs a linear discriminant analysis.

Usage

discrimin(dudi, fac, scannf = TRUE, nf = 2)
## S3 method for class 'discrimin'
plot(x, xax = 1, yax = 2, ...) 
## S3 method for class 'discrimin'
print(x, ...)

Arguments

dudi

a duality diagram, object of class dudi
fac

a factor defining the classes of discriminant analysis
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes


x

an object of class 'discrimin'
xax

the column number of the x-axis
yax

the column number of the y-axis
...

further arguments passed to or from other methods

Value

returns a list of class 'discrimin' containing :

nf

a numeric value indicating the number of kept axes
eig

a numeric vector with all the eigenvalues
fa

a matrix with the loadings: the canonical weights
li

a data frame which gives the canonical scores
va

a matrix which gives the cosines between the variables and the canonical scores
cp

a matrix which gives the cosines between the components and the canonical scores
gc

a data frame which gives the class scores

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

See Also

lda in package MASS

Examples

data(chazeb)
dis1 <- discrimin(dudi.pca(chazeb$tab, scan = FALSE), chazeb$cla, 
    scan = FALSE)
dis1
if(!adegraphicsLoaded())
  plot(dis1)

data(skulls)
plot(discrimin(dudi.pca(skulls, scan = FALSE), gl(5,30), 
    scan = FALSE))

Discriminant Correspondence Analysis

Description

performs a discriminant correspondence analysis.

Usage

discrimin.coa(df, fac, scannf = TRUE, nf = 2)

Arguments

df

a data frame containing positive or null values
fac

a factor defining the classes of discriminant analysis
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes

Value

a list of class discrimin. See discrimin

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

References

Perriere, G.,Lobry, J. R. and Thioulouse J. (1996) Correspondence discriminant analysis: a multivariate method for comparing classes of protein and nucleic acid sequences. CABIOS, 12, 519–524.

Perriere, G. and Thioulouse, J. (2003) Use of Correspondence Discriminant Analysis to predict the subcellular location of bacterial proteins. Computer Methods and Programs in Biomedicine, 70, 2, 99–105.

Examples

data(perthi02)
plot(discrimin.coa(perthi02$tab, perthi02$cla, scan = FALSE))

Computation of Distance Matrices for Binary Data

Description

computes for binary data some distance matrice.

Usage

dist.binary(df, method = NULL, diag = FALSE, upper = FALSE)

Arguments

df

a matrix or a data frame with positive or null numeric values. Used with as.matrix(1 * (df > 0))
method

an integer between 1 and 10 . If NULL the choice is made with a console message. See details
diag

a logical value indicating whether the diagonal of the distance matrix should be printed by ‘print.dist’
upper

a logical value indicating whether the upper triangle of the distance matrix should be printed by ‘print.dist’

Details

Let be the contingency table of binary data such as n11=an_{11} = a, n10=bn_{10} = b, n01=cn_{01} = c and n00=dn_{00} = d. All these distances are of type d=1−sd=\sqrt{1-s} with s a similarity coefficient.

1 = Jaccard index (1901)

S3 coefficient of Gower & Legendre s1=aa+b+cs_1 = \frac{a}{a+b+c}

2 = Simple matching coefficient of Sokal & Michener (1958)

S4 coefficient of Gower & Legendre s2=a+da+b+c+ds_2 =\frac{a+d}{a+b+c+d}

3 = Sokal & Sneath(1963)

S5 coefficient of Gower & Legendre s3=aa+2(b+c)s_3 =\frac{a}{a+2(b+c)}

4 = Rogers & Tanimoto (1960)

S6 coefficient of Gower & Legendre s4=a+d(a+2(b+c)+d)s_4 =\frac{a+d}{(a+2(b+c)+d)}

5 = Dice (1945) or Sorensen (1948)

S7 coefficient of Gower & Legendre s5=2a2a+b+cs_5 =\frac{2a}{2a+b+c}

6 = Hamann coefficient

S9 index of Gower & Legendre (1986) s6=a−(b+c)+da+b+c+ds_6 =\frac{a-(b+c)+d}{a+b+c+d}

7 = Ochiai (1957)

S12 coefficient of Gower & Legendre s7=a(a+b)(a+c)s_7 =\frac{a}{\sqrt{(a+b)(a+c)}}

8 = Sokal & Sneath (1963)

S13 coefficient of Gower & Legendre s8=ad(a+b)(a+c)(d+b)(d+c)s_8 =\frac{ad}{\sqrt{(a+b)(a+c)(d+b)(d+c)}}

9 = Phi of Pearson

S14 coefficient of Gower & Legendre s9=ad−bc(a+b)(a+c)(b+d)(d+c)s_9 =\frac{ad-bc}{\sqrt{(a+b)(a+c)(b+d)(d+c)}}

10 = S2 coefficient of Gower & Legendre

s1=aa+b+c+ds_1 = \frac{a}{a+b+c+d}

Value

returns a distance matrix of class dist between the rows of the data frame

Author(s)

Daniel Chessel
Stéphane Dray [email protected]

References

Gower, J.C. and Legendre, P. (1986) Metric and Euclidean properties of dissimilarity coefficients. Journal of Classification, 3, 5–48.

Examples

data(aviurba)
for (i in 1:10) {
    d <- dist.binary(aviurba$fau, method = i)
    cat(attr(d, "method"), is.euclid(d), "\n")}

Computation of the Distance Matrix from a Statistical Triplet

Description

computes for a statistical triplet a distance matrix.

Usage

dist.dudi(dudi, amongrow = TRUE)

Arguments

dudi

a duality diagram, object of class dudi
amongrow

a logical value computing the distance if TRUE, between rows, if FALSE between columns.

Value

an object of class dist

Author(s)

Daniel Chessel
Stéphane Dray [email protected]

Examples

data (meaudret)
pca1 <- dudi.pca(meaudret$env, scan = FALSE)
sum((dist(scalewt(meaudret$env)) - dist.dudi(pca1))^2)
#[1] 4.045e-29 the same thing

Mixed-variables coefficient of distance

Description

The mixed-variables coefficient of distance generalizes Gower's general coefficient of distance to allow the treatment of various statistical types of variables when calculating distances. This is especially important when measuring functional diversity. Indeed, most of the indices that measure functional diversity depend on variables (traits) that have various statistical types (e.g. circular, fuzzy, ordinal) and that go through a matrix of distances among species.

Usage

dist.ktab(x, type, option = c("scaledBYrange", "scaledBYsd", "noscale"),
scann = FALSE, tol = 1e-8)
ldist.ktab(x, type, option = c("scaledBYrange", "scaledBYsd",
"noscale"), scann = FALSE, tol = 1e-8)
kdist.cor(x, type, option = c("scaledBYrange", "scaledBYsd", "noscale"),
scann = FALSE, tol = 1e-8, squared = TRUE)
prep.fuzzy(df, col.blocks, row.w = rep(1, nrow(df)), labels = paste("F",
1:length(col.blocks), sep = ""))
prep.binary(df, col.blocks, labels = paste("B", 1:length(col.blocks), sep = "")) 
prep.circular(df, rangemin = apply(df, 2, min, na.rm = TRUE), rangemax =
apply(df, 2, max, na.rm = TRUE))

Arguments

x

Object of class ktab (see details)
type

Vector that provide the type of each table in x. The possible types are "Q" (quantitative), "O" (ordinal), "N" (nominal), "D" (dichotomous), "F" (fuzzy, or expressed as a proportion), "B" (multichoice nominal variables, coded by binary columns), "C" (circular). Values in type must be in the same order as in x.
option

A string that can have three values: either "scaledBYrange" if the quantitative variables must be scaled by their range, or "scaledBYsd" if they must be scaled by their standard deviation, or "noscale" if they should not be scaled. This last option can be useful if the the values have already been normalized by the known range of the whole population instead of the observed range measured on the sample. If x contains data from various types, then the option "scaledBYsd" is not suitable (a warning will appear if the option selected with that condition).
scann

A logical. If TRUE, then the user will have to choose among several possible functions of distances for the quantitative, ordinal, fuzzy and binary variables.
tol

A tolerance threshold: a value less than tol is considered as null.
squared

A logical, if TRUE, the squared distances are considered.
df

Objet of class data.frame
col.blocks

A vector that contains the number of levels per variable (in the same order as in df)
row.w

A vector of row weigths
labels

the names of the traits
rangemin

A numeric corresponding to the smallest level where the loop starts
rangemax

A numeric corresponding to the highest level where the loop closes

Details

When preparing the object of class ktab (object x), variables of type "Q", "O", "D", "F", "B" and "C" should be of class numeric (the class ordered is not yet considered by dist.ktab); variables of type "N" should be of class character or factor

Value

The functions provide the following results:

dist.ktab

returns an object of class dist;
ldist.ktab

returns a list of objects of class dist that correspond to the distances between species calculated per trait;
kdist.cor

returns a list of three objects: "paircov" provides the covariance between traits in terms of (squared) distances between species; "paircor" provides the correlations between traits in terms of (squared) distances between species; "glocor" provides the correlations between the (squared) distances obtained for each trait and the global (squared) distances obtained by mixing all the traits (= contributions of traits to the global distances);
prep.binary and prep.fuzzy

returns a data frame with the following attributes: col.blocks specifies the number of columns per fuzzy variable; col.num specifies which variable each column belongs to;
prep.circular

returns a data frame with the following attributes: max specifies the number of levels in each circular variable.

Author(s)

Sandrine Pavoine [email protected]

References

Pavoine S., Vallet, J., Dufour, A.-B., Gachet, S. and Daniel, H. (2009) On the challenge of treating various types of variables: Application for improving the measurement of functional diversity. Oikos, 118, 391–402. doi:10.1111/j.1600-0706.2008.16668.x

Appendix available at: http://www.oikosjournal.org/sites/oikosjournal.org/files/appendix/o16668.pdf http://www.oikosjournal.org/sites/oikosjournal.org/files/appendix/o16668_files.zip

See Also

daisy in the case of ratio-scale (quantitative) and nominal variables; and woangers for an application.

Examples

# With fuzzy variables
data(bsetal97)

w <- prep.fuzzy(bsetal97$biol, bsetal97$biol.blo)
w[1:6, 1:10]
ktab1 <- ktab.list.df(list(w))
dis <- dist.ktab(ktab1, type = "F")
as.matrix(dis)[1:5, 1:5]

## Not run: 
# With ratio-scale and multichoice variables
data(ecomor)

wM <- log(ecomor$morpho + 1) # Quantitative variables
wD <- ecomor$diet
# wD is a data frame containing a multichoice nominal variable
# (diet habit), with 8 modalities (Granivorous, etc)
# We must prepare it by prep.binary
head(wD)
wD <- prep.binary(wD, col.blocks = 8, label = "diet")
wF <- ecomor$forsub
# wF is also a data frame containing a multichoice nominal variable
# (foraging substrat), with 6 modalities (Foliage, etc)
# We must prepare it by prep.binary
head(wF)
wF <- prep.binary(wF, col.blocks = 6, label = "foraging")
# Another possibility is to combine the two last data frames wD and wF as
# they contain the same type of variables
wB <- cbind.data.frame(ecomor$diet, ecomor$forsub)
head(wB)
wB <- prep.binary(wB, col.blocks = c(8, 6), label = c("diet", "foraging"))
# The results given by the two alternatives are identical
ktab2 <- ktab.list.df(list(wM, wD, wF))
disecomor <- dist.ktab(ktab2, type= c("Q", "B", "B"))
as.matrix(disecomor)[1:5, 1:5]
contrib2 <- kdist.cor(ktab2, type= c("Q", "B", "B"))
contrib2

ktab3 <- ktab.list.df(list(wM, wB))
disecomor2 <- dist.ktab(ktab3, type= c("Q", "B"))
as.matrix(disecomor2)[1:5, 1:5]
contrib3 <- kdist.cor(ktab3, type= c("Q", "B"))
contrib3

# With a range of variables
data(woangers)

traits <- woangers$traits
# Nominal variables 'li', 'pr', 'lp' and 'le'
# (see table 1 in the main text for the codes of the variables)
tabN <- traits[,c(1:2, 7, 8)]
# Circular variable 'fo'
tabC <- traits[3]
tabCp <- prep.circular(tabC, 1, 12)
# The levels of the variable lie between 1 (January) and 12 (December).
# Ordinal variables 'he', 'ae' and 'un'
tabO <- traits[, 4:6]
# Fuzzy variables 'mp', 'pe' and 'di'
tabF <- traits[, 9:19]
tabFp <- prep.fuzzy(tabF, c(3, 3, 5), labels = c("mp", "pe", "di"))
# 'mp' has 3 levels, 'pe' has 3 levels and 'di' has 5 levels.
# Quantitative variables 'lo' and 'lf'
tabQ <- traits[, 20:21]
ktab1 <- ktab.list.df(list(tabN, tabCp, tabO, tabFp, tabQ))
distrait <- dist.ktab(ktab1, c("N", "C", "O", "F", "Q"))
is.euclid(distrait)
contrib <- kdist.cor(ktab1, type = c("N", "C", "O", "F", "Q"))
contrib
dotchart(sort(contrib$glocor), labels = rownames(contrib$glocor)[order(contrib$glocor[, 1])])

## End(Not run)

Computation of the Distance Matrix associated to a Neighbouring Graph

Description

This distance matrix between two points is the length of the shortest path between these points.

Usage

dist.neig(neig)

Arguments

neig

a neighbouring graph, object of class neig

Value

returns a distance matrix, object of class dist

Author(s)

Daniel Chessel
Stéphane Dray [email protected]

Examples

data(elec88)
    d0 <- dist.neig(elec88$neig)
    plot(dist(elec88$xy),d0)

Computation of Distance Matrices of Percentage Data

Description

computes for percentage data some distance matrices.

Usage

dist.prop(df, method = NULL, diag = FALSE, upper = FALSE)

Arguments

df

a data frame containing only positive or null values, used as row percentages
method

an integer between 1 and 5. If NULL the choice is made with a console message. See details
diag

a logical value indicating whether the diagonal of the distance matrix should be printed by ‘print.dist’
upper

a logical value indicating whether the upper triangle of the distance matrix should be printed by ‘print.dist’

Details

1 = Manly

d1=12∑i=1K∣pi−qi∣d_1=\frac{1}{2} \sum_{i=1}^{K}{|{p_i-q_i}|}

2 = Overlap index Manly

d2=1−∑i=1Kpiqi∑i=1Kpi2∑i=1Kqi2d_2=1-\frac{\sum_{i=1}^{K}{p_i q_i}}{\sqrt{\sum_{i=1}^{K}{p_i^2}}{\sqrt{\sum_{i=1}^{K}{q_i^2}}}}

3 = Rogers 1972 (one locus)

d3=12∑i=1K(pi−qi)2d_3=\sqrt{\frac{1}{2} \sum_{i=1}^{K}{(p_i-q_i)^2}}

4 = Nei 1972 (one locus)

d4=ln⁡∑i=1Kpiqi∑i=1Kpi2∑i=1Kqi2d_4=\ln{\frac{\sum_{i=1}^{K}{p_i q_i}}{\sqrt{\sum_{i=1}^{K}{p_i^2}}{\sqrt{\sum_{i=1}^{K}{q_i^2}}}}}

5 = Edwards 1971 (one locus)

d5=1−∑i=1Kp1qid_5=\sqrt{1-\sum_{i=1}^{K}{\sqrt{p_1 q_i}}}

Value

returns a distance matrix, object of class dist

Author(s)

Daniel Chessel
Stéphane Dray [email protected]

References

Edwards, A. W. F. (1971) Distance between populations on the basis of gene frequencies. Biometrics, 27, 873–881.

Manly, B. F. (1994) Multivariate Statistical Methods. A primer., Second edition. Chapman & Hall, London.

Nei, M. (1972) Genetic distances between populations. The American Naturalist, 106, 283–292.

Examples

data(microsatt)
w <- microsatt$tab[1:microsatt$loci.eff[1]]

if(adegraphicsLoaded()) {
  g1 <- scatter(dudi.pco(lingoes(dist.prop(w, 1)), scann = FALSE), plot = FALSE)
  g2 <- scatter(dudi.pco(lingoes(dist.prop(w, 2)), scann = FALSE), plot = FALSE)
  g3 <- scatter(dudi.pco(dist.prop(w, 3), scann = FALSE), plot = FALSE)
  g4 <- scatter(dudi.pco(lingoes(dist.prop(w, 4)), scann = FALSE), plot = FALSE)
  G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))
  
} else {
  par(mfrow = c(2, 2))
  scatter(dudi.pco(lingoes(dist.prop(w, 1)), scann = FALSE))
  scatter(dudi.pco(lingoes(dist.prop(w, 2)), scann = FALSE))
  scatter(dudi.pco(dist.prop(w, 3), scann = FALSE))
  scatter(dudi.pco(lingoes(dist.prop(w, 4)), scann = FALSE))
  par(mfrow = c(1, 1))
}

Computation of Distance Matrices on Quantitative Variables

Description

computes on quantitative variables, some distance matrices as canonical, Joreskog and Mahalanobis.

Usage

dist.quant(df, method = NULL, diag = FALSE, upper = FALSE, 
    tol = 1e-07)

Arguments

df

a data frame containing only quantitative variables
method

an integer between 1 and 3. If NULL the choice is made with a console message. See details
diag

a logical value indicating whether the diagonal of the distance matrix should be printed by ‘print.dist’
upper

a logical value indicating whether the upper triangle of the distance matrix should be printed by ‘print.dist’
tol

used in case 3 of method as a tolerance threshold for null eigenvalues

Details

All the distances are of type d=∥x−y∥A=(x−y)tA(x−y)d=\|x-y\|_A = \sqrt{(x-y)^{t}A(x-y)}

1 = Canonical

A = Identity

2 = Joreskog

A=1diag(cov)A=\frac{1}{diag(cov)}

3 = Mahalanobis

A = inv(cov)

Value

an object of class dist

Author(s)

Daniel Chessel
Stéphane Dray [email protected]

Examples

data(ecomor)

if(adegraphicsLoaded()) {
  g1 <- scatter(dudi.pco(dist.quant(ecomor$morpho, 3), scan = FALSE), plot = FALSE)
  g2 <- scatter(dudi.pco(dist.quant(ecomor$morpho, 2), scan = FALSE), plot = FALSE)
  g3 <- scatter(dudi.pco(dist(scalewt(ecomor$morpho)), scan = FALSE), plot = FALSE)
  g4 <- scatter(dudi.pco(dist.quant(ecomor$morpho, 1), scan = FALSE), plot = FALSE)
  G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))
  
} else {
  par(mfrow = c(2, 2))
  scatter(dudi.pco(dist.quant(ecomor$morpho, 3), scan = FALSE))
  scatter(dudi.pco(dist.quant(ecomor$morpho, 2), scan = FALSE))
  scatter(dudi.pco(dist(scalewt(ecomor$morpho)), scan = FALSE))
  scatter(dudi.pco(dist.quant(ecomor$morpho, 1), scan = FALSE))
  par(mfrow = c(1, 1))
}

Rao's diversity coefficient also called quadratic entropy

Description

Calculates Rao's diversity coefficient within samples.

Usage

divc(df, dis, scale)

Arguments

df

a data frame with elements as rows, samples as columns, and abundance, presence-absence or frequencies as entries
dis

an object of class dist containing distances or dissimilarities among elements. If dis is NULL, Gini-Simpson index is performed.
scale

a logical value indicating whether or not the diversity coefficient should be scaled by its maximal value over all frequency distributions.

Value

Returns a data frame with samples as rows and the diversity coefficient within samples as columns

Author(s)

Sandrine Pavoine [email protected]

References

Rao, C.R. (1982) Diversity and dissimilarity coefficients: a unified approach. Theoretical Population Biology, 21, 24–43.

Gini, C. (1912) Variabilità e mutabilità. Universite di Cagliari III, Parte II.

Simpson, E.H. (1949) Measurement of diversity. Nature, 163, 688.

Champely, S. and Chessel, D. (2002) Measuring biological diversity using Euclidean metrics. Environmental and Ecological Statistics, 9, 167–177.

Examples

data(ecomor)
dtaxo <- dist.taxo(ecomor$taxo)
divc(ecomor$habitat, dtaxo)

data(humDNAm)
divc(humDNAm$samples, sqrt(humDNAm$distances))

Maximal value of Rao's diversity coefficient also called quadratic entropy

Description

For a given dissimilarity matrix, this function calculates the maximal value of Rao's diversity coefficient over all frequency distribution. It uses an optimization technique based on Rosen's projection gradient algorithm and is verified using the Kuhn-Tucker conditions.

Usage

divcmax(dis, epsilon, comment)

Arguments

dis

an object of class dist containing distances or dissimilarities among elements.
epsilon

a tolerance threshold : a frequency is non null if it is higher than epsilon.
comment

a logical value indicating whether or not comments on the optimization technique should be printed.

Value

Returns a list

value

the maximal value of Rao's diversity coefficient.
vectors

a data frame containing four frequency distributions : sim is a simple distribution which is equal to D11tD1\frac{D1}{1^tD1}, pro is equal to z1tz1\frac{z}{1^tz1}, where z is the nonnegative eigenvector of the matrix containing the squared dissimilarities among the elements, met is equal to z2z^2, num is a frequency vector maximizing Rao's diversity coefficient.

Author(s)

Stéphane Champely [email protected]
Sandrine Pavoine [email protected]

References

Rao, C.R. (1982) Diversity and dissimilarity coefficients: a unified approach. Theoretical Population Biology, 21, 24–43.

Gini, C. (1912) Variabilità e mutabilità. Universite di Cagliari III, Parte II.

Simpson, E.H. (1949) Measurement of diversity. Nature, 163, 688.

Champely, S. and Chessel, D. (2002) Measuring biological diversity using Euclidean metrics. Environmental and Ecological Statistics, 9, 167–177.

Pavoine, S., Ollier, S. and Pontier, D. (2005) Measuring diversity from dissimilarities with Rao's quadratic entropy: are any dissimilarities suitable? Theoretical Population Biology, 67, 231–239.

Examples

data(elec88)

# Dissimilarity matrix.
d0 <- dist(elec88$xy/100)

# Frequency distribution maximizing spatial diversity in France
# according to Rao's quadratic entropy.
France.m <- divcmax(d0)
w0 <- France.m$vectors$num
v0 <- France.m$value
idx <- (1:94) [w0 > 0]

if(!adegraphicsLoaded()) {
  # Smallest circle including all the 94 departments.
  # The squared radius of that circle is the maximal value of the
  # spatial diversity.
  w1 <- elec88$xy[idx, ]/100
  w.c <- apply(w1 * w0[idx], 2, sum)
  plot(elec88$xy[, 1]/100, elec88$xy[, 2]/100, asp=1)
  symbols(w.c[1], w.c[2], circles = sqrt(v0), inches = FALSE, add = TRUE)
  s.value(elec88$xy/100, w0, add.plot = TRUE)
}

Representation of many quantitative variables in front of a phylogenetic tree

Description

dotchart.phylog represents the phylogenetic tree and draws Cleveland dot plot of each variable.

Usage

dotchart.phylog(phylog, values, y = NULL, scaling = TRUE, ranging =
TRUE, yranging = NULL, joining = TRUE, yjoining = NULL, ceti = 1, cdot =
1, csub = 1, f.phylog = 1/(1 + ncol(values)), ...)

Arguments

phylog

an object of class phylog
values

a vector or a data frame giving the variables
y

a vector which values correspond to leaves positions
scaling

if TRUE, data are scaled
ranging

if TRUE, dotplots are drawn with the same horizontal limits
yranging

a vector with two values giving the horizontal limits. If NULL, horizontal limits are defined by lower and upper values of data
joining

if TRUE, segments join each point to a central value
yjoining

a vector with the central value. If NULL, the central value equals 0
ceti

a character size for editing horizontal limits,
used with par("cex")*ceti
cdot

a character size for plotting the points of the dot plot, used with par("cex")*cdot
csub

a character size for editing the names of variables,
used with par("cex")*csub
f.phylog

a size coefficient for tree size (a parameter to draw the tree in proportion to leaves labels)
...

further arguments passed to or from other methods

Author(s)

Daniel Chessel
Sébastien Ollier [email protected]

See Also

symbols.phylog and table.phylog

Examples

# one variable
tre <- c("((A,B),(C,D));")
phy <- newick2phylog(tre)
x <- 1:4
par(mfrow = c(2,2))
dotchart.phylog(phy, x, scaling = FALSE)
dotchart.phylog(phy, x)
dotchart.phylog(phy, x, joining = FALSE)
dotchart.phylog(phy, x, scaling = FALSE,
 yjoining = 0, yranging = c(-1, 5))
par(mfrow = c(1,1))

# many variables
data(mjrochet)
phy <- newick2phylog(mjrochet$tre)
tab <- data.frame(log(mjrochet$tab))
dotchart.phylog(phy, tab, ceti = 0.5, csub = 0.6,
 cleaves = 0, cdot = 0.6)
par(mfrow=c(1,1))

Representation of n values on a circle

Description

This function represents n values on a circle. The n points are shared out regularly over the circle and put on the radius according to the value attributed to that measure.

Usage

dotcircle(z, alpha0 = pi/2, xlim = range(pretty(z)),
 labels = names(z), clabel = 1, cleg = 1)

Arguments

z

: a numeric vector
alpha0

: polar angle to put the first value
xlim

: the ranges to be encompassed by the circle radius
labels

: a vector of strings of characters for the angle labels
clabel

: a character size for the labels, used with par("cex")*clabel
cleg

: a character size for the ranges, used with par("cex")*cleg

Author(s)

Daniel Chessel

See Also

circ.plot

Examples

w <- scores.neig(neig(n.cir = 24))
par(mfrow = c(4,4))
for (k in 1:16) dotcircle(w[,k],labels = 1:24)
par(mfrow = c(1,1))

Pair of Ecological Tables

Description

This data set gives environmental variables, fish species and spatial coordinates for 30 sites.

Usage

data(doubs)

Format

doubs is a list with 4 components.

env

is a data frame with 30 rows (sites) and 11 environmental variables.

fish

is a data frame with 30 rows (sites) and 27 fish species.

xy

is a data frame with 30 rows (sites) and 2 spatial coordinates.

species

is a data frame with 27 rows (species) and 4 columns (names).

Details

The rows of doubs$env, doubs$fish and doubs$xy are 30 sites along the Doubs, a French and Switzerland river.

doubs$env contains the following variables: dfs - distance from the source (km * 10), alt - altitude (m), slo (ln⁡(x+1)\ln(x + 1) where x is the slope (per mil * 100), flo - minimum average stream flow (m3/s * 100), pH (* 10), har - total hardness of water (mg/l of Calcium), pho - phosphates (mg/l * 100), nit - nitrates (mg/l * 100), amm - ammonia nitrogen (mg/l * 100), oxy - dissolved oxygen (mg/l * 10), bdo - biological demand for oxygen (mg/l * 10).

doubs$fish contains the abundance of the following fish species: Cottus gobio (Cogo), Salmo trutta fario (Satr), Phoxinus phoxinus (Phph), Nemacheilus barbatulus (Neba), Thymallus thymallus (Thth), Telestes soufia agassizi (Teso), Chondrostoma nasus (Chna), Chondostroma toxostoma (Chto), Leuciscus leuciscus (Lele), Leuciscus cephalus cephalus (Lece), Barbus barbus (Baba), Spirlinus bipunctatus (Spbi), Gobio gobio (Gogo), Esox lucius (Eslu), Perca fluviatilis (Pefl), Rhodeus amarus (Rham), Lepomis gibbosus (Legi), Scardinius erythrophtalmus (Scer), Cyprinus carpio (Cyca), Tinca tinca (Titi), Abramis brama (Abbr), Ictalurus melas (Icme), Acerina cernua (Acce), Rutilus rutilus (Ruru), Blicca bjoerkna (Blbj), Alburnus alburnus (Alal), Anguilla anguilla (Anan).

doubs$species contains the names of the 27 fish species. The four columns correspond to: 1 = scientific name (Genus species), 2 = French common name, 3 = English common name, 4 = Four character code.

Source

Verneaux, J. (1973) Cours d'eau de Franche-Comté (Massif du Jura). Recherches écologiques sur le réseau hydrographique du Doubs. Essai de biotypologie. Thèse d'état, Besançon. 1–257.

References

See a French description of fish species at http://pbil.univ-lyon1.fr/R/pdf/pps047.pdf.
Chessel, D., Lebreton, J.D. and Yoccoz, N.G. (1987) Propriétés de l'analyse canonique des correspondances. Une illustration en hydrobiologie. Revue de Statistique Appliquée, 35, 4, 55–72.

Examples

data(doubs)
pca1 <- dudi.pca(doubs$env, scan = FALSE)
pca2 <- dudi.pca(doubs$fish, scale = FALSE, scan = FALSE)
coiner1 <- coinertia(pca1, pca2, scan = FALSE)
  
if(adegraphicsLoaded()) {
  g1 <- s.corcircle(coiner1$aX, plot = FALSE)
  g2 <- s.value(doubs$xy, coiner1$lX[, 1], plot = FALSE)
  g3 <- s.value(doubs$xy, coiner1$lX[, 2], plot = FALSE)
  g4 <- s.arrow(coiner1$c1, plot = FALSE)
  g5 <- s.match(coiner1$mX, coiner1$mY, plot = FALSE)
  g6 <- s.corcircle(coiner1$aY, plot = FALSE)
  g7 <- s.arrow(coiner1$l1, plot = FALSE)
  g8 <- s.value(doubs$xy, coiner1$lY[, 1], plot = FALSE)
  g9 <- s.value(doubs$xy, coiner1$lY[, 2], plot = FALSE)
  G <- ADEgS(list(g1, g2, g3, g4, g5, g6, g7, g8, g9), layout = c(3, 3))
  
} else {  
  par(mfrow = c(3, 3))
  s.corcircle(coiner1$aX)
  s.value(doubs$xy, coiner1$lX[, 1])
  s.value(doubs$xy, coiner1$lX[, 2])
  s.arrow(coiner1$c1)
  s.match(coiner1$mX, coiner1$mY)
  s.corcircle(coiner1$aY)
  s.arrow(coiner1$l1)
  s.value(doubs$xy, coiner1$lY[, 1])
  s.value(doubs$xy, coiner1$lY[, 2])
  par(mfrow = c(1, 1))
}

Double principal coordinate analysis

Description

Performs a double principal coordinate analysis

Usage

dpcoa(df, dis = NULL, scannf = TRUE, nf = 2, full = FALSE, tol = 1e-07,
RaoDecomp = TRUE)
## S3 method for class 'dpcoa'
plot(x, xax = 1, yax = 2, ...)
## S3 method for class 'dpcoa'
 print(x, ...)
## S3 method for class 'dpcoa'
 summary(object, ...)

Arguments

df

a data frame with samples as rows and categories (i.e. species) as columns and abundance or presence-absence as entries. Previous releases of ade4 (<=1.6-2) considered the transposed matrix as argument.
dis

an object of class dist containing the distances between the categories.
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed
RaoDecomp

a logical value indicating whether Rao diversity decomposition should be performed
nf

if scannf is FALSE, an integer indicating the number of kept axes
full

a logical value indicating whether all non null eigenvalues should be kept
tol

a tolerance threshold for null eigenvalues (a value less than tol times the first one is considered as null)
x, object

an object of class dpcoa
xax

the column number for the x-axis
yax

the column number for the y-axis
...

... further arguments passed to or from other methods

Value

Returns a list of class dpcoa containing:

call

call
nf

a numeric value indicating the number of kept axes
dw

a numeric vector containing the weights of the elements (was w1 in previous releases of ade4)
lw

a numeric vector containing the weights of the samples (was w2 in previous releases of ade4)
eig

a numeric vector with all the eigenvalues
RaoDiv

a numeric vector containing diversities within samples
RaoDis

an object of class dist containing the dissimilarities between samples
RaoDecodiv

a data frame with the decomposition of the diversity
dls

a data frame with the coordinates of the elements (was l1 in previous releases of ade4)
li

a data frame with the coordinates of the samples (was l2 in previous releases of ade4)
c1

a data frame with the scores of the principal axes of the elements

Author(s)

Daniel Chessel
Sandrine Pavoine [email protected]
Stéphane Dray [email protected]

References

Pavoine, S., Dufour, A.B. and Chessel, D. (2004) From dissimilarities among species to dissimilarities among communities: a double principal coordinate analysis. Journal of Theoretical Biology, 228, 523–537.

Examples

data(humDNAm)
dpcoahum <- dpcoa(data.frame(t(humDNAm$samples)), sqrt(humDNAm$distances), scan = FALSE, nf = 2)
dpcoahum
if(adegraphicsLoaded()) {
  g1 <- plot(dpcoahum)
} else {
  plot(dpcoahum)
}
  
## Not run: 
data(ecomor)
dtaxo <- dist.taxo(ecomor$taxo)
dpcoaeco <- dpcoa(data.frame(t(ecomor$habitat)), dtaxo, scan = FALSE, nf = 2)
dpcoaeco

if(adegraphicsLoaded()) {
  g1 <- plot(dpcoaeco)
} else {
  plot(dpcoaeco)
}

## End(Not run)

Duality Diagram

Description

as.dudi is called by many functions (dudi.pca, dudi.coa, dudi.acm, ...) and not directly by the user. It creates duality diagrams.

t.dudi returns an object of class 'dudi' where the rows are the columns and the columns are the rows of the initial dudi.

is.dudi returns TRUE if the object is of class dudi

redo.dudi computes again an analysis, eventually changing the number of kept axes. Used by other functions.

Usage

as.dudi(df, col.w, row.w, scannf, nf, call, type, tol = 1e-07, 
    full = FALSE) 
## S3 method for class 'dudi'
print(x, ...) 
is.dudi(x) 
redo.dudi(dudi, newnf = 2) 
## S3 method for class 'dudi'
t(x)
## S3 method for class 'dudi'
summary(object, ...) 
## S3 method for class 'dudi'
x[i,j]

Arguments

df

a data frame with n rows and p columns
col.w

a numeric vector containing the row weights
row.w

a numeric vector containing the column weights
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes
call

generally match.call()
type

a string of characters : the returned list will be of class c(type, "dudi")
tol

a tolerance threshold for null eigenvalues (a value less than tol times the first one is considered as null)
full

a logical value indicating whether all non null eigenvalues should be kept
x, dudi, object

objects of class dudi
...

further arguments passed to or from other methods
newnf

an integer indicating the number of kept axes
i, j

elements to extract (integer or empty): index of rows (i) and columns (j)

Value

as.dudi and all the functions that use it return a list with the following components :

tab

a data frame with n rows and p columns
cw

column weights, a vector with n components
lw

row (lines) weights, a vector with p components
eig

eigenvalues, a vector with min(n,p) components
nf

integer, number of kept axes
c1

principal axes, data frame with p rows and nf columns
l1

principal components, data frame with n rows and nf columns
co

column coordinates, data frame with p rows and nf columns
li

row coordinates, data frame with n rows and nf columns
call

original call

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]
Stéphane Dray [email protected]

References

Escoufier, Y. (1987) The duality diagram : a means of better practical applications In Development in numerical ecology, Legendre, P. & Legendre, L. (Eds.) NATO advanced Institute, Serie G. Springer Verlag, Berlin, 139–156.

Examples

data(deug)
dd1 <- dudi.pca(deug$tab, scannf = FALSE)
dd1
t(dd1)
is.dudi(dd1)
redo.dudi(dd1,3)
summary(dd1)

Multiple Correspondence Analysis

Description

dudi.acm performs the multiple correspondence analysis of a factor table.
acm.burt an utility giving the crossed Burt table of two factors table.
acm.disjonctif an utility giving the complete disjunctive table of a factor table.
boxplot.acm a graphic utility to interpret axes.

Usage

dudi.acm (df, row.w = rep(1, nrow(df)), scannf = TRUE, nf = 2)
acm.burt (df1, df2, counts = rep(1, nrow(df1))) 
acm.disjonctif (df) 
## S3 method for class 'acm'
boxplot(x, xax = 1, ...)

Arguments

df, df1, df2

data frames containing only factors
row.w, counts

vector of row weights, by default, uniform weighting
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes
x

an object of class acm
xax

the number of factor to display
...

further arguments passed to or from other methods

Value

dudi.acm returns a list of class acm and dudi (see dudi) containing

cr

a data frame which rows are the variables, columns are the kept scores and the values are the correlation ratios

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

References

Tenenhaus, M. & Young, F.W. (1985) An analysis and synthesis of multiple correspondence analysis, optimal scaling, dual scaling, homogeneity analysis ans other methods for quantifying categorical multivariate data. Psychometrika, 50, 1, 91-119.

Lebart, L., A. Morineau, and M. Piron. 1995. Statistique exploratoire multidimensionnelle. Dunod, Paris.

See Also

s.chull, s.class

Examples

data(ours)
summary(ours)

if(adegraphicsLoaded()) {
  g1 <- s1d.boxplot(dudi.acm(ours, scan = FALSE)$li[, 1], ours)
} else {
  boxplot(dudi.acm(ours, scan = FALSE))
}
## Not run: 
data(banque)
banque.acm <- dudi.acm(banque, scann = FALSE, nf = 3)

if(adegraphicsLoaded()) {
  g2 <- adegraphics:::scatter.dudi(banque.acm)
} else {
  scatter(banque.acm)
}  

apply(banque.acm$cr, 2, mean)
banque.acm$eig[1:banque.acm$nf] # the same thing

if(adegraphicsLoaded()) {
  g3 <- s1d.boxplot(banque.acm$li[, 1], banque)
  g4 <- scatter(banque.acm)
} else {
  boxplot(banque.acm)
  scatter(banque.acm)
}


s.value(banque.acm$li, banque.acm$li[,3])

bb <- acm.burt(banque, banque)
bbcoa <- dudi.coa(bb, scann = FALSE)
plot(banque.acm$c1[,1], bbcoa$c1[,1])
# mca and coa of Burt table. Lebart & coll. section 1.4

bd <- acm.disjonctif(banque)
bdcoa <- dudi.coa(bd, scann = FALSE)
plot(banque.acm$li[,1], bdcoa$li[,1]) 
# mca and coa of disjonctive table. Lebart & coll. section 1.4
plot(banque.acm$co[,1], dudi.coa(bd, scann = FALSE)$co[,1]) 

## End(Not run)

Correspondence Analysis

Description

performs a correspondence analysis.

Usage

dudi.coa(df, scannf = TRUE, nf = 2)

Arguments

df

a data frame containing positive or null values
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes

Value

returns a list of class coa and dudi (see dudi) containing

N

the sum of all the values of the initial table

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

References

Benzécri, J.P. and Coll. (1973) L'analyse des données. II L'analyse des correspondances, Bordas, Paris. 1–620.

Greenacre, M. J. (1984) Theory and applications of correspondence analysis, Academic Press, London.

Examples

data(rpjdl)
chisq.test(rpjdl$fau)$statistic
rpjdl.coa <- dudi.coa(rpjdl$fau, scannf = FALSE, nf = 4)
sum(rpjdl.coa$eig)*rpjdl.coa$N # the same

if(adegraphicsLoaded()) {
  g1 <- s.label(rpjdl.coa$co, plab.cex = 0.6, lab = rpjdl$frlab, plot = FALSE)
  g2 <- s.label(rpjdl.coa$li, plab.cex = 0.6, plot = FALSE)
  cbindADEg(g1, g2, plot = TRUE)
} else {
  par(mfrow = c(1,2))
  s.label(rpjdl.coa$co, clab = 0.6, lab = rpjdl$frlab)
  s.label(rpjdl.coa$li, clab = 0.6)
  par(mfrow = c(1,1))
}

data(bordeaux)
db <- dudi.coa(bordeaux, scan = FALSE)
db
score(db)

Decentred Correspondence Analysis

Description

performs a decentred correspondence analysis.

Usage

dudi.dec(df, eff, scannf = TRUE, nf = 2)

Arguments

df

a data frame containing positive or null values
eff

a vector containing the reference distribution. Its length is equal to the number of rows of df
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes

Value

Returns a list of class dec and dudi (see dudi) containing also

R

sum of all the values of the initial table

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

References

Dolédec, S., Chessel, D. and Olivier J. M. (1995) L'analyse des correspondances décentrée: application aux peuplements ichtyologiques du haut-Rhône. Bulletin Français de la Pêche et de la Pisciculture, 336, 29–40.

Examples

data(ichtyo)
dudi1 <- dudi.dec(ichtyo$tab, ichtyo$eff, scan = FALSE)
sum(apply(ichtyo$tab, 2, function(x)
    chisq.test(x, p = ichtyo$eff/sum(ichtyo$eff))$statistic))
sum(dudi1$eig) * sum(ichtyo$eff) # the same

s.class(dudi1$li, ichtyo$dat, wt = ichtyo$eff/sum(ichtyo$eff))

Fuzzy Correspondence Analysis and Fuzzy Principal Components Analysis

Description

Theses functions analyse a table of fuzzy variables.

A fuzzy variable takes values of type a=(a1,…,ak)a=(a_1,\dots,a_k) giving the importance of k categories.

A missing data is denoted (0,...,0).
Only the profile a/sum(a) is used, and missing data are replaced by the mean profile of the others in the function prep.fuzzy.var. See ref. for details.

Usage

prep.fuzzy.var (df, col.blocks, row.w = rep(1, nrow(df)))
dudi.fca(df, scannf = TRUE, nf = 2)
dudi.fpca(df, scannf = TRUE, nf = 2)

Arguments

df

a data frame containing positive or null values
col.blocks

a vector containing the number of categories for each fuzzy variable
row.w

a vector of row weights
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes

Value

The function prep.fuzzy.var returns a data frame with the attribute col.blocks. The function dudi.fca returns a list of class fca and dudi (see dudi) containing also

cr

a data frame which rows are the blocs, columns are the kept axes, and values are the correlation ratios.

The function dudi.fpca returns a list of class pca and dudi (see dudi) containing also

  1. cent

  2. norm

  3. blo

  4. indica

  5. FST

  6. inertia

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

References

Chevenet, F., Dolédec, S. and Chessel, D. (1994) A fuzzy coding approach for the analysis of long-term ecological data. Freshwater Biology, 31, 295–309.

Examples

w1 <- matrix(c(1,0,0,2,1,1,0,2,2,0,1,0,1,1,1,0,1,3,1,0), 4, 5)
w1 <- data.frame(w1) 
w2 <- prep.fuzzy.var(w1, c(2, 3))
w1
w2 
attributes(w2)

data(bsetal97)
w <- prep.fuzzy.var(bsetal97$biol, bsetal97$biol.blo)

if(adegraphicsLoaded()) {
  g1 <- plot(dudi.fca(w, scann = FALSE, nf = 3), plabels.cex = 1.5)
} else {
  scatter(dudi.fca(w, scann = FALSE, nf = 3), csub = 3, clab.moda = 1.5)
  scatter(dudi.fpca(w, scann = FALSE, nf = 3), csub = 3, clab.moda = 1.5)
}

## Not run: 
w1 <- prep.fuzzy.var(bsetal97$biol, bsetal97$biol.blo)
w2 <- prep.fuzzy.var(bsetal97$ecol, bsetal97$ecol.blo)
d1 <- dudi.fca(w1, scannf = FALSE, nf = 3)
d2 <- dudi.fca(w2, scannf = FALSE, nf = 3)
plot(coinertia(d1, d2, scannf = FALSE))

## End(Not run)

Ordination of Tables mixing quantitative variables and factors

Description

performs a multivariate analysis with mixed quantitative variables and factors.

Usage

dudi.hillsmith(df, row.w = rep(1, nrow(df))/nrow(df), 
   scannf = TRUE, nf = 2)

Arguments

df

a data frame with mixed type variables (quantitative and factor)

row.w

a vector of row weights, by default uniform row weights are used

scannf

a logical value indicating whether the eigenvalues bar plot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes

Details

If df contains only quantitative variables, this is equivalent to a normed PCA.
If df contains only factors, this is equivalent to a MCA.

This analysis is the Hill and Smith method and is very similar to dudi.mix function. The differences are that dudi.hillsmith allow to use various row weights, while dudi.mix deals with ordered variables.
The principal components of this analysis are centered and normed vectors maximizing the sum of :
squared correlation coefficients with quantitative variables
correlation ratios with factors

Value

Returns a list of class mix and dudi (see dudi) containing also

index

a factor giving the type of each variable : f = factor, q = quantitative
assign

a factor indicating the initial variable for each column of the transformed table
cr

a data frame giving for each variable and each score:
the squared correlation coefficients if it is a quantitative variable
the correlation ratios if it is a factor

Author(s)

Stéphane Dray [email protected]
Anne-Béatrice Dufour [email protected]

References

Hill, M. O., and A. J. E. Smith. 1976. Principal component analysis of taxonomic data with multi-state discrete characters. Taxon, 25, 249-255.

See Also

dudi.mix

Examples

data(dunedata)
attributes(dunedata$envir$use)$class <- "factor"   # use dudi.mix for ordered data
dd1 <- dudi.hillsmith(dunedata$envir, scann = FALSE)
if(adegraphicsLoaded()) {
  g <- scatter(dd1, row.plab.cex = 1, col.plab.cex = 1.5)
} else {
  scatter(dd1, clab.r = 1, clab.c = 1.5)
}

Ordination of Tables mixing quantitative variables and factors

Description

performs a multivariate analysis with mixed quantitative variables and factors.

Usage

dudi.mix(df, add.square = FALSE, scannf = TRUE, nf = 2)

Arguments

df

a data frame with mixed type variables (quantitative, factor and ordered)
add.square

a logical value indicating whether the squares of quantitative variables should be added
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes

Details

If df contains only quantitative variables, this is equivalent to a normed PCA.
If df contains only factors, this is equivalent to a MCA.
Ordered factors are replaced by poly(x,deg=2).

This analysis generalizes the Hill and Smith method.
The principal components of this analysis are centered and normed vectors maximizing the sum of the:
squared correlation coefficients with quantitative variables
squared multiple correlation coefficients with polynoms
correlation ratios with factors.

Value

Returns a list of class mix and dudi (see dudi) containing also

index

a factor giving the type of each variable : f = factor, o = ordered, q = quantitative
assign

a factor indicating the initial variable for each column of the transformed table
cr

a data frame giving for each variable and each score:
the squared correlation coefficients if it is a quantitative variable
the correlation ratios if it is a factor
the squared multiple correlation coefficients if it is ordered

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

References

Hill, M. O., and A. J. E. Smith. 1976. Principal component analysis of taxonomic data with multi-state discrete characters. Taxon, 25, 249-255.

De Leeuw, J., J. van Rijckevorsel, and . 1980. HOMALS and PRINCALS - Some generalizations of principal components analysis. Pages 231-242 in E. Diday and Coll., editors. Data Analysis and Informatics II. Elsevier Science Publisher, North Holland, Amsterdam.

Kiers, H. A. L. 1994. Simple structure in component analysis techniques for mixtures of qualitative ans quantitative variables. Psychometrika, 56, 197-212.

Examples

data(dunedata)
dd1 <- dudi.mix(dunedata$envir, scann = FALSE)
if(adegraphicsLoaded()) {
  g1 <- scatter(dd1, row.plab.cex = 1, col.plab.cex = 1.5)
} else {
  scatter(dd1, clab.r = 1, clab.c = 1.5)
}

dd2 <- dudi.mix(dunedata$envir, scann = FALSE, add.square = TRUE)
if(adegraphicsLoaded()) {
  g2 <- scatter(dd2, row.plab.cex = 1, col.plab.cex = 1.5)
} else {
  scatter(dd2, clab.r = 1, clab.c = 1.5)
}

Non symmetric correspondence analysis

Description

performs a non symmetric correspondence analysis.

Usage

dudi.nsc(df, scannf = TRUE, nf = 2)

Arguments

df

a data frame containing positive or null values
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes

Value

Returns a list of class nsc and dudi (see dudi) containing also

N

sum of the values of the initial table

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

References

Kroonenberg, P. M., and Lombardo R. (1999) Nonsymmetric correspondence analysis: a tool for analysing contingency tables with a dependence structure. Multivariate Behavioral Research, 34, 367–396.

Examples

data(housetasks)
nsc1 <- dudi.nsc(housetasks, scan = FALSE)
if(adegraphicsLoaded()) {
  g1 <- s.label(nsc1$c1, plab.cex = 1.25)
  g2 <- s.arrow(nsc1$li, add = TRUE, plab.cex = 0.75)
} else {
  s.label(nsc1$c1, clab = 1.25)
  s.arrow(nsc1$li, add.pl = TRUE, clab = 0.75) # see ref p.383
}

Principal Component Analysis

Description

dudi.pca performs a principal component analysis of a data frame and returns the results as objects of class pca and dudi.

Usage

dudi.pca(df, row.w = rep(1, nrow(df))/nrow(df), 
    col.w = rep(1, ncol(df)), center = TRUE, scale = TRUE, 
    scannf = TRUE, nf = 2)

Arguments

df

a data frame with n rows (individuals) and p columns (numeric variables)
row.w

an optional row weights (by default, uniform row weights)
col.w

an optional column weights (by default, unit column weights)
center

a logical or numeric value, centring option
if TRUE, centring by the mean
if FALSE no centring
if a numeric vector, its length must be equal to the number of columns of the data frame df and gives the decentring
scale

a logical value indicating whether the column vectors should be normed for the row.w weighting
scannf

a logical value indicating whether the screeplot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes

Value

Returns a list of classes pca and dudi (see dudi) containing the used information for computing the principal component analysis :

tab

the data frame to be analyzed depending of the transformation arguments (center and scale)
cw

the column weights
lw

the row weights
eig

the eigenvalues
rank

the rank of the analyzed matrice
nf

the number of kept factors
c1

the column normed scores i.e. the principal axes
l1

the row normed scores
co

the column coordinates
li

the row coordinates i.e. the principal components
call

the call function
cent

the p vector containing the means for variables (Note that if center = F, the vector contains p 0)
norm

the p vector containing the standard deviations for variables i.e. the root of the sum of squares deviations of the values from their means divided by n (Note that if norm = F, the vector contains p 1)

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

See Also

prcomp, princomp in the mva library

Examples

data(deug)
deug.dudi <- dudi.pca(deug$tab, center = deug$cent, scale = FALSE, scan = FALSE)
deug.dudi1 <- dudi.pca(deug$tab, center = TRUE, scale = TRUE, scan = FALSE)

if(adegraphicsLoaded()) {
  g1 <- s.class(deug.dudi$li, deug$result, plot = FALSE)
  g2 <- s.arrow(deug.dudi$c1, lab = names(deug$tab), plot = FALSE)
  g3 <- s.class(deug.dudi1$li, deug$result, plot = FALSE)
  g4 <- s.corcircle(deug.dudi1$co, lab = names(deug$tab), full = FALSE, plot = FALSE)
  G1 <- rbindADEg(cbindADEg(g1, g2, plot = FALSE), cbindADEg(g3, g4, plot = FALSE), plot = TRUE)
  
  G2 <- s1d.hist(deug.dudi$tab, breaks = seq(-45, 35, by = 5), type = "density", xlim = c(-40, 40), 
    right = FALSE, ylim = c(0, 0.1), porigin.lwd = 2)
    
} else {
  par(mfrow = c(2, 2))
  s.class(deug.dudi$li, deug$result, cpoint = 1)
  s.arrow(deug.dudi$c1, lab = names(deug$tab))
  s.class(deug.dudi1$li, deug$result, cpoint = 1)
  s.corcircle(deug.dudi1$co, lab = names(deug$tab), full = FALSE, box = TRUE)
  par(mfrow = c(1, 1))

  # for interpretations
  par(mfrow = c(3, 3))
  par(mar = c(2.1, 2.1, 2.1, 1.1))
  for(i in 1:9) {
    hist(deug.dudi$tab[,i], xlim = c(-40, 40), breaks = seq(-45, 35, by = 5), 
      prob = TRUE, right = FALSE, main = names(deug$tab)[i], xlab = "", ylim = c(0, 0.10))
  abline(v = 0, lwd = 3)
  }
  par(mfrow = c(1, 1))
}

Principal Coordinates Analysis

Description

dudi.pco performs a principal coordinates analysis of a Euclidean distance matrix and returns the results as objects of class pco and dudi.

Usage

dudi.pco(d, row.w = "uniform", scannf = TRUE, nf = 2, 
    full = FALSE, tol = 1e-07)
## S3 method for class 'pco'
scatter(x, xax = 1, yax = 2, clab.row = 1, posieig = "top", 
    sub = NULL, csub = 2, ...)

Arguments

d

an object of class dist containing a Euclidean distance matrix.
row.w

an optional distance matrix row weights. If not NULL, must be a vector of positive numbers with length equal to the size of the distance matrix
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes
full

a logical value indicating whether all the axes should be kept
tol

a tolerance threshold to test whether the distance matrix is Euclidean : an eigenvalue is considered positive if it is larger than -tol*lambda1 where lambda1 is the largest eigenvalue.



x

an object of class pco
xax

the column number for the x-axis
yax

the column number for the y-axis
clab.row

a character size for the row labels
posieig

if "top" the eigenvalues bar plot is upside, if "bottom" it is downside, if "none" no plot
sub

a string of characters to be inserted as legend
csub

a character size for the legend, used with par("cex")*csub
...

further arguments passed to or from other methods

Value

dudi.pco returns a list of class pco and dudi. See dudi

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

References

Gower, J. C. (1966) Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika, 53, 325–338.

Examples

data(yanomama)
gen <- quasieuclid(as.dist(yanomama$gen))
geo <- quasieuclid(as.dist(yanomama$geo))
ant <- quasieuclid(as.dist(yanomama$ant))
geo1 <- dudi.pco(geo, scann = FALSE, nf = 3)
gen1 <- dudi.pco(gen, scann = FALSE, nf = 3)
ant1 <- dudi.pco(ant, scann = FALSE, nf = 3)
plot(coinertia(ant1, gen1, scann = FALSE))

Dune Meadow Data

Description

dunedata is a data set containing for 20 sites, environmental variables and plant species.

Usage

data(dunedata)

Format

dunedata is a list with 2 components.

envir

is a data frame with 20 rows (sites) 5 columns (environnemental variables).

veg

is a data frame with 20 rows (sites) 30 columns (plant species).

Source

Jongman, R. H., ter Braak, C. J. F. and van Tongeren, O. F. R. (1987) Data analysis in community and landscape ecology, Pudoc, Wageningen.

Examples

data(dunedata)
summary(dunedata$envir)
is.ordered(dunedata$envir$use)
score(dudi.mix(dunedata$envir, scan = FALSE))

Electrocardiogram data

Description

These data were measured during the normal sinus rhythm of a patient who occasionally experiences arrhythmia. There are 2048 observations measured in units of millivolts and collected at a rate of 180 samples per second. This time series is a good candidate for a multiresolution analysis because its components are on different scales. For example, the large scale (low frequency) fluctuations, known as baseline drift, are due to the patient respiration, while the prominent short scale (high frequency) intermittent fluctuations between 3 and 4 seconds are evidently due to patient movement. Heart rhythm determines most of the remaining features in the series. The large spikes occurring about 0.7 seconds apart the R waves of normal heart rhythm; the smaller, but sharp peak coming just prior to an R wave is known as a P wave; and the broader peak that comes after a R wave is a T wave.

Usage

data(ecg)

Format

A vector of class ts containing 2048 observations.

Source

Gust Bardy and Per Reinhall, University of Washington

References

Percival, D. B., and Walden, A.T. (2000) Wavelet Methods for Time Series Analysis, Cambridge University Press.

Examples

## Not run: 
# figure 130 in Percival and Walden (2000)
if (requireNamespace("waveslim") == TRUE) { 
data(ecg)
ecg.level <- haar2level(ecg)
ecg.haar <- orthobasis.haar(length(ecg))
ecg.mld <- mld(ecg, ecg.haar, ecg.level, plot = FALSE)
res <- cbind.data.frame(apply(ecg.mld[,1:5],1,sum), ecg.mld[,6:11])
par(mfrow = c(8,1))
par(mar = c(2, 5, 1.5, 0.6))
plot(as.ts(ecg), ylab = "ECG")
apply(res, 2, function(x) plot(as.ts(x), ylim = range(res),
 ylab = ""))
par(mfrow = c(1,1))
}
## End(Not run)

Ecomorphological Convergence

Description

This data set gives ecomorphological informations about 129 bird species.

Usage

data(ecomor)

Format

ecomor is a list of 7 components.

forsub

is a data frame with 129 species, 6 variables (the feeding place classes): foliage, ground , twig , bush, trunk and aerial feeders. These dummy variables indicate the use (1) or no use (0) of a given feeding place by a species.

diet

is a data frame with 129 species and 8 variables (diet types): Gr (granivorous: seeds), Fr (frugivorous: berries, acorns, drupes), Ne (frugivorous: nectar), Fo (folivorous: leaves), In (invertebrate feeder: insects, spiders, myriapods, isopods, snails, worms), Ca (carnivorous: flesh of small vertebrates), Li (limnivorous: invertebrates in fresh water), and Ch (carrion feeder). These dummy variables indicate the use (1) or no use (0) of a given diet type by a species.

habitat

is a data frame with 129 species, 16 dummy variables (the habitats). These variables indicate the species presence (1) or the species absence (0) in a given habitat.

morpho

is a data frame with 129 species abd 8 morphological variables: wingl (Wing length, mm), taill (Tail length, mm), culml (Culmen length, mm), bilh (Bill height, mm), bilw (Bill width, mm), tarsl (Tarsus length, mm), midtl (Middle toe length, mm) and weig (Weight, g).

taxo

is a data frame with 129 species and 3 factors: Genus, Family and Order. It is a data frame of class 'taxo': the variables are factors giving nested classifications.

labels

is a data frame with vectors of the names of species (complete and in abbreviated form.

categ

is a data frame with 129 species, 2 factors : 'forsub' summarizing the feeding place and 'diet' the diet type.

Source

Blondel, J., Vuilleumier, F., Marcus, L.F., and Terouanne, E. (1984). Is there ecomorphological convergence among mediterranean bird communities of Chile, California, and France. In Evolutionary Biology (eds M.K. Hecht, B. Wallace and R.J. MacIntyre), 141–213, 18. Plenum Press, New York.

References

See a data description at http://pbil.univ-lyon1.fr/R/pdf/pps023.pdf (in French).

Examples

data(ecomor)
ric <- apply(ecomor$habitat, 2, sum)
s.corcircle(dudi.pca(log(ecomor$morpho), scan = FALSE)$co)

forsub <- data.frame(t(apply(ecomor$forsub, 1, function (x) x / sum(x))))
pca1 <- dudi.pca(forsub, scan = FALSE, scale = FALSE)
w1 <- as.matrix(forsub)
if(adegraphicsLoaded()) {
  g1 <- s.arrow(pca1$c1, plot = FALSE)
  g2 <- s.label(w1, plab.cex = 0, ppoi.cex = 2, plot = FALSE)
  G1 <- superpose(g1, g2, plot = TRUE)
} else {
  s.arrow(pca1$c1)
  s.label(w1, clab = 0, add.p = TRUE, cpoi = 2)
}

diet <- data.frame(t(apply(ecomor$diet, 1, function (x) x / sum(x))))
pca2 <- dudi.pca(diet, scan = FALSE, scale = FALSE)
w2 <- as.matrix(diet)
if(adegraphicsLoaded()) {
  g3 <- s.arrow(pca2$c1, plot = FALSE)
  g4 <- s.label(w2, plab.cex = 0, ppoi.cex = 2, plot = FALSE)
  G2 <- superpose(g3, g4, plot = TRUE)
} else {
  s.arrow(pca2$c1)
  s.label(w2, clab = 0, add.p = TRUE, cpoi = 2)
}


## Not run: 
dmorpho <- dist.quant(log(ecomor$morpho), 3)
dhabitat <- dist.binary(ecomor$habitat, 1)
dtaxo <- dist.taxo(ecomor$taxo)

mantel.randtest(dmorpho, dhabitat)
RV.rtest(pcoscaled(dmorpho), pcoscaled(dhabitat), 999)
procuste.randtest(pcoscaled(dmorpho), pcoscaled(dhabitat))

ecophy <- taxo2phylog(ecomor$taxo, add.tools=TRUE)
table.phylog(ecomor$habitat, ecophy, clabel.n = 0.5, f = 0.6,
     clabel.c = 0.75, clabel.r = 0.5, csi = 0.75, cleg = 0)
plot(ecophy, clabel.n = 0.75, clabel.l = 0.75,
     labels.l = ecomor$labels[,"latin"])
mantel.randtest(dmorpho, dtaxo)
mantel.randtest(dhabitat, dtaxo)

## End(Not run)

Electoral Data

Description

This data set gives the results of the presidential election in France in 1988 for each department and all the candidates.

Usage

data(elec88)

Format

elec88 is a list with the following components:

tab

a data frame with 94 rows (departments) and 9 variables (candidates)

res

the global result of the election all-over the country

lab

a data frame with two variables: elec88$lab$dep is a vector containing the names of the 94 french departments, elec88$lab$reg is a vector containing the names of the 21 French administrative regions.

area

the data frame of 3 variables returning the boundary lines of each department. The first variable is a factor. The levels of this one are the row.names of tab. The second and third variables return the coordinates (x, y) of the points of the boundary line.

contour

a data frame with 4 variables (x1, y1, x2, y2) for the contour display of France

xy

a data frame with two variables (x, y) giving the position of the center for each department

neig

the neighbouring graph between departments, object of the class neig

nb

the neighbouring graph between departments, object of the class nb

Spatial

the map of the french departments in Lambert II coordinates (an object of the class SpatialPolygons of sp)

Spatial.contour

the contour of the map of France in Lambert II coordinates (an object of the class SpatialPolygons of sp)

Source

Public data

See Also

This dataset is compatible with presid2002 and cnc2003

Examples

data(elec88)
apply(elec88$tab, 2, mean)
summary(elec88$res)
pca1 <- dudi.pca(elec88$tab, scale = FALSE, scannf = FALSE)

if(adegraphicsLoaded()) {
  if(requireNamespace("sp", quietly = TRUE)) {
    data1 <- as.data.frame(as.numeric(rownames(elec88$tab) == "D25"))
    rownames(data1) <- row.names(elec88$Spatial)
    obj1 <- sp::SpatialPolygonsDataFrame(Sr = elec88$Spatial, data = data1)
    g1 <- s.Spatial(obj1, psub.text = "", plot = FALSE)
    g2 <- s.Spatial(obj1, psub.text = "", nb = elec88$nb, pnb.node.cex = 0, plot = FALSE)

    data3 <- as.data.frame(elec88$xy[, 1] + elec88$xy[, 2])
    rownames(data3) <- row.names(elec88$Spatial)
    obj3 <- sp::SpatialPolygonsDataFrame(Sr = elec88$Spatial, data = data3)
    g3 <- s.Spatial(obj3, psub.text = "", plot = FALSE)
    
    data4 <- as.data.frame(pca1$li[, 1])
    rownames(data4) <- row.names(elec88$Spatial)
    obj4 <- sp::SpatialPolygonsDataFrame(Sr = elec88$Spatial, data = data4)
    g4 <- s.Spatial(obj4, psub.text = "F1 PCA", plot = FALSE)
    
    G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))
  }
  
} else {
  par(mfrow = c(2, 2))
  plot(elec88$area[, 2:3], type = "n", asp = 1)
  lpoly <- split(elec88$area[, 2:3], elec88$area[, 1])
  lapply(lpoly, function(x) {points(x, type = "l"); invisible()})
  polygon(elec88$area[elec88$area$V1 == "D25", 2:3], col = 1)
  area.plot(elec88$area, graph = elec88$neig, lwdg = 1)
  polygon(elec88$area[elec88$area$V1 == "D25", 2:3], col = 1)
  area.plot(elec88$area, val = elec88$xy[, 1] + elec88$xy[, 2])
  area.plot(elec88$area, val = pca1$li[, 1], sub = "F1 PCA", 
    csub = 2, cleg = 1.5)
  par(mfrow = c(1, 1))
}

K-tables of wine-tasting

Description

This data set describes 27 characteristics of 21 wines distributed in four fields : rest, visual, olfactory and global.

Usage

data(escopage)

Format

escopage is a list of 3 components.

tab

is a data frame with 21 observations (wines) and 27 variables.

tab.names

is the vector of the names of sub-tables : "rest" "visual" "olfactory" "global".

blo

is a vector of the numbers of variables for each sub-table.

Source

Escofier, B. and Pagès, J. (1990) Analyses factorielles simples et multiples : objectifs, méthodes et interprétation Dunod, Paris. 1–267.

Escofier, B. and Pagès, J. (1994) Multiple factor analysis (AFMULT package). Computational Statistics and Data Analysis, 18, 121–140.

Examples

data(escopage)
w <- data.frame(scale(escopage$tab))
w <- ktab.data.frame(w, escopage$blo)
names(w)[1:4] <- escopage$tab.names
plot(mfa(w, scan = FALSE))

Triangular Data

Description

This data set gives the proportions of employement in the primary, secondary and tertiary sectors for 12 European countries in 1978, 1986 and 1997.

Usage

data(euro123)

Format

euro123 is a list of 4 components.

in78

is a data frame with 12 rows and 3 variables.

in86

: idem in 1986

in97

: idem in 1997

plan

is a data frame with two factors to both organize the 3 tables.

Source

Encyclopaedia Universalis, Symposium, Les chiffres du Monde. Encyclopaedia Universalis, Paris. 519.

Examples

data(euro123)

if(adegraphicsLoaded()) {
  g1 <- triangle.label(euro123$in78, addaxes = TRUE, plabels.cex = 0, 
    plot = FALSE)
  g2 <- triangle.label(euro123$in86, addaxes = TRUE, plabels.cex = 0, 
    plot = FALSE)
  g3 <- triangle.label(euro123$in97, addaxes = TRUE, plabels.cex = 0, 
    plot = FALSE)
  g4 <- triangle.match(euro123$in78, euro123$in97, plot = FALSE)
  G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))
  
} else {
  par(mfrow = c(2,2))
  triangle.plot(euro123$in78, addaxes = TRUE)
  triangle.plot(euro123$in86, addaxes = TRUE)
  triangle.plot(euro123$in97, addaxes = TRUE)
  triangle.biplot(euro123$in78, euro123$in97)
  par(mfrow = c(1,1))
}

Fission pattern and heritable morphological traits

Description

This data set contains the mean values of five highly heritable linear combinations of cranial metric (GM1-GM3) and non metric (GN1-GN2) for 8 social groups of Rhesus Macaques on Cayo Santiago. It also describes the fission tree depicting the historical phyletic relationships.

Usage

data(fission)

Format

fission is a list containing the 2 following objects :

tre

is a character string giving the fission tree in Newick format.

tab

is a data frame with 8 social groups and five traits : cranial metrics (GM1, GM2, GM3) and cranial non metrics (GN1, GN2)

References

Cheverud, J. and Dow, M.M. (1985) An autocorrelation analysis of genetic variation due to lineal fission in social groups of rhesus macaques. American Journal of Physical Anthropology, 67, 113–122.

Examples

data(fission)
fis.phy <- newick2phylog(fission$tre)
table.phylog(fission$tab[names(fis.phy$leaves),], fis.phy, csi = 2)
gearymoran(fis.phy$Amat, fission$tab)

K-tables Correspondence Analysis with the same rows and the same columns

Description

K tables have the same rows and the same columns.
Each table is transformed by P = X/sum(X). The average of P is computing.
A correspondence analysis is realized on this average.
The initial rows and the initial columns are projected in supplementary elements.

Usage

foucart(X, scannf = TRUE, nf = 2)
## S3 method for class 'foucart'
plot(x, xax = 1, yax = 2, clab = 1, csub = 2, 
    possub = "bottomright", ...) 
## S3 method for class 'foucart'
print(x, ...)

Arguments

X

a list of data frame where the row names and the column names are the same for each table
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes


x

an object of class 'foucart'
xax

the column number of the x-axis
yax

the column number of the y-axis
clab

if not NULL, a character size for the labels, used with par("cex")*clab
csub

a character size for the legend, used with par("cex")*csub
possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")
...

further arguments passed to or from other methods

Value

foucart returns a list of the classes 'dudi', 'coa' and 'foucart'

call

origine
nf

axes-components saved
rank

rank
blo

useful vector
cw

vector: column weights
lw

vector: row weights
eig

vector: eigen values
tab

data.frame: modified array
li

data.frame: row coordinates
l1

data.frame: row normed scores
co

data.frame: column coordinates
c1

data.frame: column normed scores
Tli

data.frame: row coordinates (each table)
Tco

data.frame: col coordinates (each table)
TL

data.frame: factors for Tli
TC

data.frame: factors for Tco

Author(s)

Pierre Bady [email protected]
Anne-Béatrice Dufour [email protected]

References

Foucart, T. (1984) Analyse factorielle de tableaux multiples, Masson, Paris.

Examples

data(bf88)
fou1 <- foucart(bf88, scann = FALSE, nf = 3)
fou1
plot(fou1)

data(meaudret)
l1 <- split(meaudret$spe, meaudret$design$season)
l1 <- lapply(l1, function(x) 
    {row.names(x) <- paste("Sit",1:5,sep="");x})
fou2 <- foucart(l1, scan = FALSE)

if(adegraphicsLoaded()) {
  kplot(fou2, row.plabels.cex = 2)
} else {
  kplot(fou2, clab.r = 2)
}

Functions to compute the fourth-corner statistic

Description

These functions allow to compute the fourth-corner statistic for abundance or presence-absence data. The fourth-corner statistic has been developed by Legendre et al (1997) and extended in Dray and Legendre (2008). The statistic measures the link between three tables: a table L (n x p) containing the abundances of p species at n sites, a second table R (n x m) containing the measurements of m environmental variables for the n sites, and a third table Q (p x s) describing s species traits for the p species.

Usage

fourthcorner(tabR, tabL, tabQ, modeltype = 6, nrepet = 999, tr01 =
FALSE, p.adjust.method.G = p.adjust.methods, p.adjust.method.D =
p.adjust.methods, p.adjust.D = c("global", "levels"), ...)
fourthcorner2(tabR, tabL, tabQ, modeltype = 6, nrepet = 999, tr01 =
FALSE, p.adjust.method.G = p.adjust.methods, ...)
## S3 method for class '4thcorner'
print(x, varQ = 1:length(x$varnames.Q), varR =
1:length(x$varnames.R), stat = c("D", "D2"), ...)
## S3 method for class '4thcorner'
summary(object,...)
## S3 method for class '4thcorner'
plot(x, stat = c("D", "D2", "G"), type = c("table",
"biplot"), xax = 1, yax = 2, x.rlq = NULL, alpha = 0.05, col =
c("lightgrey", "red", "deepskyblue", "purple"), ...)
fourthcorner.rlq(xtest, nrepet = 999, modeltype = 6, typetest =
c("axes", "Q.axes", "R.axes"), p.adjust.method.G = p.adjust.methods,
p.adjust.method.D = p.adjust.methods, p.adjust.D = c("global",
"levels"), ...)

Arguments

tabR

a dataframe containing the measurements (numeric values or factors) of m environmental variables (columns) for the n sites (rows).
tabL

a dataframe containing the abundances of p species (columns) at n sites (rows).
tabQ

a dataframe containing numeric values or factors describing s species traits (columns) for the p species (rows).
modeltype

an integer (1-6) indicating the permutation model used in the testing procedure (see details).

nrepet

the number of permutations

tr01

a logical indicating if data in tabL must be transformed to presence-absence data (FALSE by default)
object

an object of the class 4thcorner
x

an object of the class 4thcorner
varR

a vector containing indices for variables in tabR
varQ

a vector containing indices for variables in tabQ
type

results are represented by a table or on a biplot (see x.rlq)
alpha

a value of significance level
p.adjust.method.G

a string indicating a method for multiple adjustment used for output tabG, see p.adjust.methods for possible choices
p.adjust.method.D

a string indicating a method for multiple adjustment used for output tabD/tabD2, see p.adjust.methods for possible choices
p.adjust.D

a string indicating if multiple adjustment for tabD/tabD2 should be done globally or only between levels of a factor ("levels", as in the original paper of Legendre et al. 1997)
stat

a character to specify if results should be plotted for cells (D and D2) or variables (G)
xax

an integer indicating which rlq axis should be plotted on the x-axis
yax

an integer indicating which rlq axis should be plotted on the y-axis
x.rlq

an object created by the rlq function. Used to represent results on a biplot (type should be "biplot" and object created by the fourthcorner functions)
col

a vector of length 4 containing four colors used for the graphical representations. The first is used to represent non-significant associations, the second positive significant, the third negative significant. For the 'biplot' method and objects created by the fourthcorner.rlq function, the second corresponds to variables significantly linked to the x-axis, the third for the y-axis and the fourth for both axes
xtest

an object created by the rlq function
typetest

a string indicating which tests should be performed
...

further arguments passed to or from other methods

Details

For the fourthcorner function, the link is measured by a Pearson correlation coefficient for two quantitative variables (trait and environmental variable), by a Pearson Chi2 and G statistic for two qualitative variables and by a Pseudo-F and Pearson r for one quantitative variable and one qualitative variable. The fourthcorner2 function offers a multivariate statistic (equal to the sum of eigenvalues of RLQ analysis) and measures the link between two variables by a square correlation coefficient (quant/quant), a Chi2/sum(L) (qual/qual) and a correlation ratio (quant/qual). The significance is tested by a permutation procedure. Different models are available:

  • model 1 (modeltype=1): Permute values for each species independently (i.e., permute within each column of table L)

  • model 2 (modeltype=2): Permute values of sites (i.e., permute entire rows of table L)

  • model 3 (modeltype=3): Permute values for each site independently (i.e., permute within each row of table L)

  • model 4 (modeltype=4): Permute values of species (i.e., permute entire columns of table L)

  • model 5 (modeltype=5): Permute values of species and after (or before) permute values of sites (i.e., permute entire columns and after (or before) entire rows of table L)

  • model 6 (modeltype=6): combination of the outputs of models 2 and 4. Dray and Legendre (2008) and ter Braak et al. (20012) showed that all models (except model 6) have inflated type I error.

Note that the model 5 is strictly equivalent to permuting simultaneously the rows of tables R and Q, as proposed by Doledec et al. (1996).

The function summary returns results for variables (G). The function print returns results for cells (D and D2). In the case of qualitative variables, Holm's corrected pvalues are also provided.

The function plot produces a graphical representation of the results (white for non significant, light grey for negative significant and dark grey for positive significant relationships). Results can be plotted for variables (G) or for cells (D and D2). In the case of qualitative / quantitative association, homogeneity (D) or correlation (D2) are plotted.

Value

The fourthcorner function returns a a list where:

tabD is a krandtest object giving the results of tests for cells of the fourth-corner (homogeneity for quant./qual.). tabD2 is a krandtest object giving the results of tests for cells of the fourth-corner (Pearson r for quant./qual.). tabG is a krandtest object giving the results of tests for variables (Pearson's Chi2 for qual./qual.).

The fourthcorner2 function returns a list where:

tabG is a krandtest object giving the results of tests for variables. trRLQ is a krandtest object giving the results of tests for the multivariate statistic (i.e. equivalent to randtest.rlq function).

Author(s)

Stéphane Dray [email protected]

References

Doledec, S., Chessel, D., ter Braak, C.J.F. and Champely, S. (1996) Matching species traits to environmental variables: a new three-table ordination method. Environmental and Ecological Statistics, 3, 143–166.

Legendre, P., R. Galzin, and M. L. Harmelin-Vivien. (1997) Relating behavior to habitat: solutions to the fourth-corner problem. Ecology, 78, 547–562.

Dray, S. and Legendre, P. (2008) Testing the species traits-environment relationships: the fourth-corner problem revisited. Ecology, 89, 3400–3412.

ter Braak, C., Cormont, A., and Dray, S. (2012) Improved testing of species traits-environment relationships in the fourth corner problem. Ecology, 93, 1525–1526.

Dray, S., Choler, P., Doledec, S., Peres-Neto, P.R., Thuiller, W., Pavoine, S. and ter Braak, C.J.F (2014) Combining the fourth-corner and the RLQ methods for assessing trait responses to environmental variation. Ecology, 95, 14–21. doi:10.1890/13-0196.1

See Also

rlq, combine.4thcorner, p.adjust.methods

Examples

data(aviurba)

## Version using the sequential test (ter Braak et al 2012)
## as recommended in Dray et al (2013), 
## using Holm correction of P-values (only 99 permutations here)
four.comb.default <- fourthcorner(aviurba$mil,aviurba$fau,aviurba$traits,nrepet=99)
summary(four.comb.default)
plot(four.comb.default, stat = "G")

## using fdr correction of P-values
four.comb.fdr <- fourthcorner(aviurba$mil, aviurba$fau, aviurba$traits,
nrepet = 99, p.adjust.method.G = 'fdr', p.adjust.method.D = 'fdr')  
summary(four.comb.fdr)
plot(four.comb.fdr, stat = "G")

## Explicit procedure to combine the results of two models
## proposed in Dray and Legendre (2008);the above does this implicitly
four2 <- fourthcorner(aviurba$mil,aviurba$fau,aviurba$traits,nrepet=99,modeltype=2)
four4 <- fourthcorner(aviurba$mil,aviurba$fau,aviurba$traits,nrepet=99,modeltype=4)
four.comb <- combine.4thcorner(four2, four4)
summary(four.comb)
plot(four.comb, stat = "G")

Faunistic K-tables

Description

This data set gives informations about sites, species and environmental variables.

Usage

data(friday87)

Format

friday87 is a list of 4 components.

fau

is a data frame containing a faunistic table with 16 sites and 91 species.

mil

is a data frame with 16 sites and 11 environmental variables.

fau.blo

is a vector of the number of species per group.

tab.names

is the name of each group of species.

Source

Friday, L.E. (1987) The diversity of macroinvertebrate and macrophyte communities in ponds, Freshwater Biology, 18, 87–104.

Examples

data(friday87)
wfri <- data.frame(scale(friday87$fau, scal = FALSE))
wfri <- ktab.data.frame(wfri, friday87$fau.blo, 
    tabnames = friday87$tab.names)

if(adegraphicsLoaded()) {    
  g1 <- kplot(sepan(wfri), row.plabels.cex = 2)
} else {
  kplot(sepan(wfri), clab.r = 2, clab.c = 1)
}

Pair of Tables

Description

28 batches of fruits -two types- are judged by two different ways.
They are classified in order of preference, without ex aequo, by 16 individuals.
15 quantitative variables described the batches of fruits.

Usage

data(fruits)

Format

fruits is a list of 3 components:

typ

is a vector returning the type of the 28 batches of fruits (peaches or nectarines).

jug

is a data frame of 28 rows and 16 columns (judges).

var

is a data frame of 28 rows and 16 measures (average of 2 judgements).

Details

fruits$var is a data frame of 15 variables:

  1. taches: quantity of cork blemishes (0=absent - maximum 5)

  2. stries: quantity of stria (1/none - maximum 4)

  3. abmucr: abundance of mucron (1/absent - 4)

  4. irform: shape irregularity (0/none - 3)

  5. allong: length of the fruit (1/round fruit - 4)

  6. suroug: percentage of the red surface (minimum 40% - maximum 90%)

  7. homlot: homogeneity of the intra-batch coloring (1/strong - 4)

  8. homfru: homogeneity of the intra-fruit coloring (1/strong - 4)

  9. pubesc: pubescence (0/none - 4)

  10. verrou: intensity of green in red area (1/none - 4)

  11. foncee: intensity of dark area (0/pink - 4)

  12. comucr: intensity of the mucron color (1=no contrast - 4/dark)

  13. impres: kind of impression (1/watched - 4/pointillé)

  14. coldom: intensity of the predominating color (0/clear - 4)

  15. calibr: grade (1/<90g - 5/>200g)

Source

Kervella, J. (1991) Analyse de l'attrait d'un produit : exemple d'une comparaison de lots de pêches. Agro-Industrie et méthodes statistiques. Compte-rendu des secondes journées européennes. Nantes 13-14 juin 1991. Association pour la Statistique et ses Utilisations, Paris, 313–325.

Examples

data(fruits)
pcajug <- dudi.pca(fruits$jug, scann = FALSE)
pcavar <- dudi.pca(fruits$var, scann = FALSE)

if(adegraphicsLoaded()) {
  g1 <- s.corcircle(pcajug$co, plot = FALSE)
  g2 <- s.class(pcajug$li, fac = fruits$type, plot = FALSE)
  g3 <- s.corcircle(pcavar$co, plot = FALSE)
  g4 <- s.class(pcavar$li, fac = fruits$type, plot = FALSE)
  
  G1 <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))
  G2 <- plot(coinertia(pcajug, pcavar, scan = FALSE))

} else {
  par(mfrow = c(2,2)) 
  s.corcircle(pcajug$co)
  s.class(pcajug$li, fac = fruits$type)
  s.corcircle(pcavar$co)
  s.class(pcavar$li, fac = fruits$type)
  
  par(mfrow = c(1,1))
  plot(coinertia(pcajug, pcavar, scan = FALSE))
}

Moran's I and Geary'c randomization tests for spatial and phylogenetic autocorrelation

Description

This function performs Moran's I test using phylogenetic and spatial link matrix (binary or general). It uses neighbouring weights so Moran's I and Geary's c randomization tests are equivalent.

Usage

gearymoran(bilis, X, nrepet = 999, alter=c("greater", "less", "two-sided"))

Arguments

bilis

: a n by n link matrix where n is the row number of X
X

: a data frame with continuous variables
nrepet

: number of random vectors for the randomization test
alter

a character string specifying the alternative hypothesis, must be one of "greater" (default), "less" or "two-sided"

Details

bilis is a squared symmetric matrix which terms are all positive or null.

bilis is firstly transformed in frequency matrix A by dividing it by the total sum of data matrix :

aij=bilisij∑i=1n∑j=1nbilisija_{ij} = \frac{bilis_{ij}}{\sum_{i=1}^{n}\sum_{j=1}^{n}bilis_{ij}}

The neighbouring weights is defined by the matrix D=diag(d1,d2,…)D = diag(d_1,d_2, \ldots) where di=∑j=1nbilisijd_i = \sum_{j=1}^{n}bilis_{ij}. For each vector x of the data frame X, the test is based on the Moran statistic xtAxx^{t}Ax where x is D-centred.

Value

Returns an object of class krandtest (randomization tests).

Author(s)

Sébastien Ollier [email protected]
Daniel Chessel

References

Cliff, A. D. and Ord, J. K. (1973) Spatial autocorrelation, Pion, London.

Thioulouse, J., Chessel, D. and Champely, S. (1995) Multivariate analysis of spatial patterns: a unified approach to local and global structures. Environmental and Ecological Statistics, 2, 1–14.

See Also

moran.test and geary.test for classical versions of Moran's test and Geary's one

Examples

# a spatial example
data(mafragh)
tab0 <- (as.data.frame(scalewt(mafragh$env)))
bilis0 <- neig2mat(mafragh$neig)
gm0 <- gearymoran(bilis0, tab0, 999)
gm0
plot(gm0, nclass = 20)

## Not run: 
# a phylogenetic example
data(mjrochet)
mjr.phy <- newick2phylog(mjrochet$tre)
mjr.tab <- log(mjrochet$tab)
gearymoran(mjr.phy$Amat, mjr.tab)
gearymoran(mjr.phy$Wmat, mjr.tab)

if(adegraphicsLoaded()) {
  g1 <- table.value(mjr.phy$Wmat, ppoints.cex = 0.35, nclass = 5,
    axis.text = list(cex = 0), plot = FALSE)
  g2 <- table.value(mjr.phy$Amat, ppoints.cex = 0.35, nclass = 5,
    axis.text = list(cex = 0), plot = FALSE)
  G <- cbindADEg(g1, g2, plot = TRUE)
  
} else {
  par(mfrow = c(1, 2))
  table.value(mjr.phy$Wmat, csi = 0.25, clabel.r = 0)
  table.value(mjr.phy$Amat, csi = 0.35, clabel.r = 0)
  par(mfrow = c(1, 1))
}

## End(Not run)

Microsatellites of Galapagos tortoises populations

Description

This data set gives genetic relationships between Galapagos tortoises populations with 10 microsatellites.

Usage

data(ggtortoises)

Format

ggtortoises is a list with the following components:

area

a data frame designed to be used in the area.plot function

ico

a list of three pixmap icons representing the tortoises morphotypes

pop

a data frame containing meta informations about populations

misc

a data frame containing the coordinates of the island labels

loc

a numeric vector giving the number of alleles by marker

tab

a data frame containing the number of alleles by populations for 10 microsatellites

Spatial

an object of the class SpatialPolygons of sp, containing the map

Source

M.C. Ciofi, C. Milinkovitch, J.P. Gibbs, A. Caccone, and J.R. Powell (2002) Microsatellite analysis of genetic divergence among populations of giant galapagos tortoises. Molecular Ecology 11: 2265-2283.

References

M.C. Ciofi, C. Milinkovitch, J.P. Gibbs, A. Caccone, and J.R. Powell (2002). Microsatellite analysis of genetic divergence among populations of giant galapagos tortoises. Molecular Ecology 11: 2265-2283.

See a data description at http://pbil.univ-lyon1.fr/R/pdf/pps069.pdf (in French).

Examples

if(requireNamespace("pixmap", quietly=TRUE)) {
  data(ggtortoises)
  
  if(adegraphicsLoaded()) {
    if(requireNamespace("sp", quietly = TRUE)) {
      g1 <- s.logo(ggtortoises$pop, ggtortoises$ico[as.character(ggtortoises$pop$carap)], 
        Sp = ggtortoises$Spatial, pbackground.col = "lightblue", pSp.col = "white", 
        pgrid.draw = FALSE, ppoints.cex = 0.5)
      g1 <- s.label(ggtortoises$misc, pgrid.draw = FALSE, porigin.include = FALSE, 
        paxes.draw = FALSE, add = TRUE)
    }

  } else {    
  	a1 <- ggtortoises$area
  	area.plot(a1)
  	rect(min(a1$x), min(a1$y), max(a1$x), max(a1$y), col = "lightblue")
  	invisible(lapply(split(a1, a1$id), function(x) polygon(x[, -1], col = "white")))
  	s.label(ggtortoises$misc, grid = FALSE, include.ori = FALSE, addaxes = FALSE, add.p = TRUE)
  	listico <- ggtortoises$ico[as.character(ggtortoises$pop$carap)]
  	s.logo(ggtortoises$pop, listico, add.p = TRUE)
  }
}

Granulometric Curves

Description

This data set gives the repartition in diameter classes of deposit samples.

Usage

data(granulo)

Format

granulo is a list of 2 components.

tab

contains the 49 deposit samples, 9 diameter classes, weight of grains by size class

born

contains the boundaries of the diameter classes

Source

Gaschignard-Fossati, O. (1986) Répartition spatiale des macroinvertébrés benthiques d'un bras vif du Rhône. Rôle des crues et dynamique saisonnière. Thèse de doctorat, Université Lyon 1.

Examples

data(granulo)
w <- t(apply(granulo$tab, 1, function (x) x / sum(x)))
w <- data.frame(w)
wtr <- data.frame(t(w))
wmoy <- data.frame(matrix(apply(wtr, 1, mean), 1))
d1 <- dudi.pca(w, scal = FALSE, scan = FALSE)
wmoy <- suprow(d1, wmoy)$lisup

if(adegraphicsLoaded()) {
  s.arrow(d1$c1, plab.cex = 1.5)
  s.distri(d1$c1, wtr, starSize = 0.33, ellipseSize = 0, 
    add = TRUE, plab.cex = 0.75)
  s.label(wmoy, ppoints.cex = 5, plab.cex = 0, add = TRUE)
} else {
  
  s.arrow(d1$c1, clab = 1.5)
  s.distri(d1$c1, wtr, cstar = 0.33, cell = 0, 
    axesell = FALSE, add.p = TRUE, clab = 0.75)
  s.label(wmoy, cpoi = 5, clab = 0, add.p = TRUE)
}

Complete regular grid analysis

Description

This function defines objects to analyse data sets associated with complete regular grid.

Usage

gridrowcol(nrow, ncol, cell.names = NULL)

Arguments

nrow

size of the grid (number of rows)
ncol

size of the grid (number of columns)
cell.names

grid cell labels

Value

Returns a list containing the following items :

xy

: a data frame with grid cell coordinates
area

: a data frame with three variables to display grid cells as areas
neig

: an object of class 'neig' corresponding to a neighbouring graph of the grid (rook case)
orthobasis

: an object of class 'orthobasis' corresponding to the analytical solution for the neighbouring graph

Author(s)

Sébastien Ollier [email protected]
Daniel Chessel

References

Méot, A., Chessel, D. and Sabatier, D. (1993) Opérateurs de voisinage et analyse des données spatio-temporelles. in J.D. Lebreton and B. Asselain, editors. Biométrie et environnement. Masson, 45-72.

Cornillon, P.A. (1998) Prise en compte de proximités en analyse factorielle et comparative. Thèse, Ecole Nationale Supérieure Agronomique, Montpellier.

See Also

orthobasis, orthogram, mld

Examples

w <- gridrowcol(8, 5)
par(mfrow = c(1, 2))
area.plot(w$area, center = w$xy, graph = w$neig, clab = 0.75)
area.plot(w$area, center = w$xy, graph = w$neig, clab = 0.75, label = as.character(1:40))
par(mfrow = c(1, 1))

if(adegraphicsLoaded()) {
  fac1 <- w$orthobasis
  names(fac1) <- as.character(signif(attr(w$orthobasis, "values"), 3))
  s.value(w$xy, fac1, porigin.include = FALSE, plegend.drawKey = FALSE, pgrid.text.cex = 0,
    ylim = c(0, 10))

} else {
  par(mfrow = c(5,8))
  for(k in 1:39)
    s.value(w$xy, w$orthobasis[, k], csi = 3, cleg = 0, csub = 2,
     sub = as.character(signif(attr(w$orthobasis, "values")[k], 3)),
      incl = FALSE, addax = FALSE, cgr = 0, ylim = c(0,10))
  par(mfrow = c(1,1))
}

Genetic Variation In Human Populations

Description

This data set gives genotypes variation of 1066 individuals belonging to 52 predefined populations, for 404 microsatellite markers.

Usage

data(hdpg)

Format

hdpg is a list of 3 components.

tab

is a data frame with the genotypes of 1066 individuals encoded with 6 characters (individuals in row, locus in column), for example ‘123098’ for a heterozygote carrying alleles ‘123’ and ‘098’, ‘123123’ for a homozygote carrying two alleles ‘123’ and, ‘000000’ for a not classified locus (missing data).

ind

is a a data frame with 4 columns containing information about the 1066 individuals: hdpg$ind$id containing the Diversity Panel identification number of each individual, and three factors hdpg$ind$sex, hdpg$ind$population and hdpg$ind$region containing the names of the 52 populations belonging to 7 major geographic regions (see details).

locus

is a dataframe containing four columns: hdpg$locus$marknames a vector of names of the microsatellite markers, hdpg$locus$allbyloc a vector containing the number of alleles by loci, hdpg$locus$chromosome a factor defining a number for one chromosome and, hdpg$locus$maposition indicating the position of the locus in the chromosome.

Details

The rows of hdpg$pop are the names of the 52 populations belonging to the geographic regions contained in the rows of hdpg$region. The chosen regions are: America, Asia, Europe, Middle East North Africa, Oceania, Subsaharan AFRICA.

The 52 populations are: Adygei, Balochi, Bantu, Basque, Bedouin, Bergamo, Biaka Pygmies, Brahui, Burusho, Cambodian, Columbian, Dai, Daur, Druze, French, Han, Hazara, Hezhen, Japanese, Kalash, Karitiana, Lahu, Makrani, Mandenka, Maya, Mbuti Pygmies, Melanesian, Miaozu, Mongola, Mozabite, Naxi, NewGuinea, Nilote, Orcadian, Oroqen, Palestinian, Pathan, Pima, Russian, San, Sardinian, She, Sindhi, Surui, Tu, Tujia, Tuscan, Uygur, Xibo, Yakut, Yizu, Yoruba.

hdpg$freq is a data frame with 52 rows, corresponding to the 52 populations described above, and 4992 microsatellite markers.

Source

Extract of data prepared by the Human Diversity Panel Genotypes (invalid http://research.marshfieldclinic.org/genetics/Freq/FreqInfo.htm)

prepared by Hinda Haned, from data used in: Noah A. Rosenberg, Jonatahan K. Pritchard, James L. Weber, Howard M. Cabb, Kenneth K. Kidds, Lev A. Zhivotovsky, Marcus W. Feldman (2002) Genetic Structure of human Populations Science, 298, 2381–2385.

Lev A. Zhivotovsky, Noah Rosenberg, and Marcus W. Feldman (2003). Features of Evolution and Expansion of Modern Humans, Inferred from Genomewide Microsatellite Markers Am. J. Hum. Genet, 72, 1171–1186.

Examples

data(hdpg)
names(hdpg)
str(hdpg)

Morphometric data set

Description

Morphometric data set describing the shape of the first upper molar in populations of the Western European house mouse (Mus musculus domesticus)

Usage

data(houmousr)

Format

houmousr is a list with 2 components.

dfcc

is a data frame with 214 rows (mice) and 128 morphometric variables.

faccc

is a factor giving the sampling location of the 214 mice.

Details

The rows of houmousr$dfcc correspond to 214 mice sampled in five locations in France and Italy. The 128 columns are 128 aligned coordinates describing the shape of the occlusal surface of the first upper molar (UM1).

houmousr$faccc is a factor giving the location where mice were sampled: Montpellier, Frontignan, Gardouch (South of France), Lombardy (Northern Italy), and Corsica.

Source

Thioulouse, J., Renaud, S., Dufour, AB. et al. Overcoming the Spurious Groups Problem in Between-Group PCA. Evol Biol (2021). https://doi.org/10.1007/s11692-021-09550-0

References

Renaud S, Pantalacci S, Auffray J (2011) Differential evolvability along lines of least resistance of upper and lower molars in island house mice. PLoS ONE 6, https://doi.org/10.1371/journal.pone.0018951

Renaud S, Dufour A, Hardouin E, Ledevin R, Auffray J (2015) Once upon multivariate analyses: when they tell several stories about biological evolution. PLoS ONE 10, https://doi.org/10.1371/journal.pone.0132801

Renaud S, Ledevin R, Souquet L, Gomes Rodrigues H, Ginot S, Agret S, Claude J, Herrel A, Hautier L (2018) Evolving teeth within a stable masticatory apparatus in Orkney mice. Evolutionary Biology 45:405–424

Examples

data(houmousr)
fac1 <- houmousr$faccc
df1 <- houmousr$dfcc
nf1 <- nlevels(fac1) - 1
# Compute PCA 
pca1 <- dudi.pca(df1, scale = FALSE, scannf = FALSE, nf = nf1)
# Compute BGA
bca1 <- bca(pca1, fac1, scannf = FALSE, nf = nf1)
if(adegraphicsLoaded()) {
	s.class(bca1$ls, fac1, starSize = 0, chullSize = 1, ellipseSize = 0, ppoint.cex = 0,
	plabel.cex = 0, plegend.drawKey = FALSE, col = TRUE)
	s.class(bca1$ls, fac1, starSize = 1, ellipseSize = 0, col = TRUE, add = T)                                                           
} else {
	col1 <- c("#E41A1C", "#377EB8", "#4DAF4A", "#984EA3", "#FF7F00")
	s.class(bca1$ls, fac1, cstar = 1, cellipse = 0, col = col1)
	s.chull(bca1$ls, fac1, optchull = 1, add.plot = TRUE, col = col1)
}
## Not run: 
# Compute cross-validated coordinates
xbca1 <- loocv(bca1)
plot(xbca1)
## End(Not run)

Contingency Table

Description

The housetasks data frame gives 13 housetasks and their repartition in the couple.

Usage

data(housetasks)

Format

This data frame contains four columns : wife, alternating, husband and jointly. Each column is a numeric vector.

Source

Kroonenberg, P. M. and Lombardo, R. (1999) Nonsymmetric correspondence analysis: a tool for analysing contingency tables with a dependence structure. Multivariate Behavioral Research, 34, 367–396

Examples

data(housetasks)
nsc1 <- dudi.nsc(housetasks, scan = FALSE)

if(adegraphicsLoaded()) {
  s.label(nsc1$c1, plab.cex = 1.25)
  s.arrow(nsc1$li, add = TRUE, plab.cex = 0.75)
} else {
  s.label(nsc1$c1, clab = 1.25)
  s.arrow(nsc1$li, add.pl = TRUE, clab = 0.75) 
}

human mitochondrial DNA restriction data

Description

This data set gives the frequencies of haplotypes of mitochondrial DNA restriction data in ten populations all over the world.
It gives also distances among the haplotypes.

Usage

data(humDNAm)

Format

humDNAm is a list of 3 components.

distances

is an object of class dist with 56 haplotypes. These distances are computed by counting the number of differences in restriction sites between two haplotypes.

samples

is a data frame with 56 haplotypes, 10 abundance variables (populations). These variables give the haplotype abundance in a given population.

structures

is a data frame with 10 populations, 1 variable (classification). This variable gives the name of the continent in which a given population is located.

Source

Excoffier, L., Smouse, P.E. and Quattro, J.M. (1992) Analysis of molecular variance inferred from metric distances among DNA haplotypes: application to human mitochondrial DNA restriction data. Genetics, 131, 479–491.

Examples

data(humDNAm)
dpcoahum <- dpcoa(data.frame(t(humDNAm$samples)), 
    sqrt(humDNAm$distances), scan = FALSE, nf = 2)
plot(dpcoahum)

Point sampling of fish community

Description

This data set gives informations between a faunistic array, the total number of sampling points made at each sampling occasion and the year of the sampling occasion.

Usage

data(ichtyo)

Format

ichtyo is a list of 3 components.

tab

is a faunistic array with 9 columns and 32 rows.

eff

is a vector of the 32 sampling effort.

dat

is a factor where the levels are the 10 years of the sampling occasion.

Details

The value n(i,j) at the ith row and the jth column in tab corresponds to the number of sampling points of the ith sampling occasion (in eff) that contains the jth species.

Source

Dolédec, S., Chessel, D. and Olivier, J. M. (1995) L'analyse des correspondances décentrée: application aux peuplements ichtyologiques du haut-Rhône. Bulletin Français de la Pêche et de la Pisciculture, 336, 29–40.

Examples

data(ichtyo)
dudi1 <- dudi.dec(ichtyo$tab, ichtyo$eff, scannf = FALSE)
s.class(dudi1$li, ichtyo$dat, wt = ichtyo$eff / sum(ichtyo$eff))

Decomposition of inertia (i.e. contributions) in multivariate methods

Description

Computes the decomposition of inertia to measure the contributions of row and/or columns in multivariate methods

Usage

## S3 method for class 'dudi'
inertia(x, row.inertia = FALSE, col.inertia = FALSE, ...)
## S3 method for class 'inertia'
print(x, ...)
## S3 method for class 'inertia'
summary(object, sort.axis = 1, subset = 5, ...)

Arguments

x, object

a duality diagram, object of class dudi for inertia.dudi. An object of class inertia for the methods print and summary
row.inertia

if TRUE, returns the decomposition of inertia for the rows
col.inertia

if TRUE, returns the decomposition of inertia for the columns
sort.axis

the kept axis used to sort the contributions in decreasing order
subset

the number of rows and/or columns to display in the summary
...

further arguments passed to or from other methods

Details

Contributions are printed in percentage and the sign is the sign of the coordinates

Value

An object of class inertia, i.e. a list containing :

tot.inertia

repartition of the total inertia between axes
row.contrib

contributions of the rows to the total inertia
row.abs

absolute contributions of the rows (i.e. decomposition per axis)
row.rel

relative contributions of the rows
row.cum

cumulative relative contributions of the rows (i.e. decomposition per row)
col.contrib

contributions of the columns to the total inertia
col.abs

absolute contributions of the columns (i.e. decomposition per axis)
col.rel

relative contributions of the columns
col.cum

cumulative relative contributions of the columns (i.e. decomposition per column)
nf

the number of kept axes

Author(s)

Daniel Chessel
Stéphane Dray [email protected]
Anne-Béatrice Dufour [email protected]

References

Lebart, L., Morineau, A. and Tabart, N. (1977) Techniques de la description statistique, méthodes et logiciels pour la description des grands tableaux, Dunod, Paris, 61–62.

Volle, M. (1981) Analyse des données, Economica, Paris, 89–90 and 118

Lebart, L., Morineau, L. and Warwick, K.M. (1984) Multivariate descriptive analysis: correspondence and related techniques for large matrices, John Wiley and Sons, New York.

Greenacre, M. (1984) Theory and applications of correspondence analysis, Academic Press, London, 66.

Rouanet, H. and Le Roux, B. (1993) Analyse des données multidimensionnelles, Dunod, Paris, 143–144.

Tenenhaus, M. (1994) Méthodes statistiques en gestion, Dunod, Paris, p. 160, 161, 166, 204.

Lebart, L., Morineau, A. and Piron, M. (1995) Statistique exploratoire multidimensionnelle, Dunod, Paris, p. 56,95-96.

Examples

data(housetasks)
coa1 <- dudi.coa(housetasks, scann = FALSE)
res <- inertia(coa1, col = TRUE, row = FALSE)
res
summary(res)

Geary's Irish Data

Description

This data set contains geographical informations about 25 counties of Ireland.

Usage

data(irishdata)

Format

irishdata is a list of 13 components:

area

a data frame with polygons for each of the 25 contiguous counties

county.names

a vector with the names of the 25 counties

xy

a data frame with the coordinates centers of the 25 counties

tab

a data frame with 25 rows (counties) and 12 variables

contour

a data frame with the global polygon of all the 25 counties

link

a matrix containing the common length between two counties from area

area.utm

a data frame with polygons for each of the 25 contiguous counties expressed in Universal Transverse Mercator (UTM) coordinates

xy.utm

a data frame with the UTM coordinates centers of the 25 counties

link.utm

a matrix containing the common length between two counties from area.utm

tab.utm

a data frame with the 25 counties (explicitly named) and 12 variables

contour.utm

a data frame with the global polygon of all the 25 counties expressed in UTM coordinates

Spatial

the map of the 25 counties of Ireland (an object of the class SpatialPolygons of sp)

Spatial.contour

the contour of the map of the 25 counties of Ireland (an object of the class SpatialPolygons of sp)

Source

Geary, R.C. (1954) The contiguity ratio and statistical mapping. The incorporated Statistician, 5, 3, 115–145.

Cliff, A.D. and Ord, J.K. (1973) Spatial autocorrelation, Pion, London. 1–178.

Examples

data(irishdata)

if(adegraphicsLoaded()) {

  if(requireNamespace("sp", quietly = TRUE)){
  g1 <- s.label(irishdata$xy.utm, Sp = irishdata$Spatial, pSp.col = "white", plot = FALSE)
  
  g21 <- s.label(irishdata$xy.utm, Sp = irishdata$Spatial, pSp.col = "white", plab.cex = 0, 
    ppoints.cex = 0, plot = FALSE)
  g22 <- s.label(irishdata$xy.utm, Sp = irishdata$Spatial.contour, pSp.col = "transparent", 
    plab.cex = 0, ppoints.cex = 0, pSp.lwd = 3, plot = FALSE)
  g2 <- superpose(g21, g22)   

  g3 <- s.corcircle(dudi.pca(irishdata$tab, scan = FALSE)$co, plot = FALSE)
  
  score <- dudi.pca(irishdata$tab, scannf = FALSE, nf = 1)$li$Axis1
  names(score) <- row.names(irishdata$Spatial)
  
  obj <- sp::SpatialPolygonsDataFrame(Sr = irishdata$Spatial, data = as.data.frame(score))
  g4 <- s.Spatial(obj, plot = FALSE)
  
  G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))
  }
  
} else {
  par(mfrow = c(2, 2))
  area.plot(irishdata$area, lab = irishdata$county.names, clab = 0.75)
  area.plot(irishdata$area)
  apply(irishdata$contour, 1, function(x) segments(x[1], x[2], x[3], x[4], lwd = 3))
  s.corcircle(dudi.pca(irishdata$tab, scannf = FALSE)$co)
  score <- dudi.pca(irishdata$tab, scannf = FALSE, nf = 1)$li$Axis1
  names(score) <- row.names(irishdata$tab)
  area.plot(irishdata$area, score)
  par(mfrow = c(1, 1))
}

Is a Distance Matrix Euclidean?

Description

Confirmation of the Euclidean nature of a distance matrix by the Gower's theorem.
is.euclid is used in summary.dist.

Usage

is.euclid(distmat, plot = FALSE, print = FALSE, tol = 1e-07)
## S3 method for class 'dist'
summary(object, ...)

Arguments

distmat

an object of class 'dist'
plot

a logical value indicating whether the eigenvalues bar plot of the matrix of the term −12dij2-\frac{1}{2} {d_{ij}^2} centred by rows and columns should be diplayed
print

a logical value indicating whether the eigenvalues of the matrix of the term −12dij2-\frac{1}{2} {d_{ij}^2} centred by rows and columns should be printed
tol

a tolerance threshold : an eigenvalue is considered positive if it is larger than -tol*lambda1 where lambda1 is the largest eigenvalue.
object

an object of class 'dist'
...

further arguments passed to or from other methods

Value

returns a logical value indicating if all the eigenvalues are positive or equal to zero

Author(s)

Daniel Chessel
Stéphane Dray [email protected]

References

Gower, J.C. and Legendre, P. (1986) Metric and Euclidean properties of dissimilarity coefficients. Journal of Classification, 3, 5–48.

Examples

w <- matrix(runif(10000), 100, 100)
w <- dist(w)
summary(w)
is.euclid (w) # TRUE
w <- quasieuclid(w) # no correction need in: quasieuclid(w)
w <- lingoes(w) # no correction need in: lingoes(w)
w <- cailliez(w) # no correction need in: cailliez(w)
rm(w)

Seed dispersal

Description

This data set gives the spatial distribution of seeds (quadrats counts) of seven species in the understorey of tropical rainforest.

Usage

data(julliot)

Format

julliot is a list with the following components:

tab

a data frame with 160 rows (quadrats) and 7 variables (species)

xy

a data frame with the coordinates of the 160 quadrats (positioned by their centers)

area

a data frame with 3 variables returning the boundary lines of each quadrat. The first variable is a factor. The levels of this one are the row.names of tab. The second and third variables return the coordinates (x,y) of the points of the boundary line.

Spatial

an object of the class SpatialPolygons of sp, containing the map

Details

Species names of julliot$tab are: Pouteria torta, Minquartia guianensis, Quiina obovata, Chrysophyllum lucentifolium, Parahancornia fasciculata, Virola michelii, and Pourouma spp.

References

Julliot, C. (1992). Utilisation des ressources alimentaires par le singe hurleur roux, Alouatta seniculus (Atelidae, Primates), en Guyane : impact de la dissémination des graines sur la régénération forestière. Thèse de troisième cycle, Université de Tours.

Julliot, C. (1997). Impact of seed dispersal by red howler monkeys Alouatta seniculus on the seedling population in the understorey of tropical rain forest. Journal of Ecology, 85, 431–440.

Examples

data(julliot)

## Not run: 
if(adegraphicsLoaded()) {
  if(requireNamespace("sp", quietly = TRUE)) {
    obj1 <- sp::SpatialPolygonsDataFrame(Sr = julliot$Spatial, data = log(julliot$tab + 1))
    g1 <- s.Spatial(obj1)
    g2 <- s.value(julliot$xy, scalewt(log(julliot$tab + 1)), Sp = julliot$Spatial, 
      pSp.col = "white", pgrid.draw = FALSE)
  }
} else {
  if(requireNamespace("splancs", quietly = TRUE)) {
    par(mfrow = c(3, 3))
    for(k in 1:7)
      area.plot(julliot$area, val = log(julliot$tab[, k] + 1),
        sub = names(julliot$tab)[k], csub = 2.5)
    par(mfrow = c(1, 1))
    
    par(mfrow = c(3, 3))
    for(k in 1:7) {
      area.plot(julliot$area)
      s.value(julliot$xy, scalewt(log(julliot$tab[, k] + 1)),
        sub = names(julliot$tab)[k], csub = 2.5, add.p = TRUE)
    }
    par(mfrow = c(1, 1))
  }
}
## End(Not run)


if(adegraphicsLoaded()) {
  if(requireNamespace("sp", quietly = TRUE)) {
    g3 <- s.image(julliot$xy, log(julliot$tab + 1), span = 0.25)
  }
  g4 <- s.value(julliot$xy, log(julliot$tab + 1))
  
} else {
  if(requireNamespace("splancs", quietly = TRUE)) {
    par(mfrow = c(3, 3))
    for(k in 1:7)
      s.image(julliot$xy, log(julliot$tab[, k] + 1), kgrid = 3, span = 0.25,
        sub = names(julliot$tab)[k], csub = 2.5)
    par(mfrow = c(1, 1))
    
    par(mfrow = c(3, 3))
    for(k in 1:7)
      s.value(julliot$xy, log(julliot$tab[, k] + 1),
        sub = names(julliot$tab)[k], csub = 2.5)
    par(mfrow = c(1, 1))    
  }
}
        
## Not run: 
if (requireNamespace("spdep", quietly = TRUE)) {
  neig0 <- nb2neig(spdep::dnearneigh(as.matrix(julliot$xy), 1, 1.8))
  if(adegraphicsLoaded()) {
    g5 <- s.label(julliot$xy, nb = spdep::dnearneigh(as.matrix(julliot$xy), 1, 1.8))
  
  } else {
    par(mfrow = c(1, 1))
    s.label(julliot$xy, neig = neig0, clab = 0.75, incl = FALSE,
     addax = FALSE, grid = FALSE)
  }
  gearymoran(ade4:::neig.util.LtoG(neig0), log(julliot$tab + 1))
  
  if (requireNamespace("adephylo", quietly = TRUE)) {
    adephylo::orthogram(log(julliot$tab[, 3] + 1), ortho = scores.neig(neig0))
  }
}
## End(Not run)

K-tables Multi-Regions

Description

This data set gives physical and physico-chemical variables, fish species, spatial coordinates about 92 sites.

Usage

data(jv73)

Format

jv73 is a list with the following components:

morpho

a data frame with 92 sites and 6 physical variables

phychi

a data frame with 92 sites and 12 physico-chemical variables

poi

a data frame with 92 sites and 19 fish species

xy

a data frame with 92 sites and 2 spatial coordinates

contour

a data frame for mapping

fac.riv

a factor distributing the 92 sites on 12 rivers

Spatial

an object of the class SpatialLines of sp, containing the map

Source

Verneaux, J. (1973) Cours d'eau de Franche-Comté (Massif du Jura). Recherches écologiques sur le réseau hydrographique du Doubs. Essai de biotypologie. Thèse d'Etat, Besançon.

References

See a data description at http://pbil.univ-lyon1.fr/R/pdf/pps047.pdf (in French).

Examples

data(jv73)

w <- split(jv73$morpho, jv73$fac.riv)
w <- lapply(w, function(x) t(dudi.pca(x, scann = FALSE)))
w <- ktab.list.dudi(w)

if(adegraphicsLoaded()) {
  if(requireNamespace("sp", quietly = TRUE)) {
    g11 <- s.label(jv73$xy, Sp = jv73$Spatial, pori.incl = FALSE, plab.cex = 0.75, plot = FALSE)
    g12 <- s.class(jv73$xy, jv73$fac.riv, ellipseSize = 0, pellipses.axes.draw = FALSE, 
      starSize = 0, ppoints.cex = 0, plab.cex = 1.25, plot = FALSE)
    g1 <- superpose(g11, g12, plot = TRUE)
  
    g2 <- kplot(sepan(w), perm = TRUE, row.plab.cex = 0, posieig = "none")
  }
  
} else {
  s.label(jv73$xy, contour = jv73$contour, incl = FALSE, clab = 0.75)
  s.class(jv73$xy, jv73$fac.riv, add.p = TRUE, cell = 0, axese = FALSE, csta = 0, 
    cpoi = 0, clab = 1.25)
  
  kplot(sepan(w), perm = TRUE, clab.r = 0, clab.c = 2, show = FALSE)
}

Ponds in a nature reserve

Description

This data set contains informations about 33 ponds in De Maten reserve (Genk, Belgium).

Usage

data(kcponds)

Format

kponds is a list with the following components:

tab

a data frame with 15 environmental variables (columns) on 33 ponds (rows)

area

an object of class area

xy

a data frame with the coordinates of ponds

neig

an object of class neig

nb

the neighbourhood graph of the 33 sites (an object of class nb)

Spatial

an object of the class SpatialPolygons of sp, containing the map

Details

Variables of kcponds$tab are the following ones : depth, area, O2 (oxygen concentration), cond (conductivity), pH, Fe (Fe concentration), secchi (Secchi disk depth), N (NNO concentration), TP (total phosphorus concentration), chla (chlorophyll-a concentration), EM (emergent macrophyte cover), FM (floating macrophyte cover), SM (submerged macrophyte cover), denMI (total density of macroinvertebrates), divMI (diversity macroinvertebrates)

Source

Cottenie, K. (2002) Local and regional processes in a zooplankton metacommunity. PhD, Katholieke Universiteit Leuven, Leuven, Belgium.
https://bio.kuleuven.be/eco/phdkarlcottenie.pdf

Examples

data(kcponds)
w <- as.numeric(scalewt(kcponds$tab$N))

if(adegraphicsLoaded()) {
  if(requireNamespace("sp", quietly = TRUE)) {
    g1 <- s.label(kcponds$xy, Sp = kcponds$Spatial, pSp.col = "white", nb = kcponds$nb, 
      plab.cex = 0, paxes.asp = "fill", plot = FALSE)
    g2 <- s.label(kcponds$xy, Sp = kcponds$Spatial, pSp.col = "white", plabels.cex = 0.8, 
      paxes.asp = "fill", plot = FALSE)
    g3 <- s.value(kcponds$xy, w, psub.text = "Nitrogen concentration", paxe.asp = "fill", 
      plot = FALSE)
    G <- rbindADEg(g1, g2, g3, plot = TRUE)
  }

} else {
  par(mfrow=c(3, 1))
  area.plot(kcponds$area)
  s.label(kcponds$xy, add.p = TRUE, cpoi = 2, clab = 0)
  s.label(kcponds$xy, add.p = TRUE, cpoi = 3, clab = 0)
  s.label(kcponds$xy, add.p = TRUE, cpoi = 0, clab = 0, neig = kcponds$neig, cneig = 1)
  area.plot(kcponds$area)
  s.label(kcponds$xy, add.p = TRUE, clab = 1.5)
  s.value(kcponds$xy, w, cleg = 2, sub = "Nitrogen concentration", csub = 4, 
    possub = "topright", include = FALSE)
  par(mfrow = c(1, 1))
}

## Not run: 
  par(mfrow = c(3, 1))
  pca1 <- dudi.pca(kcponds$tab, scan = FALSE, nf = 4)
  if(requireNamespace("spdep", quietly = TRUE)) {
    multi1 <- multispati(pca1, spdep::nb2listw(neig2nb(kcponds$neig)), scannf = FALSE, nfposi = 2, 
      nfnega = 1)
    summary(multi1)
  }
  par(mfrow = c(1, 1))

## End(Not run)

the class of objects 'kdist' (K distance matrices)

Description

An object of class kdist is a list of distance matrices observed on the same individuals

Usage

kdist(..., epsi = 1e-07, upper = FALSE)

Arguments

...

a sequence of objects of the class kdist.

epsi

a tolerance threshold to test if distances are Euclidean (Gower's theorem) using λnλ1\frac{\lambda_n}{\lambda_1} is larger than -epsi.

upper

a logical value indicating whether the upper of a distance matrix is used (TRUE) or not (FALSE).

Details

The attributs of a 'kdist' object are:
names: the names of the distances
size: the number of points between distances are known
labels: the labels of points
euclid: a logical vector indicating whether each distance of the list is Euclidean or not.
call: a call order
class: object 'kdist'

Value

returns an object of class 'kdist' containing a list of semidefinite matrices.

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

References

Gower, J. C. (1966) Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika, 53, 325–338.

Examples

# starting from a list of matrices 
data(yanomama)
lapply(yanomama,class)  
kd1 = kdist(yanomama)
print(kd1)

# giving the correlations of Mantel's test
cor(as.data.frame(kd1))
pairs(as.data.frame(kd1))

# starting from a list of objects 'dist'
data(friday87)
fri.w <- ktab.data.frame(friday87$fau, friday87$fau.blo, 
    tabnames = friday87$tab.names)
fri.kd = lapply(1:10, function(x) dist.binary(fri.w[[x]],2))
names(fri.kd) = friday87$tab.names
unlist(lapply(fri.kd,class)) # a list of distances
fri.kd = kdist(fri.kd)
fri.kd
s.corcircle(dudi.pca(as.data.frame(fri.kd), scan = FALSE)$co)

# starting from several distances
data(ecomor)
d1 <- dist.binary(ecomor$habitat, 1)
d2 <- dist.prop(ecomor$forsub, 5)
d3 <- dist.prop(ecomor$diet, 5)
d4 <- dist.quant(ecomor$morpho, 3)
d5 <- dist.taxo(ecomor$taxo)
ecomor.kd <- kdist(d1, d2, d3, d4, d5)
names(ecomor.kd) = c("habitat", "forsub", "diet", "morpho", "taxo")
class(ecomor.kd)
s.corcircle(dudi.pca(as.data.frame(ecomor.kd), scan = FALSE)$co)

data(bsetal97)
X <- prep.fuzzy.var(bsetal97$biol, bsetal97$biol.blo)
w1 <- attr(X, "col.num")
w2 <- levels(w1)
w3 <- lapply(w2, function(x) dist.quant(X[,w1==x], method = 1))
names(w3) <- names(attr(X, "col.blocks"))
w3 <- kdist(list = w3)
s.corcircle(dudi.pca(as.data.frame(w3), scan = FALSE)$co)

data(rpjdl)
w1 = lapply(1:10, function(x) dist.binary(rpjdl$fau, method = x))
w2 = c("JACCARD", "SOKAL_MICHENER", "SOKAL_SNEATH_S4", "ROGERS_TANIMOTO")
w2 = c(w2, "CZEKANOWSKI", "S9_GOWER_LEGENDRE", "OCHIAI", "SOKAL_SNEATH_S13")
w2 <- c(w2, "Phi_PEARSON", "S2_GOWER_LEGENDRE")
names(w1) <- w2
w3 = kdist(list = w1)
w4 <- dudi.pca(as.data.frame(w3), scan = FALSE)$co
w4

Transformation of K distance matrices (object 'kdist') into K Euclidean representations (object 'ktab')

Description

The function creates a ktab object with the Euclidean representations from a kdist object. Notice that the euclid attribute must be TRUE for all elements.

Usage

kdist2ktab(kd, scale = TRUE, tol = 1e-07)

Arguments

kd

an object of class kdist

scale

a logical value indicating whether the inertia of Euclidean representations are equal to 1 (TRUE) or not (FALSE).

tol

a tolerance threshold, an eigenvalue is considered equal to zero if eig$values > (eig$values[1 * tol)

Value

returns a list of class ktab containing for each distance of kd the data frame of its Euclidean representation

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

Examples

data(friday87)
fri.w <- ktab.data.frame(friday87$fau, friday87$fau.blo, tabnames = friday87$tab.names)
fri.kd <- lapply(1:10, function(x) dist.binary(fri.w[[x]], 10))
names(fri.kd) <- substr(friday87$tab.names, 1, 4)
fri.kd <- kdist(fri.kd)
fri.ktab <- kdist2ktab(kd = fri.kd)
fri.sepan <- sepan(fri.ktab)
plot(fri.sepan)

tapply(fri.sepan$Eig, fri.sepan$TC[,1], sum)
# the sum of the eigenvalues is constant and equal to 1, for each K tables

fri.statis <- statis(fri.ktab, scan = FALSE, nf = 2)
round(fri.statis$RV, dig = 2)

fri.mfa <- mfa(fri.ktab, scan = FALSE, nf = 2)
fri.mcoa <- mcoa(fri.ktab, scan = FALSE, nf = 2)

apply(fri.statis$RV, 1, mean) 
fri.statis$RV.tabw 
plot(apply(fri.statis$RV, 1, mean), fri.statis$RV.tabw)
plot(fri.statis$RV.tabw, fri.statis$RV.tabw)

a way to obtain Euclidean distance matrices

Description

a way to obtain Euclidean distance matrices

Usage

kdisteuclid(obj, method = c("lingoes", "cailliez", "quasi"))

Arguments

obj

an object of class kdist
method

a method to convert a distance matrix in a Euclidean one

Value

returns an object of class kdist with all distances Euclidean.

Author(s)

Daniel Chessel
Stéphane Dray [email protected]

References

Gower, J.C. and Legendre, P. (1986) Metric and Euclidean properties of dissimilarity coefficients. Journal of Classification, 3, 5–48.

Cailliez, F. (1983) The analytical solution of the additive constant problem. Psychometrika, 48, 305–310.

Lingoes, J.C. (1971) Somme boundary conditions for a monotone analysis of symmetric matrices. Psychometrika, 36, 195–203.

Legendre, P. and Anderson, M.J. (1999) Distance-based redundancy analysis: testing multispecies responses in multifactorial ecological experiments. Ecological Monographs, 69, 1–24.

Legendre, P., and L. Legendre. (1998) Numerical ecology, 2nd English edition edition. Elsevier Science BV, Amsterdam.

Examples

w <- c(0.8, 0.8, 0.377350269, 0.8, 0.377350269, 0.377350269) # see ref.
w <- kdist(w)
w1 <- c(kdisteuclid(kdist(w), "lingoes"), kdisteuclid(kdist(w), "cailliez"), 
  kdisteuclid(kdist(w), "quasi"))
print(w, print = TRUE)
print(w1, print = TRUE)

data(eurodist)
par(mfrow = c(1, 3))
eu1 <- kdist(eurodist) # an object of class 'dist'
plot(data.frame(unclass(c(eu1, kdisteuclid(eu1, "quasi")))), asp = 1)
title(main = "Quasi")
abline(0,1)
plot(data.frame(unclass(c(eu1, kdisteuclid(eu1, "lingoes")))), asp = 1)
title(main = "Lingoes")
abline(0,1)
plot(data.frame(unclass(c(eu1, kdisteuclid(eu1, "cailliez")))), asp = 1)
title(main = "Cailliez")
abline(0,1)

Generic Function for Multiple Graphs in a K-tables Analysis

Description

Methods for foucart, mcoa, mfa, pta, sepan, sepan.coa and statis

Usage

kplot(object, ...)

Arguments

object

an object used to select a method
...

further arguments passed to or from other methods

Examples

methods(plot)
methods(scatter)
methods(kplot)

Multiple Graphs for the Foucart's Correspondence Analysis

Description

performs high level plots of a Foucart's Correspondence Analysis, using an object of class foucart.

Usage

## S3 method for class 'foucart'
kplot(object, xax = 1, yax = 2, mfrow = NULL, 
    which.tab = 1:length(object$blo), clab.r = 1, clab.c = 1.25, 
    csub = 2, possub = "bottomright", ...)

Arguments

object

an object of class foucart

xax, yax

the numbers of the x-axis and the y-axis
mfrow

a vector of the form 'c(nr,nc)', otherwise computed by as special own function n2mfrow
which.tab

vector of table numbers for analyzing
clab.r

a character size for the row labels
clab.c

a character size for the column labels
csub

a character size for the sub-titles used with par("cex")*csub
possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")
...

further arguments passed to or from other methods

Examples

data(bf88)
fou1 <- foucart(bf88, scann = FALSE, nf = 3)

if(adegraphicsLoaded()) {
  g <- kplot(fou1, row.plab.cex = 0, psub.cex = 2)
} else {
  kplot(fou1, clab.c = 2, clab.r = 0, csub = 3)
}

Multiple Graphs for a Multiple Co-inertia Analysis

Description

performs high level plots of a Multiple Co-inertia Analysis, using an object of class mcoa.

Usage

## S3 method for class 'mcoa'
kplot(object, xax = 1, yax = 2, which.tab = 1:nrow(object$cov2), 
    mfrow = NULL, option = c("points", "axis", "columns"), 
    clab = 1, cpoint = 2, csub = 2, possub = "bottomright",...)

Arguments

object

an object of class mcoa
xax, yax

the numbers of the x-axis and the y-axis
which.tab

a numeric vector containing the numbers of the tables to analyse
mfrow

a vector of the form 'c(nr,nc)', otherwise computed by as special own function n2mfrow
option

a string of characters for the drawing option

"points"

plot of the projected scattergram onto the co-inertia axes

"axis"

projections of inertia axes onto the co-inertia axes.

"columns"

projections of variables onto the synthetic variables planes.
clab

a character size for the labels
cpoint

a character size for plotting the points, used with par("cex")*cpoint. If zero, no points are drawn.
csub

a character size for the sub-titles, used with par("cex")*csub
possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")
...

further arguments passed to or from other methods

Author(s)

Daniel Chessel

Examples

data(friday87)
w1 <- data.frame(scale(friday87$fau, scal = FALSE))
w2 <- ktab.data.frame(w1, friday87$fau.blo, tabnames = friday87$tab.names)
mcoa1 <- mcoa(w2, "lambda1", scan = FALSE)
kplot(mcoa1, option = "axis")
kplot(mcoa1)
kplot(mcoa1, option = "columns")

Multiple Graphs for a Multiple Factorial Analysis

Description

performs high level plots of a Multiple Factorial Analysis, using an object of class mfa.

Usage

## S3 method for class 'mfa'
kplot(object, xax = 1, yax = 2, mfrow = NULL, 
    which.tab = 1:length(object$blo), row.names = FALSE, col.names = TRUE, 
    traject = FALSE, permute.row.col = FALSE, 
    clab = 1, csub = 2, possub = "bottomright", ...)

Arguments

object

an object of class mfa
xax, yax

the numbers of the x-axis and the y-axis
mfrow

a vector of the form 'c(nr,nc'), otherwise computed by a special own function n2mfrow
which.tab

vector of the numbers of tables used for the analysis
row.names

a logical value indicating whether the row labels should be inserted
col.names

a logical value indicating whether the column labels should be inserted
traject

a logical value indicating whether the trajectories of the rows should be drawn in a natural order
permute.row.col

if TRUE, the rows are represented by vectors and columns by points, otherwise it is the opposite
clab

a character size for the labels
csub

a character size for the sub-titles, used with par("cex")*csub
possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")
...

further arguments passed to or from other methods

Author(s)

Daniel Chessel

Examples

data(friday87)
w1 <- data.frame(scale(friday87$fau, scal = FALSE))
w2 <- ktab.data.frame(w1, friday87$fau.blo, tabnames = friday87$tab.names)
mfa1 <- mfa(w2, scann = FALSE)
kplot(mfa1)

Multiple Graphs for a Partial Triadic Analysis

Description

performs high level plots of a Partial Triadic Analysis, using an object of class pta.

Usage

## S3 method for class 'pta'
kplot(object, xax = 1, yax = 2, which.tab = 1:nrow(object$RV), 
    mfrow = NULL, which.graph = 1:4, clab = 1, cpoint = 2, csub = 2, 
    possub = "bottomright", ask = par("ask"), ...)

Arguments

object

an object of class pta
xax, yax

the numbers of the x-axis and the y-axis
which.tab

a numeric vector containing the numbers of the tables to analyse
mfrow

parameter of the array of figures to be drawn, otherwise the graphs associated to a table are drawn on the same row
which.graph

an option for drawing, an integer between 1 and 4. For each table of which.tab, are drawn :

1

the projections of the principal axes

2

the projections of the rows

3

the projections of the columns

4

the projections of the principal components onto the planes of the compromise
clab

a character size for the labels
cpoint

a character size for plotting the points, used with par("cex")*cpoint. If zero, no points are drawn.
csub

a character size for the sub-titles, used with par("cex")*csub
possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")
ask

a logical value indicating if the graphs requires several arrays of figures
...

further arguments passed to or from other methods

Author(s)

Daniel Chessel

Examples

data(meaudret)
wit1 <- wca(dudi.pca(meaudret$spe, scan = FALSE, scal = FALSE), 
  meaudret$design$season, scan = FALSE)
kta1 <- ktab.within(wit1, colnames = rep(c("S1", "S2", "S3", "S4", "S5"), 4))
kta2 <- t(kta1)
pta1 <- pta(kta2, scann = FALSE)
kplot(pta1)
kplot(pta1, which.graph = 3)

Multiple Graphs for Separated Analyses in a K-tables

Description

performs high level plots for Separed Analyses in a K-tables, using an object of class sepan.

Usage

## S3 method for class 'sepan'
kplot(object, xax = 1, yax = 2, which.tab = 1:length(object$blo), 
    mfrow = NULL, permute.row.col = FALSE, clab.row = 1, 
    clab.col = 1.25, traject.row = FALSE, csub = 2, 
    possub = "bottomright", show.eigen.value = TRUE,...)

kplotsepan.coa(object, xax = 1, yax = 2, which.tab = 1:length(object$blo), 
    mfrow = NULL, permute.row.col = FALSE, clab.row = 1, 
    clab.col = 1.25, csub = 2, possub = "bottomright", 
    show.eigen.value = TRUE, poseig = c("bottom", "top"), ...)

Arguments

object

an object of class sepan
xax, yax

the numbers of the x-axis and the y-axis
which.tab

a numeric vector containing the numbers of the tables to analyse
mfrow

parameter for the array of figures to be drawn, otherwise use n2mfrow
permute.row.col

if TRUE the rows are represented by arrows and the columns by points, if FALSE it is the opposite
clab.row

a character size for the row labels
clab.col

a character size for the column labels
traject.row

a logical value indicating whether the trajectories between rows should be drawn in a natural order
csub

a character size for the sub-titles, used with par("cex")*csub
possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")
show.eigen.value

a logical value indicating whether the eigenvalues bar plot should be drawn
poseig

if "top" the eigenvalues bar plot is upside, if "bottom", it is downside
...

further arguments passed to or from other methods

Details

kplot.sepan superimposes the points for the rows and the arrows for the columns using an adapted rescaling such as the scatter.dudi.
kplotsepan.coa superimposes the row coordinates and the column coordinates with the same scale.

Author(s)

Daniel Chessel

Examples

data(escopage)
w1 <- data.frame(scale(escopage$tab))
w1 <- ktab.data.frame(w1, escopage$blo, tabnames = escopage$tab.names)
sep1 <- sepan(w1)
if(adegraphicsLoaded()) {
  kplot(sep1, posieig = "none")
} else {
  kplot(sep1, show = FALSE)
}

data(friday87)
w2 <- data.frame(scale(friday87$fau, scal = FALSE))
w2 <- ktab.data.frame(w2, friday87$fau.blo, tabnames = friday87$tab.names)
if(adegraphicsLoaded()) {
  kplot(sepan(w2), row.plabel.cex = 1.25, col.plab.cex = 0)
} else {
  kplot(sepan(w2), clab.r = 1.25, clab.c = 0)
}

data(microsatt)
w3 <- dudi.coa(data.frame(t(microsatt$tab)), scann = FALSE)
loci.fac <- factor(rep(microsatt$loci.names, microsatt$loci.eff))
wit <- wca(w3, loci.fac, scann = FALSE)
microsatt.ktab <- ktab.within(wit)
if(adegraphicsLoaded()) {
  kplotsepan.coa(sepan(microsatt.ktab), posieig = "none", col.plab.cex = 0, row.plab.cex = 1.5)
} else {
  kplotsepan.coa(sepan(microsatt.ktab), show = FALSE, clab.c = 0, 
    mfrow = c(3,3), clab.r = 1.5)
}

Multiple Graphs of a STATIS Analysis

Description

performs high level plots for a STATIS analysis, using an object of class statis.

Usage

## S3 method for class 'statis'
kplot(object, xax = 1, yax = 2, mfrow = NULL, 
    which.tab = 1:length(object$tab.names), clab = 1.5, cpoi = 2, 
    traject = FALSE, arrow = TRUE, class = NULL, 
    unique.scale = FALSE, csub = 2, possub = "bottomright",...)

Arguments

object

an object of class statis
xax, yax

the numbers of the x-axis and the y-axis
mfrow

parameter for the array of figures to be drawn
which.tab

a numeric vector containing the numbers of the tables to analyse
clab

a character size for the labels
cpoi

the size of points
traject

a logical value indicating whether the trajectories should be drawn in a natural order
arrow

a logical value indicating whether the column factorial diagrams should be plotted
class

if not NULL, a factor of length equal to the number of the total columns of the K-tables
unique.scale

if TRUE, all the arrays of figures have the same scale
csub

a character size for the labels of the arrays of figures used with par("cex")*csub
possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")
...

further arguments passed to or from other methods

Author(s)

Daniel Chessel

Examples

data(jv73)
dudi1 <- dudi.pca(jv73$poi, scann = FALSE, scal = FALSE)
wit1 <- wca(dudi1, jv73$fac.riv, scann = FALSE)
kta1 <- ktab.within(wit1)
statis1 <- statis(kta1, scann = FALSE)

if(adegraphicsLoaded()) {
  g1 <- kplot(statis1, traj = TRUE, arrow = FALSE, plab.cex = 0, psub.cex = 2, ppoi.cex = 2)
} else {
  kplot(statis1, traj = TRUE, arrow = FALSE, unique = TRUE, clab = 0, csub = 2, cpoi = 2)
}

Class of the Permutation Tests (in C).

Description

Plot, print and extract permutation tests. Objects of class 'krandtest' are lists.

Usage

as.krandtest(sim, obs, alter = "greater", call = match.call(),
  names = colnames(sim), p.adjust.method = "none", output = c("light", "full"))

## S3 method for class 'krandtest'
plot(x, mfrow = NULL, nclass = 10, main.title = x$names, ...)
## S3 method for class 'krandtest'
print(x, ...)
## S3 method for class 'krandtest'
x[i]
## S3 method for class 'krandtest'
x[[i]]

Arguments

sim

a matrix or data.frame of simulated values (repetitions as rows, number of tests as columns
obs

a numeric vector of observed values for each test
alter

a vector of character specifying the alternative hypothesis for each test. Each element must be one of "greater" (default), "less" or "two-sided". The length must be equal to the length of the vector obs, values are recycled if shorter.
call

a call order
names

a vector of names for tests
p.adjust.method

a string indicating a method for multiple adjustment, see p.adjust.methods for possible choices.
output

a character string specifying if all simulations should be stored ("full"). This was the default until ade4 1.7-5. Now, by default ("light"), only the distribution of simulated values is stored in element plot as produced by the hist function.
x

an object of class 'krandtest'
mfrow

a vector of the form 'c(nr,nc)', otherwise computed by as special own function n2mfrow
nclass

a number of intervals for the histogram. Ignored if object output is "light"
main.title

a string of character for the main title
...

further arguments passed to or from other methods
i

numeric indices specifying elements to extract

Value

plot.krandtest draws the p simulated values histograms and the position of the observed value. [.krandtest returns a krandtest object and [[.krandtest returns a randtest object.

Author(s)

Daniel Chessel and Stéphane Dray [email protected]

See Also

randtest

Examples

wkrandtest <- as.krandtest(obs = c(0, 1.2, 2.4, 3.4, 5.4, 20.4), 
  sim = matrix(rnorm(6*200), 200, 6))
wkrandtest
plot(wkrandtest)
wkrandtest[c(1, 4, 6)]
wkrandtest[[1]]

the class of objects 'ktab' (K-tables)

Description

an object of class ktab is a list of data frames with the same row.names in common.
a list of class 'ktab' contains moreover :

blo

: the vector of the numbers of columns for each table

lw

: the vector of the row weightings in common for all tables

cw

: the vector of the column weightings

TL

: a data frame of two components to manage the parameter positions associated with the rows of tables

TC

: a data frame of two components to manage the parameter positions associated with the columns of tables

T4

: a data frame of two components to manage the parameter positions of 4 components associated to an array

Usage

## S3 method for class 'ktab'
c(...)
## S3 method for class 'ktab'
x[i,j,k]
is.ktab(x)
## S3 method for class 'ktab'
t(x)
## S3 method for class 'ktab'
row.names(x)
## S3 method for class 'ktab'
col.names(x)
tab.names(x)
col.names(x)
ktab.util.names(x)

Arguments

x

an object of the class ktab
...

a sequence of objects of the class ktab
i, j, k

elements to extract (integer or empty): index of tables (i), rows (j) and columns (k)

Details

A 'ktab' object can be created with :
a list of data frame : ktab.list.df
a list of dudi objects : ktab.list.dudi
a data.frame : ktab.data.frame
an object within : ktab.within
a couple of ktabs : ktab.match2ktabs

Value

c.ktab returns an object ktab. It concatenates K-tables with the same rows in common.
t.ktab returns an object ktab. It permutes each data frame into a K-tables. All tables have the same column names and the same column weightings (a data cube).
"[" returns an object ktab. It allows to select some arrays in a K-tables.
is.ktab returns TRUE if x is a K-tables.
row.names returns the vector of the row names common with all the tables of a K-tables and allowes to modifie them.
col.names returns the vector of the column names of a K-tables and allowes to modifie them.
tab.names returns the vector of the array names of a K-tables and allowes to modifie them.
ktab.util.names is a useful function.

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected] Stéphane Dray [email protected]

Examples

data(friday87)
wfri <- data.frame(scale(friday87$fau, scal = FALSE))
wfri <- ktab.data.frame(wfri, friday87$fau.blo)
wfri[2:4, 1:5, 1:3]
c(wfri[2:4], wfri[5])

data(meaudret)
wit1 <- withinpca(meaudret$env, meaudret$design$season, scan = FALSE, 
    scal = "partial")
kta1 <- ktab.within(wit1, colnames = rep(c("S1","S2","S3","S4","S5"), 4))
kta2 <- t(kta1)

if(adegraphicsLoaded()) {
  kplot(sepan(kta2), row.plab.cex = 1.5, col.plab.cex = 0.75)
} else {
  kplot(sepan(kta2), clab.r = 1.5, clab.c = 0.75)
}

Creation of K-tables from a data frame

Description

creates K tables from a data frame.

Usage

ktab.data.frame(df, blocks, rownames = NULL, colnames = NULL, 
    tabnames = NULL, w.row = rep(1, nrow(df)) / nrow(df), 
    w.col = rep(1, ncol(df)))

Arguments

df

a data frame
blocks

an integer vector for which the sum must be the number of variables of df. Its length is the number of arrays of the K-tables
rownames

the row names of the K-tables (otherwise the row names of df)
colnames

the column names of the K-tables (otherwise the column names of df)
tabnames

the names of the arrays of the K-tables (otherwise "Ana1", "Ana2", ...)
w.row

a vector of the row weightings
w.col

a vector of the column weightings

Value

returns a list of class ktab. See ktab.

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

Examples

data(escopage)
wescopage <- data.frame(scalewt(escopage$tab))
wescopage <- ktab.data.frame(wescopage, escopage$blo,
        tabnames = escopage$tab.names)
plot(sepan(wescopage))
data(friday87)
w <- data.frame(scale(friday87$fau, scal = FALSE))
w <- ktab.data.frame(w, friday87$fau.blo, tabnames = friday87$tab.names)
kplot(sepan(w))

Creating a K-tables from a list of data frames.

Description

creates a list of class ktab from a list of data frames

Usage

ktab.list.df(obj, rownames = NULL, colnames = NULL, tabnames = NULL, 
    w.row = rep(1, nrow(obj[[1]])), w.col = lapply(obj, function(x) 
    rep(1 / ncol(x), ncol(x))))

Arguments

obj

a list of data frame
rownames

the names of the K-tables rows (otherwise, the row names of the arrays)
colnames

the names of the K-tables columns (otherwise, the column names of the arrays)
tabnames

the names of the arrays of the K-tables (otherwise, the names of the obj if they exist, or else "Ana1", "Ana2", ...)
w.row

a vector of the row weightings in common with all the arrays
w.col

a list of the vector of the column weightings for each array

Details

Each element of the initial list have to possess the same names and row numbers

Value

returns a list of class ktab. See ktab

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

Examples

data(jv73)
l0 <- split(jv73$morpho, jv73$fac.riv)
l0 <- lapply(l0, function(x) data.frame(t(scalewt(x))))
kta <- ktab.list.df(l0)
kplot(sepan(kta[c(2, 5, 7, 10)]), perm = TRUE)

Creation of a K-tables from a list of duality diagrams

Description

creates a list of class ktab from a list of duality diagrams.

Usage

ktab.list.dudi(obj, rownames = NULL, colnames = NULL, tabnames = NULL)

Arguments

obj

a list of objects of class 'dudi'. Each element of the list must have the same row names for $tab and even for $lw
rownames

the row names of the K-tables (otherwise the row names of the $tab)
colnames

the column names of the K-tables (otherwise the column names of the $tab)
tabnames

the names of the arrays of the K-tables (otherwise the names of the obj if they exist, or else "Ana1", "Ana2", ...)

Value

returns a list of class ktab. See ktab

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

Examples

data(euro123)
pca1 <- dudi.pca(euro123$in78, scale = FALSE, scann = FALSE)
pca2 <- dudi.pca(euro123$in86, scale = FALSE, scann = FALSE)
pca3 <- dudi.pca(euro123$in97, scale = FALSE, scann = FALSE)
ktabeuro <- ktab.list.dudi(list(pca1, pca2, pca3), 
    tabnames = c("1978", "1986", "1997"))
if(adegraphicsLoaded()) {
  kplot(sepan(ktabeuro))
} else {
  kplot(sepan(ktabeuro), mfr = c(2, 2), clab.c = 1.5)
}

data(meaudret)
w1 <- split(meaudret$env,meaudret$design$season)
ll <- lapply(w1, dudi.pca, scann = FALSE)
kta <- ktab.list.dudi(ll, rownames <- paste("Site", 1:5, sep = ""))
if(adegraphicsLoaded()) {
  kplot(sepan(kta), row.plab.cex = 1.5, col.plab.cex = 0.75)
} else {
  kplot(sepan(kta), clab.r = 1.5, clab.c = 0.75)
}

data(jv73)
w <- split(jv73$poi, jv73$fac.riv)
wjv73poi <- lapply(w, dudi.pca, scal = FALSE, scan = FALSE)
wjv73poi <- lapply(wjv73poi, t)
wjv73poi <- ktab.list.dudi(wjv73poi)
kplot(sepan(wjv73poi), permut = TRUE, traj = TRUE)

STATIS and Co-Inertia : Analysis of a series of paired ecological tables

Description

Prepares the analysis of a series of paired ecological tables. Partial Triadic Analysis (see pta) can be used thereafter to perform the analysis of this k-table.

Usage

ktab.match2ktabs(KTX, KTY)

Arguments

KTX

an objet of class ktab
KTY

an objet of class ktab

Value

a list of class ktab, subclass kcoinertia. See ktab

WARNING

IMPORTANT : KTX and KTY must have the same k-tables structure, the same number of columns, and the same column weights.

Author(s)

Jean Thioulouse [email protected]

References

Thioulouse J., Simier M. and Chessel D. (2004). Simultaneous analysis of a sequence of paired ecological tables. Ecology 85, 272-283..

Simier, M., Blanc L., Pellegrin F., and Nandris D. (1999). Approche simultanée de K couples de tableaux : Application a l'étude des relations pathologie végétale - environnement. Revue de Statistique Appliquée, 47, 31-46.

Examples

data(meau)
wit1 <- withinpca(meau$env, meau$design$season, scan = FALSE, scal = "total")
pcaspe <- dudi.pca(meau$spe, scale = FALSE, scan = FALSE, nf = 2)
wit2 <- wca(pcaspe, meau$design$season, scan = FALSE, nf = 2)
kta1 <- ktab.within(wit1, colnames = rep(c("S1","S2","S3","S4","S5","S6"), 4))
kta2 <- ktab.within(wit2, colnames = rep(c("S1","S2","S3","S4","S5","S6"), 4))
kcoi <- ktab.match2ktabs(kta1, kta2)
ptacoi <- pta(kcoi, scan = FALSE, nf = 2)
plot(ptacoi)
kplot(ptacoi)

Process to go from a Within Analysis to a K-tables

Description

performs the process to go from a Within Analysis to a K-tables.

Usage

ktab.within(dudiwit, rownames = NULL, colnames = NULL, tabnames = NULL)

Arguments

dudiwit

an objet of class within
rownames

the row names of the K-tables (otherwise the row names of dudiwit$tab)
colnames

the column names of the K-tables (otherwise the column names
of dudiwit$tab)
tabnames

the names of the arrays of the K-tables (otherwise the levels of the factor which defines the within-classes)

Value

a list of class ktab. See ktab

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

Examples

data(bacteria)
w1 <- data.frame(t(bacteria$espcodon))
dudi1 <- dudi.coa(w1, scann = FALSE, nf = 4)
wit1 <- wca(dudi1, bacteria$code, scannf = FALSE)
kta1 <- ktab.within(wit1)
plot(statis(kta1, scann = FALSE))

kta2 <- kta1[kta1$blo>3]
kplot(mfa(kta2, scann = FALSE))

Genetic/Environment and types of variables

Description

This data set gives meristic, genetic and morphological data frame for 306 trouts.

Usage

data(lascaux)

Format

lascaux is a list of 9 components.

riv

is a factor returning the river where 306 trouts are captured

code

vector of characters : code of the 306 trouts

sex

factor sex of the 306 trouts

meris

data frame 306 trouts - 5 meristic variables

tap

data frame of the total number of red and black points

gen

factor of the genetic code of the 306 trouts

morpho

data frame 306 trouts 37 morphological variables

colo

data frame 306 trouts 15 variables of coloring

ornem

data frame 306 trouts 15 factors (ornementation)

Source

Lascaux, J.M. (1996) Analyse de la variabilité morphologique de la truite commune (Salmo trutta L.) dans les cours d'eau du bassin pyrénéen méditerranéen. Thèse de doctorat en sciences agronomiques, INP Toulouse.

References

See a data description at http://pbil.univ-lyon1.fr/R/pdf/pps022.pdf (in French).

Examples

data(lascaux)

if(adegraphicsLoaded()) {
  g1 <- s1d.barchart(dudi.pca(lascaux$meris, scan = FALSE)$eig, psub.text = "Meristic", 
    p1d.horizontal = FALSE, plot = FALSE)
  g2 <- s1d.barchart(dudi.pca(lascaux$colo, scan = FALSE)$eig, psub.text = "Coloration", 
    p1d.horizontal = FALSE, plot = FALSE)
  g3 <- s1d.barchart(dudi.pca(na.omit(lascaux$morpho), scan = FALSE)$eig, 
    psub.text = "Morphometric", p1d.horizontal = FALSE, plot = FALSE)
  g4 <- s1d.barchart(dudi.acm(na.omit(lascaux$orne), scan = FALSE)$eig, 
    psub.text = "Ornemental", p1d.horizontal = FALSE, plot = FALSE)
  
  G <- ADEgS(c(g1, g2, g3, g4), layout = c(2, 2))
  
} else {
  par(mfrow = c(2,2))
  barplot(dudi.pca(lascaux$meris, scan = FALSE)$eig)
  title(main = "Meristic")
  barplot(dudi.pca(lascaux$colo, scan = FALSE)$eig)
  title(main = "Coloration")
  barplot(dudi.pca(na.omit(lascaux$morpho), scan = FALSE)$eig)
  title(main = "Morphometric")
  barplot(dudi.acm(na.omit(lascaux$orne), scan = FALSE)$eig)
  title(main = "Ornemental")
  par(mfrow = c(1,1))
}

Transformation of a Distance Matrix for becoming Euclidean

Description

transforms a distance matrix in a Euclidean one.

Usage

lingoes(distmat, print = FALSE, tol = 1e-07, cor.zero = TRUE)

Arguments

distmat

an object of class dist
print

if TRUE, prints the eigenvalues of the matrix
tol

a tolerance threshold for zero
cor.zero

if TRUE, zero distances are not modified

Details

The function uses the smaller positive constant k which transforms the matrix of dij2+2∗k\sqrt{d_{ij}^2 + 2 \ast k} in an Euclidean one

Value

returns an object of class dist with a Euclidean distance

Author(s)

Daniel Chessel
Stéphane Dray [email protected]

References

Lingoes, J.C. (1971) Some boundary conditions for a monotone analysis of symmetric matrices. Psychometrika, 36, 195–203.

Examples

data(capitales)
d0 <- capitales$dist
is.euclid(d0) # FALSE
d1 <- lingoes(d0, TRUE)
# Lingoes constant = 2120982
is.euclid(d1) # TRUE
plot(d0, d1)
x0 <- sort(unclass(d0))
lines(x0, sqrt(x0^2 + 2 * 2120982), lwd = 3)
 
is.euclid(sqrt(d0^2 + 2 * 2120981), tol = 1e-10) # FALSE
is.euclid(sqrt(d0^2 + 2 * 2120982), tol = 1e-10) # FALSE
is.euclid(sqrt(d0^2 + 2 * 2120983), tol = 1e-10) 
    # TRUE the smaller constant

Phylogeny and quantitative traits of lizards

Description

This data set describes the phylogeny of 18 lizards as reported by Bauwens and Díaz-Uriarte (1997). It also gives life-history traits corresponding to these 18 species.

Usage

data(lizards)

Format

lizards is a list containing the 3 following objects :

traits

is a data frame with 18 species and 8 traits.

hprA

is a character string giving the phylogenetic tree (hypothesized phylogenetic relationships based on immunological distances) in Newick format.

hprB

is a character string giving the phylogenetic tree (hypothesized phylogenetic relationships based on morphological characteristics) in Newick format.

Details

Variables of lizards$traits are the following ones : mean.L (mean length (mm)), matur.L (length at maturity (mm)), max.L (maximum length (mm)), hatch.L (hatchling length (mm)), hatch.m (hatchling mass (g)), clutch.S (Clutch size), age.mat (age at maturity (number of months of activity)), clutch.F (clutch frequency).

References

Bauwens, D., and Díaz-Uriarte, R. (1997) Covariation of life-history traits in lacertid lizards: a comparative study. American Naturalist, 149, 91–111.

See a data description at http://pbil.univ-lyon1.fr/R/pdf/pps063.pdf (in French).

Examples

data(lizards)
w <- data.frame(scalewt(log(lizards$traits)))
par(mfrow = c(1,2))
wphy <- newick2phylog(lizards$hprA)
table.phylog(w, wphy, csi = 3)
wphy <- newick2phylog(lizards$hprB)
table.phylog(w, wphy, csi = 3)
par(mfrow = c(1,1))

Leave-one-out cross-validation for a bca

Description

Leave-one-out cross-validation for bca.

Usage

## S3 method for class 'between'
loocv(x, nax = 0, progress = FALSE, parallel = FALSE, ...)
## S3 method for class 'bcaloocv'
print(x, ...)
## S3 method for class 'bcaloocv'
plot(x, xax = 1, yax = 2, ...)

Arguments

x

dudi of the bca on which cross-validation should be done

nax

list of axes for mean overlap index computation (0 = all axes)

progress

logical, TRUE = display a progress bar during computations

parallel

logical, TRUE = process cross-validation in parallel computing

xax, yax

the numbers of the x-axis and the y-axis

...

further arguments passed to or from other methods

Details

This function returns a list containing the cross-validated coordinates of the rows (the rows of the original analysis, not the rows of the bca). The dudi on which the bca was computed is redone after removing each row of the data table, one at a time. A bca is done on this new dudi and the coordinates of the missing row are computed by projection as supplementary element in the corresponding bca. This is most useful in the case p >> n (many variables and few samples), where bca graphs can show spurious groups (see Refs.)

For parallel computing (parallel argument = TRUE), the new dudi, bca and cross-validation computations are processed in parallel on all the available nodes of the computer processor(s).

Value

A list with:

- XValCoord: the cross-validated row coordinates

- PRESS: the Predicted Residual Error Sum for each row

- PRESSTot: the sum of PRESS for each bca axis

- Oij_bga: the mean overlap index for BGA

- Oij_XVal: the mean overlap index for cross-validation

- DeltaOij: the spuriousness index

Author(s)

Jean Thioulouse

References

Thioulouse J, Renaud S, Dufour AB, Dray S. Overcoming the Spurious Groups Problem in Between-Group PCA. Evolutionary Biology (2021). (Accepted).

Cardini A, Polly D. Cross-validated Between Group PCA Scatterplots: A Solution to Spurious Group Separation ? Evolutionary Biology (2020) 47:85–95. doi:10.1007/s11692-020-09494-x

Cardini A, O'Higgins P, Rohlf J. Seeing Distinct Groups Where There are None: Spurious Patterns from Between-Group PCA. Evolutionary Biology (2019) 46:303-316. doi:10.1007/s11692-019-09487-5

Bookstein F. Pathologies of Between-Groups Principal Components Analysis in Geometric Morphometrics. Evolutionary Biology (2019) 46:271-302. doi:10.1007/s11692-019-09484-8

See Also

loocv.dudi loocv.discrimin

Examples

# Data = meaudret
data(meaudret)
pca1 <- dudi.pca(meaudret$env, scannf = FALSE, nf = 3)
bca1 <- bca(pca1, meaudret$design$site, scannf = FALSE, nf = 3)
pst1 <- paste0("Meaudret BGA randtest: p=",
randtest(bca1)$pvalue, " ratio=", round(bca1$ratio, 2))
xbca1 <- loocv(bca1, progress = TRUE)

if(adegraphicsLoaded()){
    sc1 <- s.class(bca1$ls, meaudret$design$site, col = TRUE,
    psub.text = pst1, ellipseSize=0, chullSize=1, plot = FALSE)
    sc2 <- s.class(xbca1$XValCoord, meaudret$design$site,
    col = TRUE, psub.text = "Meaudret cross-validation",
    ellipseSize=0, chullSize=1, plot = FALSE)
    ADEgS(list(sc1, sc2))
} else {
	par(mfrow=c(2,2))
	s.chull(dfxy = bca1$ls, fac = meaudret$design$site, cpoint = 1, 
    	col = hcl.colors(5, "Dark 2"), sub = pst1)
    s.class(bca1$ls, meaudret$design$site, col = hcl.colors(5, "Dark 2"),
    	cellipse = 0, add.plot = TRUE)
	s.chull(dfxy = xbca1$XValCoord, fac = meaudret$design$site, cpoint = 1, 
    	col = hcl.colors(5, "Dark 2"), sub = "Meaudret cross-validation")
    s.class(xbca1$XValCoord, meaudret$design$site, col = hcl.colors(5, "Dark 2"),
    	cellipse = 0, add.plot = TRUE)
}
## Not run: 
# Data = rnorm()
set.seed(9)
fac1 <- as.factor(rep(1:3, each = 10))
tab <- as.data.frame(matrix(rnorm(10800), nrow = 30))
pca2 <- dudi.pca(tab, scannf = FALSE)
bca2 <- bca(pca2, fac1, scannf = FALSE)
pst2 <- paste0("rnorm spurious groups: p=",
randtest(bca2)$pvalue, " ratio=", round(bca2$ratio, 2))
xbca2 <- loocv(bca2, progress = TRUE)
if(adegraphicsLoaded()){
	sc3 <- s.class(bca2$ls, fac1, col = TRUE,
		psub.text = pst2, ellipseSize=0, chullSize=1,
		xlim = c(-8, 8), ylim = c(-8, 8), plot = FALSE)
	sc4 <- s.class(xbca2$XValCoord, fac1, col = TRUE,
		psub.text = "rnorm cross-validation", ellipseSize=0,
		chullSize=1, xlim = c(-8, 8), ylim = c(-8, 8), plot = FALSE)
	ADEgS(list(sc3, sc4))
} else {
	par(mfrow=c(2,2))
	s.chull(bca2$ls, fac1, optchull = 1, cpoint = 1, xlim = c(-8, 8), ylim = c(-8, 8),
    	col = hcl.colors(3, "Dark 2"), sub = pst2)
    s.class(bca2$ls, fac1, xlim = c(-8, 8), ylim = c(-8, 8),
    	col = hcl.colors(3, "Dark 2"), cellipse = 0, add.plot = TRUE)
	s.chull(xbca2$XValCoord, fac1, optchull = 1, cpoint = 1, xlim = c(-8, 8),
		ylim = c(-8, 8), col = hcl.colors(3, "Dark 2"), sub = "rnorm cross-validation")
    s.class(xbca2$XValCoord, fac1, xlim = c(-8, 8), ylim = c(-8, 8),
    	col = hcl.colors(3, "Dark 2"), cellipse = 0, add.plot = TRUE)
}

## End(Not run)

Leave-one-out cross-validation for a discrimin analysis

Description

Leave-one-out cross-validation to test the existence of groups in a discrimin analysis.

Usage

## S3 method for class 'discrimin'
loocv(x, nax = 0, progress = FALSE, ...)
## S3 method for class 'discloocv'
print(x, ...)
## S3 method for class 'discloocv'
plot(x, xax = 1, yax = 2, ...)

Arguments

x

the discrimin analysis on which cross-validation should be done

nax

list of axes for mean overlap index computation (0 = all axes)

progress

logical to display a progress bar during computations (see the progress package)

xax, yax

the numbers of the x-axis and the y-axis

...

further arguments passed to or from other methods

Details

This function returns a list containing the cross-validated coordinates of the rows. The analysis on which the discrimin was computed is redone after removing each row of the data table, one at a time. A discrimin analysis is done on this new analysis and the coordinates of the missing row are computed by projection as supplementary element in the new discrimin analysis. This can be useful to check that the groups evidenced by the discrimin analysis are supported.

Value

A list with:

- XValCoord: the cross-validated row coordinates

- PRESS: the Predicted Residual Error Sum for each row

- PRESSTot: the sum of PRESS for each bca axis

- Oij_disc: the mean overlap index for the discriminant analysis

- Oij_XVal: the mean overlap index for cross-validation

- DeltaOij: the spuriousness index

Author(s)

Jean Thioulouse

See Also

loocv.dudi loocv.between

Examples

## Not run: 
# Data = skulls
data(skulls)
pcaskul <- dudi.pca(skulls, scan = FALSE)
facskul <- gl(5,30)
diskul <- discrimin(pcaskul, facskul, scan = FALSE)
xdiskul <- loocv(diskul, progress = TRUE)
oijdisc <- xdiskul$Oij_disc
oijxval <- xdiskul$Oij_XVal
Doij <- (oijxval - oijdisc)/0.5*100
pst1 <- paste0("Skulls discrimin randtest: p=", round(randtest(diskul)$pvalue, 4), 
", Oij = ", round(oijdisc,2))
pst2 <- paste0("Skulls cross-validation: Oij = ", round(oijxval,2), ", dOij = ",
round(Doij), "%")
if (adegraphicsLoaded()) {
	sc1 <- s.class(diskul$li, facskul, col = TRUE, psub.text = pst1, ellipseSize=0,
	chullSize=1, plot = FALSE)
	sc2 <- s.class(xdiskul$XValCoord, facskul, col = TRUE, psub.text = pst2,
	ellipseSize=0, chullSize=1, plot = FALSE)
	ADEgS(list(sc1, sc2), layout=c(2,2))
} else {
	par(mfrow=c(2,2))
	s.class(diskul$li, facskul, sub = pst1)
	s.class(xdiskul$XValCoord, facskul, sub = pst2)
}
data(chazeb)
pcacz <- dudi.pca(chazeb$tab, scan = FALSE)
discz <- discrimin(pcacz, chazeb$cla, scan = FALSE)
xdiscz <- loocv(discz, progress = TRUE)
oijdiscz <- xdiscz$Oij_disc
oijxvalz <- xdiscz$Oij_XVal
Doijz <- (oijxvalz - oijdiscz)/0.5*100
pst1 <- paste0("Chazeb discrimin randtest: p=", round(randtest(discz)$pvalue, 4), 
", Oij = ", round(oijdiscz,2))
pst2 <- paste0("Chazeb cross-validation: Oij = ", round(oijxvalz,2), ", dOij = ", 
round(Doijz), "%")
if (adegraphicsLoaded()) {
	tabi <- cbind(discz$li, pcacz$tab)
	gr1 <- s.class(tabi, xax=1, yax=2:7, chazeb$cla, col = TRUE, plot = FALSE)
	for (i in 1:6) gr1[[i]] <- update(gr1[[i]], psub.text = names(tabi)[i+1],
	plot = FALSE)
	pos1 <- gr1@positions
	pos1[,1] <- c(0, .3333, .6667, 0, .3333, .6667)
	pos1[,2] <- c(.6667, .6667, .6667, .3333, .3333, .3333)
	pos1[,3] <- c(.3333, .6667, 1, .3333, .6667, 1)
	pos1[,4] <- c(1, 1, 1, .6667, .6667, .6667)
	gr1@positions <- pos1
	sc1 <- s1d.gauss(discz$li, chazeb$cla, col = TRUE, psub.text = pst1,
	plot = FALSE)
	sc2 <- s1d.gauss(xdiscz$XValCoord, chazeb$cla, col = TRUE, psub.text = pst2,
	plot = FALSE)
	ADEgS(list(gr1[[1]], gr1[[2]], gr1[[3]], gr1[[4]], gr1[[5]], gr1[[6]], sc1, sc2))
} else {
	dev.new()
	sco.gauss(discz$li[,1], as.data.frame(chazeb$cla), sub = pst1)
	dev.new()
	sco.gauss(xdiscz$XValCoord[,1], as.data.frame(chazeb$cla), sub = pst2)
}

## End(Not run)

Leave-one-out cross-validation for a dudi

Description

Leave-one-out cross-validation to check the dispersion of row coordinates in a dudi.

Usage

## S3 method for class 'dudi'
loocv(x, progress = FALSE, ...)

Arguments

x

the dudi of the bca on which cross-validation should be done

progress

logical to display a progress bar during computations (see the progress package)

...

further arguments passed to or from other methods

Details

This function does a cross-validation of the row coordinates of a dudi. Each row is removed from the table one at a time, and its coordinates are computed by projection of this row in the analysis of the table with the removed row. This can be used to check the sensitivity of an analysis to outliers. The cross-validated and original coordinates can be compared with the s.match function (see example).

Value

A list with:

- XValCoord: the cross-validated row coordinates

- PRESS: the Predicted Residual Error Sum for each row

- PRESSTot: the sum of PRESS for each bca axis

Author(s)

Jean Thioulouse

See Also

loocv.between, loocv.discrimin, suprow, s.match

Examples

data(meaudret)
envpca <- dudi.pca(meaudret$env, scannf = FALSE, nf = 3)
xvpca <- loocv(envpca)
s.match(envpca$li, xvpca$XValCoord)

Landmarks

Description

This data set gives the landmarks of a macaca at the ages of 0.9 and 5.77 years.

Usage

data(macaca)

Format

macaca is a list of 2 components.

xy1

is a data frame with 72 points and 2 coordinates.

xy2

is a data frame with 72 points and 2 coordinates.

Source

Olshan, A.F., Siegel, A.F. and Swindler, D.R. (1982) Robust and least-squares orthogonal mapping: Methods for the study of cephalofacial form and growth. American Journal of Physical Anthropology, 59, 131–137.

Examples

data(macaca)
pro1 <- procuste(macaca$xy1, macaca$xy2, scal = FALSE)
pro2 <- procuste(macaca$xy1, macaca$xy2)
  
if(adegraphicsLoaded()) {
  g1 <- s.match(macaca$xy1, macaca$xy2, plab.cex = 0, plot = FALSE)
  g2 <- s.match(pro1$tabX, pro1$rotY, plab.cex = 0.7, plot = FALSE)
  g3 <- s.match(pro1$tabY, pro1$rotX, plab.cex = 0.7, plot = FALSE)
  g4 <- s.match(pro2$tabY, pro2$rotX, plab.cex = 0.7, plot = FALSE)
  G <- ADEgS(c(g1, g2, g3, g4), layout = c(2, 2))

} else {
  par(mfrow = c(2,2))
  s.match(macaca$xy1, macaca$xy2, clab = 0)
  s.match(pro1$tabX, pro1$rotY, clab = 0.7)
  s.match(pro1$tabY, pro1$rotX, clab = 0.7)
  s.match(pro2$tabY, pro2$rotX, clab = 0.7)
  par(mfrow = c(1,1))
}

Wine Tasting

Description

The macon data frame has 8 rows-wines and 25 columns-tasters. Each column is a classification of 8 wines (Beaujolais, France).

Usage

data(macon)

Source

Foire Nationale des Vins de France, Mâcon, 1985

Examples

data(macon)
s.corcircle(dudi.pca(macon, scan = FALSE)$co)

Assemblages of Macroinvertebrates in the Loire River (France)

Description

A total of 38 sites were surveyed along 800 km of the Loire River yielding 40 species of Trichoptera and Coleoptera sampled from riffle habitats. The river was divided into three regions according to geology: granitic highlands (Region#1), limestone lowlands (Region#2) and granitic lowlands (Region#3). This data set has been collected for analyzing changes in macroinvertebrate assemblages along the course of a large river. Four criterias are given here: variation in 1/ species composition and relative abundance, 2/ taxonomic composition, 3/ Body Sizes, 4/ Feeding habits.

Usage

data(macroloire)

Format

macroloire is a list of 5 components.

fau

is a data frame containing the abundance of each species in each station.

traits

is a data frame describes two traits : the maximal sizes and feeding habits for each species. Each trait is divided into categories. The maximal size achieved by the species is divided into four length categories: <= 5mm ; >5-10mm ; >10-20mm ; >20-40mm. Feeding habits comprise seven categories: engulfers, shredders, scrapers, deposit-feeders, active filter-feeders, passive filter-feeders and piercers, in this order. The affinity of each species to each trait category is quantified using a fuzzy coding approach. A score is assigned to each species for describing its affinity for a given trait category from "0" which indicates no affinity to "3" which indicates high affinity. These affinities are further transformed into percentage per trait per species.

taxo

is a data frame with species and 3 factors: Genus, Family and Order. It is a data frame of class "taxo": the variables are factors giving nested classifications.

envir

is a data frame giving for each station, its name (variable "SamplingSite"), its distance from the source (km, variable "Distance"), its altitude (m, variable "Altitude"), its position regarding the dams [1: before the first dam; 2: after the first dam; 3: after the second dam] (variable "Dam"), its position in one of the three regions defined according to geology: granitic highlands, limestone lowlands and granitic lowlands (variable "Morphoregion"), presence of confluence (variable "Confluence")

labels

is a data frame containing the latin names of the species.

Source

Ivol, J.M., Guinand, B., Richoux, P. and Tachet, H. (1997) Longitudinal changes in Trichoptera and Coleoptera assemblages and environmental conditions in the Loire River (France). Archiv for Hydrobiologie, 138, 525–557.

Pavoine S. and Doledec S. (2005) The apportionment of quadratic entropy: a useful alternative for partitioning diversity in ecological data. Environmental and Ecological Statistics, 12, 125–138.

Examples

data(macroloire)
    apqe.Equi <- apqe(macroloire$fau, , macroloire$morphoregions)
    apqe.Equi
    #test.Equi <- randtest.apqe(apqe.Equi, method = "aggregated", 99)
    #plot(test.Equi)

    ## Not run:  

    m.phy <- taxo2phylog(macroloire$taxo)
    apqe.Tax <- apqe(macroloire$fau, m.phy$Wdist, macroloire$morphoregions)
    apqe.Tax
    #test.Tax <- randtest.apqe(apqe.Tax, method = "aggregated", 99)
    #plot(test.Tax)

    dSize <- sqrt(dist.prop(macroloire$traits[ ,1:4], method = 2))
    apqe.Size <- apqe(macroloire$fau, dSize, macroloire$morphoregions)
    apqe.Size
    #test.Size <- randtest.apqe(apqe.Size, method = "aggregated", 99)
    #plot(test.Size)

    dFeed <- sqrt(dist.prop(macroloire$traits[ ,-(1:4)], method = 2))
    apqe.Feed <- apqe(macroloire$fau, dFeed, macroloire$morphoregions)
    apqe.Feed
    #test.Feed <- randtest.apqe(apqe.Feed, method = "aggregated", 99)
    #plot(test.Size)

    
## End(Not run)

Phyto-Ecological Survey

Description

This data set gives environmental and spatial informations about species and sites.

Usage

data(mafragh)

Format

mafragh is a list with the following components:

xy

the coordinates of 97 sites

flo

a data frame with 97 sites and 56 species

neig

the neighbourhood graph of the 97 sites (an object of class neig)

env

a data frame with 97 sites and 11 environmental variables

partition

a factor classifying the 97 sites in 7 classes

area

a data frame of class area

tre

a character providing the phylogeny as a newick object

traits

a list of data frame. Each data frame provides the value of biological traits for plant species

nb

the neighbourhood graph of the 97 Mafragh sites (an object of class nb)

Spatial

the map of the 97 Mafragh sites (an object of the class SpatialPolygons of sp)

spenames

a data frame with 56 rows (species) and 2 columns (names)

Spatial.contour

the contour of the Magragh map (an object of the class SpatialPolygons of sp)

Source

de Bélair, Gérard and Bencheikh-Lehocine, Mahmoud (1987) Composition et déterminisme de la végétation d'une plaine côtière marécageuse : La Mafragh (Annaba, Algérie). Bulletin d'Ecologie, 18(4), 393–407.

Pavoine, S., Vela, E., Gachet, S., de Bélair, G. and Bonsall, M. B. (2011) Linking patterns in phylogeny, traits, abiotic variables and space: a novel approach to linking environmental filtering and plant community assembly. Journal of Ecology, 99, 165–175. doi:10.1111/j.1365-2745.2010.01743.x

References

See a data description at http://pbil.univ-lyon1.fr/R/pdf/pps053.pdf (in French).

Examples

data(mafragh)
coa1 <- dudi.coa(mafragh$flo, scan = FALSE)
pca1 <- dudi.pca(mafragh$xy, scan = FALSE)
if(adegraphicsLoaded()) {
  g1 <- s.label(mafragh$xy, nb = mafragh$nb, psub.text = "Samples & Neighbourhood graph", 
    plot = FALSE)
  g2 <- s.value(mafragh$xy, coa1$li[, 1], psub.text = "Axis 1 - COA", plot = FALSE)
  g3 <- s.value(mafragh$xy, pca1$li[, 1], psub.text = "Axis 1 - PCA", plot = FALSE)
  g4 <- s.class(pca1$li, mafragh$partition, psub.text = "Plane 1-2 - PCA", plot = FALSE)
  g5 <- s.class(coa1$li, mafragh$partition, psub.text = "Plane 1-2 - COA", plot = FALSE)
  g6 <- s.class(mafragh$xy, mafragh$partition, chullSize = 1, ellipseSize = 0, starSize = 0, 
    ppoints.cex = 0, plot = FALSE)
  G <- ADEgS(c(g1, g2, g3, g4, g5, g6), layout = c(3, 2))

} else {
  par(mfrow = c(3, 2))
  s.label(mafragh$xy, inc = FALSE, neig = mafragh$neig, sub = "Samples & Neighbourhood graph")
  s.value(mafragh$xy, coa1$li[, 1], sub = "Axis 1 - COA")
  s.value(mafragh$xy, pca1$li[, 1], sub = "Axis 1 - PCA")
  s.class(pca1$li, mafragh$partition, sub = "Plane 1-2 - PCA")
  s.class(coa1$li, mafragh$partition, sub = "Plane 1-2 - COA")
  s.chull(mafragh$xy, mafragh$partition, optchull = 1)
  par(mfrow = c(1, 1))
}

## Not run: 
link1 <- area2link(mafragh$area)
neig1 <- neig(mat01 = 1*(link1 > 0))
nb1 <- neig2nb(neig1)

if(adegraphicsLoaded()) {
  if(requireNamespace("sp", quietly = TRUE)) {
    g7 <- s.label(mafragh$xy, Sp = mafragh$Spatial, pSp.col = "white", plot = FALSE)
    g8 <- s.label(mafragh$xy, Sp = mafragh$Spatial, pSp.col = "white", nb = nb1, plab.cex = 0, 
      pnb.node.cex = 0, ppoints.cex = 0, plot = FALSE)
    G <- ADEgS(c(g7, g8), layout = c(2, 1))
  }

} else {
  par(mfrow = c(2, 1))
  area.plot(mafragh$area, center = mafragh$xy, clab = 0.75)
  area.plot(mafragh$area, center = mafragh$xy, graph = neig1)
  par(mfrow = c(1, 1))
}

if(requireNamespace("spdep", quietly = TRUE)) {
  lw1 <- apply(link1, 1, function(x) x[x > 0])
  listw1 <- spdep::nb2listw(nb1, lw1)
  coa1 <- dudi.coa(mafragh$flo, scan = FALSE, nf = 4)
  ms1 <- multispati(coa1, listw1, scan = FALSE, nfp = 2, nfn = 0)
  summary(ms1)
  
  if(adegraphicsLoaded()) {
    if(requireNamespace("lattice", quietly = TRUE)) {
      g9 <- s1d.barchart(coa1$eig, p1d.hori = FALSE, plot = FALSE)
      g10 <- s1d.barchart(ms1$eig, p1d.hori = FALSE, plot = FALSE)
      g11 <- s.corcircle(ms1$as, plot = FALSE)
      g12 <- lattice::xyplot(ms1$li[, 1] ~ coa1$li[, 1])
      G <- ADEgS(list(g9, g10, g11, g12), layout = c(2, 2))
    }
    
  } else {    
    par(mfrow = c(2, 2))
    barplot(coa1$eig)
    barplot(ms1$eig)
    s.corcircle(ms1$as)
    plot(coa1$li[, 1], ms1$li[, 1])
    par(mfrow = c(1, 1))
  }
}

## End(Not run)

Mantel test (correlation between two distance matrices (in C).)

Description

Performs a Mantel test between two distance matrices.

Usage

mantel.randtest(m1, m2, nrepet = 999, ...)

Arguments

m1

an object of class dist
m2

an object of class dist
nrepet

the number of permutations
...

further arguments passed to or from other methods

Value

an object of class randtest (randomization tests)

Author(s)

Jean Thioulouse [email protected]

References

Mantel, N. (1967) The detection of disease clustering and a generalized regression approach. Cancer Research, 27, 209–220.

Examples

data(yanomama)
gen <- quasieuclid(as.dist(yanomama$gen))
geo <- quasieuclid(as.dist(yanomama$geo))
plot(r1 <- mantel.randtest(geo,gen), main = "Mantel's test")
r1

Mantel test (correlation between two distance matrices (in R).)

Description

Performs a Mantel test between two distance matrices.

Usage

mantel.rtest(m1, m2, nrepet = 99, ...)

Arguments

m1

an object of class dist
m2

an object of class dist
nrepet

the number of permutations
...

further arguments passed to or from other methods

Value

an object of class rtest (randomization tests)

Author(s)

Daniel Chessel
Stéphane Dray [email protected]

References

Mantel, N. (1967) The detection of disease clustering and a generalized regression approach. Cancer Research, 27, 209–220.

Examples

data(yanomama)
    gen <- quasieuclid(as.dist(yanomama$gen))
    geo <- quasieuclid(as.dist(yanomama$geo))
    plot(r1 <- mantel.rtest(geo,gen), main = "Mantel's test")
    r1

Phylogeny and quantitative traits of flowers

Description

This data set describes the phylogeny of 17 flowers as reported by Ackerly and Donoghue (1998). It also gives 31 traits corresponding to these 17 species.

Usage

data(maples)

Format

tithonia is a list containing the 2 following objects :

tre

is a character string giving the phylogenetic tree in Newick format.

tab

is a data frame with 17 species and 31 traits

References

Ackerly, D. D. and Donoghue, M.J. (1998) Leaf size, sapling allometry, and Corner's rules: phylogeny and correlated evolution in Maples (Acer). American Naturalist, 152, 767–791.

Examples

data(maples)
phy <- newick2phylog(maples$tre)
dom <- maples$tab$Dom
bif <- maples$tab$Bif
if (requireNamespace("adephylo", quietly = TRUE) & requireNamespace("ape", quietly = TRUE)) {
  phylo <- ape::read.tree(text = maples$tre)
  adephylo::orthogram(dom, tre = phylo)
  adephylo::orthogram(bif, tre = phylo)
  par(mfrow = c(1, 2))
  dotchart.phylog(phy, dom)
  dotchart.phylog(phy, bif, clabel.nodes = 0.7)
  par(mfrow = c(1, 1))
  plot(bif, dom, pch = 20)
  abline(lm(dom~bif))
  summary(lm(dom~bif))
  cor.test(bif, dom)
  pic.bif <- ape::pic(bif, phylo)
  pic.dom <- ape::pic(dom, phylo)
  cor.test(pic.bif, pic.dom)
}

Correspondence Analysis Table

Description

This array contains the socio-professionnal repartitions of 5850 couples.

Usage

data(mariages)

Format

The mariages data frame has 9 rows and 9 columns. The rows represent the wife's socio-professionnal category and the columns the husband's socio-professionnal category (1982).

Codes for rows and columns are identical : agri (Farmers), ouva (Farm workers), pat (Company directors (commerce and industry)), sup (Liberal profession, executives and higher intellectual professions), moy (Intermediate professions), emp (Other white-collar workers), ouv (Manual workers), serv (Domestic staff), aut (other workers).

Source

Vallet, L.A. (1986) Activité professionnelle de la femme mariée et détermination de la position sociale de la famille. Un test empirique : la France entre 1962 et 1982. Revue Française de Sociologie, 27, 656–696.

Examples

data(mariages)
w <- dudi.coa(mariages, scan = FALSE, nf = 3)

if(adegraphicsLoaded()) {
  g1 <- scatter(w, met = 1, posi = "bottomleft", plot = FALSE)
  g2 <- scatter(w, met = 2, posi = "bottomleft", plot = FALSE)
  g3 <- scatter(w, met = 3, posi = "bottomleft", plot = FALSE)
  ## g4 <- score(w, 3)
  G <- ADEgS(list(g1, g2, g3), layout = c(2, 2))

} else {
  par(mfrow = c(2, 2))
  scatter(w, met = 1, posi = "bottom")
  scatter(w, met = 2, posi = "bottom")
  scatter(w, met = 3, posi = "bottom")
  score(w, 3)
  par(mfrow = c(1, 1))
}

Multiblock principal component analysis with instrumental variables

Description

Function to perform a multiblock redundancy analysis of several explanatory blocks (X1,…,Xk)(X_1, \dots, X_k), defined as an object of class ktab, to explain a dependent dataset $Y$, defined as an object of class dudi

Usage

mbpcaiv(dudiY, ktabX, scale = TRUE, option = c("uniform", "none"), scannf = TRUE, nf = 2)

Arguments

dudiY

an object of class dudi containing the dependent variables
ktabX

an object of class ktab containing the blocks of explanatory variables
scale

logical value indicating whether the explanatory variables should be standardized
option

an option for the block weighting. If uniform, the block weight is equal to $1/K$ for (X1,…,XK)(X_1, \dots, X_K) and to $1$ for $X$ and $Y$. If none, the block weight is equal to the block inertia
scannf

logical value indicating whether the eigenvalues bar plot should be displayed
nf

integer indicating the number of kept dimensions

Value

A list containing the following components is returned:

call

the matching call
tabY

data frame of dependent variables centered, eventually scaled (if scale=TRUE) and weighted (if option="uniform")
tabX

data frame of explanatory variables centered, eventually scaled (if scale=TRUE) and weighted (if option="uniform")
TL, TC

data frame useful to manage graphical outputs
nf

numeric value indicating the number of kept dimensions
lw

numeric vector of row weights
X.cw

numeric vector of column weighs for the explanalatory dataset
blo

vector of the numbers of variables in each explanatory dataset
rank

maximum rank of the analysis
eig

numeric vector containing the eigenvalues
lX

matrix of the global components associated with the whole explanatory dataset (scores of the individuals)
lY

matrix of the components associated with the dependent dataset
Yc1

matrix of the variable loadings associated with the dependent dataset
Tli

matrix containing the partial components associated with each explanatory dataset
Tl1

matrix containing the normalized partial components associated with each explanatory dataset
Tfa

matrix containing the partial loadings associated with each explanatory dataset
cov2

squared covariance between lY and Tl1
Yco

matrix of the regression coefficients of the dependent dataset onto the global components
faX

matrix of the regression coefficients of the whole explanatory dataset onto the global components
XYcoef

list of matrices of the regression coefficients of the whole explanatory dataset onto the dependent dataset
bip

block importances for a given dimension
bipc

cumulated block importances for a given number of dimensions
vip

variable importances for a given dimension
vipc

cumulated variable importances for a given number of dimensions

Author(s)

Stéphanie Bougeard ([email protected]) and Stéphane Dray ([email protected])

References

Bougeard, S., Qannari, E.M. and Rose, N. (2011) Multiblock Redundancy Analysis: interpretation tools and application in epidemiology. Journal of Chemometrics, 23, 1-9

Bougeard, S. and Dray S. (2018) Supervised Multiblock Analysis in R with the ade4 Package. Journal of Statistical Software, 86 (1), 1-17. doi:10.18637/jss.v086.i01

See Also

mbpls, testdim.multiblock, randboot.multiblock

Examples

data(chickenk)
Mortality <- chickenk[[1]]
dudiY.chick <- dudi.pca(Mortality, center = TRUE, scale = TRUE, scannf =
FALSE)
ktabX.chick <- ktab.list.df(chickenk[2:5])
resmbpcaiv.chick <- mbpcaiv(dudiY.chick, ktabX.chick, scale = TRUE,
option = "uniform", scannf = FALSE)
summary(resmbpcaiv.chick)
if(adegraphicsLoaded())
plot(resmbpcaiv.chick)

Multiblock partial least squares

Description

Function to perform a multiblock partial least squares (PLS) of several explanatory blocks (X1,…,Xk)(X_1, \dots, X_k) defined as an object of class ktab, to explain a dependent dataset $Y$ defined as an object of class dudi

Usage

mbpls(dudiY, ktabX, scale = TRUE, option = c("uniform", "none"), scannf = TRUE, nf = 2)

Arguments

dudiY

an object of class dudi containing the dependent variables
ktabX

an object of class ktab containing the blocks of explanatory variables
scale

logical value indicating whether the explanatory variables should be standardized
option

an option for the block weighting. If uniform, the block weight is equal to $1/K$ for (X1,…,XK)(X_1, \dots, X_K) and to $1$ for $X$ and $Y$. If none, the block weight is equal to the block inertia
scannf

logical value indicating whether the eigenvalues bar plot should be displayed
nf

integer indicating the number of kept dimensions

Value

A list containing the following components is returned:

call

the matching call
tabY

data frame of dependent variables centered, eventually scaled (if scale=TRUE) and weighted (if option="uniform")
tabX

data frame of explanatory variables centered, eventually scaled (if scale=TRUE) and weighted (if option="uniform")
TL, TC

data frame useful to manage graphical outputs
nf

numeric value indicating the number of kept dimensions
lw

numeric vector of row weights
X.cw

numeric vector of column weighs for the explanalatory dataset
blo

vector of the numbers of variables in each explanatory dataset
rank

maximum rank of the analysis
eig

numeric vector containing the eigenvalues
lX

matrix of the global components associated with the whole explanatory dataset (scores of the individuals)
lY

matrix of the components associated with the dependent dataset
Yc1

matrix of the variable loadings associated with the dependent dataset
cov2

squared covariance between lY and TlX
Tc1

matrix containing the partial loadings associated with each explanatory dataset (unit norm)
TlX

matrix containing the partial components associated with each explanatory dataset
faX

matrix of the regression coefficients of the whole explanatory dataset onto the global components
XYcoef

list of matrices of the regression coefficients of the whole explanatory dataset onto the dependent dataset
bip

block importances for a given dimension
bipc

cumulated block importances for a given number of dimensions
vip

variable importances for a given dimension
vipc

cumulated variable importances for a given number of dimensions

Author(s)

Stéphanie Bougeard ([email protected]) and Stéphane Dray ([email protected])

References

Bougeard, S., Qannari, E.M., Lupo, C. and Hanafi, M. (2011). From multiblock partial least squares to multiblock redundancy analysis. A continuum approach. Informatica, 22(1), 11-26

Bougeard, S. and Dray S. (2018) Supervised Multiblock Analysis in R with the ade4 Package. Journal of Statistical Software, 86 (1), 1-17. doi:10.18637/jss.v086.i01

See Also

mbpls, testdim.multiblock, randboot.multiblock

Examples

data(chickenk)
Mortality <- chickenk[[1]]
dudiY.chick <- dudi.pca(Mortality, center = TRUE, scale = TRUE, scannf =
FALSE)
ktabX.chick <- ktab.list.df(chickenk[2:5])
resmbpls.chick <- mbpls(dudiY.chick, ktabX.chick, scale = TRUE,
option = "uniform", scannf = FALSE)
summary(resmbpls.chick)
if(adegraphicsLoaded())
plot(resmbpls.chick)

Multiple CO-inertia Analysis

Description

performs a multiple CO-inertia analysis, using an object of class ktab.

Usage

mcoa(X, option = c("inertia", "lambda1", "uniform", "internal"), 
    scannf = TRUE, nf = 3, tol = 1e-07)
## S3 method for class 'mcoa'
print(x, ...)
## S3 method for class 'mcoa'
summary(object, ...)
## S3 method for class 'mcoa'
plot(x, xax = 1, yax = 2, eig.bottom = TRUE, ...)

Arguments

X

an object of class ktab
option

a string of characters for the weightings of the arrays options :

"inertia"

weighting of group k by the inverse of the total inertia of the array k

"lambda1"

weighting of group k by the inverse of the first eigenvalue of the k analysis

"uniform"

uniform weighting of groups

"internal"

weighting included in X$tabw
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes
tol

a tolerance threshold, an eigenvalue is considered positive if it is larger than -tol*lambda1 where lambda1 is the largest eigenvalue.
x, object

an object of class 'mcoa'
...

further arguments passed to or from other methods
xax, yax

the numbers of the x-axis and the y-axis
eig.bottom

a logical value indicating whether the eigenvalues bar plot should be added

Value

mcoa returns a list of class 'mcoa' containing :

pseudoeig

a numeric vector with the all pseudo eigenvalues
call

the call-up order
nf

a numeric value indicating the number of kept axes
SynVar

a data frame with the synthetic scores
axis

a data frame with the co-inertia axes
Tli

a data frame with the co-inertia coordinates
Tl1

a data frame with the co-inertia normed scores
Tax

a data frame with the inertia axes onto co-inertia axis
Tco

a data frame with the column coordinates onto synthetic scores
TL

a data frame with the factors for Tli Tl1
TC

a data frame with the factors for Tco
T4

a data frame with the factors for Tax
lambda

a data frame with the all eigenvalues (computed on the separate analyses)
cov2

a numeric vector with the all pseudo eigenvalues (synthetic analysis)

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

References

Chessel, D. and Hanafi, M. (1996) Analyses de la co-inertie de K nuages de points, Revue de Statistique Appliquée, 44, 35–60.

Examples

data(friday87)
w1 <- data.frame(scale(friday87$fau, scal = FALSE))
w2 <- ktab.data.frame(w1, friday87$fau.blo, tabnames = friday87$tab.names)
mcoa1 <- mcoa(w2, "lambda1", scan = FALSE)
mcoa1
summary(mcoa1)
plot(mcoa1)

Multiple Double Principal Coordinate Analysis

Description

The DPCoA analysis (see dpcoa) has been developed by Pavoine et al. (2004). It has been used in genetics for describing inter-population nucleotide diversity. However, this procedure can only be used with one locus. In order to measure and describe nucleotide diversity with more than one locus, we developed three versions of multiple DPCoA by using three ordination methods: multiple co-inertia analysis, STATIS, and multiple factorial analysis. The multiple DPCoA allows the impact of various loci in the measurement and description of diversity to be quantified and described. This method is general enough to handle a large variety of data sets. It complements existing methods such as the analysis of molecular variance or other analyses based on linkage disequilibrium measures, and is very useful to study the impact of various loci on the measurement of diversity.

Usage

mdpcoa(msamples, mdistances = NULL, method = 
    c("mcoa", "statis", "mfa"), 
    option = c("inertia", "lambda1", "uniform", "internal"), 
    scannf = TRUE, nf = 3, full = TRUE, 
    nfsep = NULL, tol = 1e-07)
kplotX.mdpcoa(object, xax = 1, yax = 2, mfrow = NULL, 
    which.tab = 1:length(object$nX), includepop = FALSE, 
    clab = 0.7, cpoi = 0.7, unique.scale = FALSE, 
    csub = 2, possub = "bottomright")
prep.mdpcoa(dnaobj, pop, model, ...)

Arguments

msamples

A list of data frames with the populations as columns, alleles as rows and abundances as entries. All the tables should have equal numbers of columns (populations). Each table corresponds to a locus;
mdistances

A list of objects of class 'dist', corresponding to the distances among alleles. The order of the loci should be the same in msamples as in mdistances;
method

One of the three possibilities: "mcoa", "statis", or "mfa". If a vector is given, only its first value is considered;
option

One of the four possibilities for normalizing the population coordinates over the loci: "inertia", "lambda1", "uniform", or "internal". These options are used with MCoA and MFA only;
scannf

a logical value indicating whether the eigenvalues bar plots should be displayed;
nf

if scannf is FALSE, an integer indicating the number of kept axes for the multiple analysis;
full

a logical value indicating whether all the axes should be kept in the separated analyses (one analysis, DPCoA, per locus);
nfsep

if full is FALSE, a vector indicating the number of kept axes for each of the separated analyses;
tol

a tolerance threshold for null eigenvalues (a value less than tol times the first one is considered as null);
object

an object of class 'mdpcoa';
xax

the number of the x-axis;
yax

the number of the y-axis;
mfrow

a vector of the form 'c(nr,nc)', otherwise computed by as special own function 'n2mfrow';
which.tab

a numeric vector containing the numbers of the loci to analyse;
includepop

a logical indicating if the populations must be displayed. In that case, the alleles are displayed by points and the populations by labels;
clab

a character size for the labels;
cpoi

a character size for plotting the points, used with 'par("cex")'*cpoint. If zero, no points are drawn;
unique.scale

if TRUE, all the arrays of figures have the same scale;
csub

a character size for the labels of the arrays of figures used with 'par("cex")*csub';
possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright");
dnaobj

a list of dna sequences that can be obtained with the function read.dna of the ape package;
pop

a factor that gives the name of the population to which each sequence belongs;
model

a vector giving the model to be applied for the calculations of the distances for each locus. One model should be attributed to each locus, given that the loci are in alphabetical order. The models can take the following values: "raw", "JC69", "K80" (the default), "F81", "K81", "F84", "BH87", "T92", "TN93", "GG95", "logdet", or "paralin". See the help documentation for the function "dist.dna" of ape for a describtion of the models.
...

... further arguments passed to or from other methods

Details

An object obtained by the function mdpcoa has two classes. The first one is "mdpcoa" and the second is either "mcoa", or "statis", or "mfa", depending on the method chosen. Consequently, other functions already available in ade4 for displaying graphical results can be used: With MCoA, - plot.mcoa: this function displays (1) the differences among the populations according to each locus and the compromise, (2) the projection of the principal axes of the individual analyses onto the synthetic variables, (3) the projection of the principal axes of the individual analyses onto the co-inertia axes, (4) the squared vectorial covariance among the coinertia scores and the synthetic variables; - kplot.mcoa: this function divides previous displays (figures 1, 2, or 3 described in plot.mcoa) by giving one plot per locus.

With STATIS, - plot.statis: this function displays (1) the scores of each locus according to the two first eigenvectors of the matrix Rv, (2) the scatter diagram of the differences among populations according to the compromise, (3) the weight attributed to each locus in abscissa and the vectorial covariance among each individual analysis with the notations in the main text of the paper) and the compromise analysis in ordinates, (4) the covariance between the principal component inertia axes of each locus and the axes of the compromise space; - kplot.statis: this function displays for each locus the projection of the principal axes onto the compromise space.

With MFA, - plot.mfa: this function displays (1) the differences among the populations according to each locus and the compromise, (2) the projection of the principal axes of the individual analyses onto the compromise, (3) the covariance between the principal component inertia axes of each locus and the axes of the compromise space, (4) for each axis of the compromise, the amount of inertia conserved by the projection of the individual analyses onto the common space. - kplot.mfa: this function displays for each locus the projection of the principal axes and populations onto the compromise space.

Value

The functions provide the following results:

dist.ktab

returns an object of class dist;

Author(s)

Sandrine Pavoine [email protected]

References

Pavoine, S. and Bailly, X. (2007) New analysis for consistency among markers in the study of genetic diversity: development and application to the description of bacterial diversity. BMC Evolutionary Biology, 7, e156.

Pavoine, S., Dufour, A.B. and Chessel, D. (2004) From dissimilarities among species to dissimilarities among communities: a double principal coordinate analysis. Journal of Theoretical Biology, 228, 523–537.

See Also

dpcoa

Examples

# The functions used below require the package ape
data(rhizobium)
if (requireNamespace("ape", quietly = TRUE)) {
dat <- prep.mdpcoa(rhizobium[[1]], rhizobium[[2]], 
    model = c("F84", "F84", "F84", "F81"), pairwise.deletion = TRUE)
sam <- dat$sam
dis <- dat$dis
# The distances should be Euclidean. 
# Several transformations exist to render a distance object Euclidean 
# (see functions cailliez, lingoes and quasieuclid in the ade4 package). 
# Here we use the quasieuclid function.
dis <- lapply(dis, quasieuclid)
mdpcoa1 <- mdpcoa(sam, dis, scannf = FALSE, nf = 2)

# Reference analysis
plot(mdpcoa1)

# Differences between the loci
kplot(mdpcoa1)

# Alleles projected on the population maps.
kplotX.mdpcoa(mdpcoa1)
}

Ecological Data : sites-variables, sites-species, where and when

Description

This data set contains information about sites, environmental variables and Ephemeroptera Species.

Usage

data(meau)

Format

meau is a list of 3 components.

env

is a data frame with 24 sites and 10 physicochemical variables.

fau

is a data frame with 24 sites and 13 Ephemeroptera Species.

design

is a data frame with 24 sites and 2 factors.

  • season: is a factor with 4 levels = seasons.

  • site: is a factor with 6 levels = sites.

Details

Data set equivalents to meaudret, except that one site (6) along the Bourne (a Meaudret affluent) and one physico chemical variable - the oxygen concentration were added.

Source

Pegaz-Maucet, D. (1980) Impact d'une perturbation d'origine organique sur la dérive des macro-invertébrés benthiques d'un cours d'eau. Comparaison avec le benthos. Thèse de 3ème cycle, Université Lyon 1, 130 p.

Thioulouse, J., Simier, M. and Chessel, D. (2004) Simultaneous analysis of a sequence of paired ecological tables. Ecology, 85, 1, 272–283.

Examples

data(meau)
pca1 <- dudi.pca(meau$env, scan = FALSE, nf = 4)
pca2 <- bca(pca1, meau$design$season, scan = FALSE, nf = 2)

if(adegraphicsLoaded()) {
  g1 <- s.class(pca1$li, meau$design$season, psub.text = "Principal Component Analysis", 
    plot = FALSE)
  g2 <- s.class(pca2$ls, meau$design$season, 
    psub.text = "Between seasons Principal Component Analysis", plot = FALSE)
  g3 <- s.corcircle(pca1$co, plot = FALSE)
  g4 <- s.corcircle(pca2$as, plot = FALSE)
  G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))
  
} else {
  par(mfrow = c(2, 2))
  s.class(pca1$li, meau$design$season, 
      sub = "Principal Component Analysis")
  s.class(pca2$ls, meau$design$season, sub = "Between seasons Principal Component Analysis")
  s.corcircle(pca1$co)
  s.corcircle(pca2$as)
  par(mfrow = c(1, 1))
}

Ecological Data : sites-variables, sites-species, where and when

Description

This data set contains information about sites, environmental variables and Ephemeroptera Species.

Usage

data(meaudret)

Format

meaudret is a list of 4 components.

env

is a data frame with 20 sites and 9 variables.

fau

is a data frame with 20 sites and 13 Ephemeroptera Species.

design

is a data frame with 20 sites and 2 factors.

  • season is a factor with 4 levels = seasons.

  • site is a factor with 5 levels = sites along the Meaudret river.

spe.names

is a character vector containing the names of the 13 species.

Details

Data set equivalents to meau: site (6) on the Bourne (a Meaudret affluent) and oxygen concentration were removed.

Source

Pegaz-Maucet, D. (1980) Impact d'une perturbation d'origine organique sur la dérive des macro-invertébrés benthiques d'un cours d'eau. Comparaison avec le benthos. Thèse de 3ème cycle, Université Lyon 1, 130 p.

Thioulouse, J., Simier, M. and Chessel, D. (2004) Simultaneous analysis of a sequence of paired ecological tables. Ecology, 85, 1, 272–283.

Examples

data(meaudret)
pca1 <- dudi.pca(meaudret$env, scan = FALSE, nf = 4)
pca2 <- bca(pca1, meaudret$design$season, scan = FALSE, nf = 2)
  
if(adegraphicsLoaded()) {
  g1 <- s.class(pca1$li, meaudret$design$season, 
    psub.text = "Principal Component Analysis", plot = FALSE)
  g2 <- s.class(pca2$ls, meaudret$design$season, 
    psub.text = "Between dates Principal Component Analysis", plot = FALSE)
  g3 <- s.corcircle(pca1$co, plot = FALSE)
  g4 <- s.corcircle(pca2$as, plot = FALSE)
  G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))

} else {
  par(mfrow = c(2, 2))
  s.class(pca1$li, meaudret$design$season, sub = "Principal Component Analysis")
  s.class(pca2$ls, meaudret$design$season, sub = "Between dates Principal Component Analysis")
  s.corcircle(pca1$co)
  s.corcircle(pca2$as)
  par(mfrow = c(1, 1))
}

Multiple Factorial Analysis

Description

performs a multiple factorial analysis, using an object of class ktab.

Usage

mfa(X, option = c("lambda1", "inertia", "uniform", "internal"), 
    scannf = TRUE, nf = 3)
## S3 method for class 'mfa'
plot(x, xax = 1, yax = 2, option.plot = 1:4, ...) 
## S3 method for class 'mfa'
print(x, ...) 
## S3 method for class 'mfa'
summary(object, ...)

Arguments

X

K-tables, an object of class ktab
option

a string of characters for the weighting of arrays options :

lambda1

weighting of group k by the inverse of the first eigenvalue of the k analysis

inertia

weighting of group k by the inverse of the total inertia of the array k

uniform

uniform weighting of groups

internal

weighting included in X$tabw
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes
x, object

an object of class 'mfa'
xax, yax

the numbers of the x-axis and the y-axis
option.plot

an integer between 1 and 4, otherwise the 4 components of the plot are displayed
...

further arguments passed to or from other methods

Value

Returns a list including :

tab

a data frame with the modified array
rank

a vector of ranks for the analyses
eig

a numeric vector with the all eigenvalues
li

a data frame with the coordinates of rows
TL

a data frame with the factors associated to the rows (indicators of table)
co

a data frame with the coordinates of columns
TC

a data frame with the factors associated to the columns (indicators of table)
blo

a vector indicating the number of variables for each table
lisup

a data frame with the projections of normalized scores of rows for each table
link

a data frame containing the projected inertia and the links between the arrays and the reference array

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

References

Escofier, B. and Pagès, J. (1994) Multiple factor analysis (AFMULT package), Computational Statistics and Data Analysis, 18, 121–140.

Examples

data(friday87)
w1 <- data.frame(scale(friday87$fau, scal = FALSE))
w2 <- ktab.data.frame(w1, friday87$fau.blo, 
    tabnames = friday87$tab.names)
mfa1 <- mfa(w2, scann = FALSE)
mfa1
plot(mfa1)

data(escopage)
w <- data.frame(scale(escopage$tab))
w <- ktab.data.frame(w, escopage$blo, tabnames = escopage$tab.names)
plot(mfa(w, scann = FALSE))

Genetic Relationships between cattle breeds with microsatellites

Description

This data set gives genetic relationships between cattle breeds with microsatellites.

Usage

data(microsatt)

Format

microsatt is a list of 4 components.

tab

contains the allelic frequencies for 18 cattle breeds (Taurine or Zebu,French or African) and 9 microsatellites.

loci.names

is a vector of the names of loci.

loci.eff

is a vector of the number of alleles per locus.

alleles.names

is a vector of the names of alleles.

Source

Extract of data prepared by D. Laloë [email protected] from data used in:

Moazami-Goudarzi, K., D. Laloë, J. P. Furet, and F. Grosclaude (1997) Analysis of genetic relationships between 10 cattle breeds with 17 microsatellites. Animal Genetics, 28, 338–345.

Souvenir Zafindrajaona, P.,Zeuh V. ,Moazami-Goudarzi K., Laloë D., Bourzat D., Idriss A., and Grosclaude F. (1999) Etude du statut phylogénétique du bovin Kouri du lac Tchad à l'aide de marqueurs moléculaires. Revue d'Elevage et de Médecine Vétérinaire des pays Tropicaux, 55, 155–162.

Moazami-Goudarzi, K., Belemsaga D. M. A., Ceriotti G., Laloë D. , Fagbohoun F., Kouagou N. T., Sidibé I., Codjia V., Crimella M. C., Grosclaude F. and Touré S. M. (2001)
Caractérisation de la race bovine Somba à l'aide de marqueurs moléculaires. Revue d'Elevage et de Médecine Vétérinaire des pays Tropicaux, 54, 1–10.

References

See a data description at http://pbil.univ-lyon1.fr/R/pdf/pps055.pdf (in French).

Examples

## Not run: 
data(microsatt)
fac <- factor(rep(microsatt$loci.names, microsatt$loci.eff))
w <- dudi.coa(data.frame(t(microsatt$tab)), scann = FALSE)
wit <- wca(w, fac, scann = FALSE)
microsatt.ktab <- ktab.within(wit)

plot(sepan(microsatt.ktab)) # 9 separated correspondence analyses
plot(mcoa(microsatt.ktab, scan = FALSE))
plot(mfa(microsatt.ktab, scan = FALSE))
plot(statis(microsatt.ktab, scan = FALSE))

## End(Not run)

Phylogeny and quantitative traits of teleos fishes

Description

This data set describes the phylogeny of 49 teleos fishes as reported by Rochet et al. (2000). It also gives life-history traits corresponding to these 49 species.

Usage

data(mjrochet)

Format

mjrochet is a list containing the 2 following objects :

tre

is a character string giving the phylogenetic tree in Newick format.

tab

is a data frame with 49 rows and 7 traits.

Details

Variables of mjrochet$tab are the following ones : tm (age at maturity (years)), lm (length at maturity (cm)), l05 (length at 5 per cent survival (cm)), t05 (time to 5 per cent survival (years)), fb (slope of the log-log fecundity-length relationship), fm (fecundity the year of maturity), egg (volume of eggs (mm3mm^{3})).

Source

Data taken from:
Summary of data - Clupeiformes : http://www.ifremer.fr/maerha/clupe.html
Summary of data - Argentiniformes : http://www.ifremer.fr/maerha/argentin.html
Summary of data - Salmoniformes : http://www.ifremer.fr/maerha/salmon.html
Summary of data - Gadiformes : http://www.ifremer.fr/maerha/gadi.html
Summary of data - Lophiiformes : http://www.ifremer.fr/maerha/loph.html
Summary of data - Atheriniformes : http://www.ifremer.fr/maerha/ather.html
Summary of data - Perciformes : http://www.ifremer.fr/maerha/perci.html
Summary of data - Pleuronectiformes : http://www.ifremer.fr/maerha/pleuro.html
Summary of data - Scorpaeniformes : http://www.ifremer.fr/maerha/scorpa.html
Phylogenetic tree : http://www.ifremer.fr/maerha/life_history.html

References

Rochet, M. J., Cornillon, P-A., Sabatier, R. and Pontier, D. (2000) Comparative analysis of phylogenic and fishing effects in life history patterns of teleos fishes. Oïkos, 91, 255–270.

Examples

data(mjrochet)
mjrochet.phy <- newick2phylog(mjrochet$tre)
tab <- log((mjrochet$tab))
tab0 <- data.frame(scalewt(tab))
table.phylog(tab0, mjrochet.phy, csi = 2, clabel.r = 0.75)
if (requireNamespace("adephylo", quietly = TRUE)) {
  adephylo::orthogram(tab0[,1], ortho = mjrochet.phy$Bscores)
}

Multi Level Decomposition of unidimensional data

Description

The function mld performs an additive decomposition of the input vector x onto sub-spaces associated to an orthonormal orthobasis. The sub-spaces are defined by levels of the input factor level. The function haar2level builds the factor level such that the multi level decomposition corresponds exactly to a multiresolution analysis performed with the haar basis.

Usage

mld(x, orthobas, level, na.action = c("fail", "mean"),
 plot = TRUE, dfxy = NULL, phylog = NULL, ...)
haar2level(x)

Arguments

x

is a vector or a time serie containing the data to be decomposed. This must be a dyadic length vector (power of 2) for the function haar2level.
orthobas

is a data frame containing the vectors of the orthonormal basis.
level

is a factor which levels define the sub-spaces on which the function mld performs the additive decomposition.
na.action

if 'fail' stops the execution of the current expression when x contains any missing value. If 'mean' replaces any missing values by mean(x).
plot

if TRUE plot x and the components resulting from the decomposition.
dfxy

is a data frame with two coordinates.
phylog

is an object of class phylog.
...

further arguments passed to or from other methods.

Value

A data frame with the components resulting from the decomposition.

Author(s)

Sébastien Ollier [email protected]

References

Mallat, S. G. (1989) A theory for multiresolution signal decomposition: the wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, 7, 674–693.

Percival, D. B. and Walden, A. T. (2000) Wavelet Methods for Time Series Analysis, Cambridge University Press.

See Also

gridrowcol, orthobasis, orthogram, mra for multiresolution analysis with various families of wavelets

Examples

## Not run: 
# decomposition of a time serie
data(co2)
x <- log(co2)
orthobas <- orthobasis.line(length(x))
level<-rep("D", 467)
level[1:3]<-rep("A", 3)
level[c(77,78,79,81)]<-rep("B", 4)
level[156]<-"C"
level<-as.factor(level)
res <- mld(x, orthobas, level)
sum(scale(x, scale = FALSE) - apply(res, 1, sum))

## End(Not run)
# decomposition of a biological trait on a phylogeny
data(palm)
vfruit<-palm$traits$vfruit
vfruit<-scalewt(vfruit)   
palm.phy<-newick2phylog(palm$tre)
level <- rep("F", 65)
level[c(4, 21, 3, 6, 13)] <- LETTERS[1:5]
level <- as.factor(level)
res <- mld(as.vector(vfruit), palm.phy$Bscores, level,
 phylog = palm.phy, clabel.nod = 0.7, f.phylog=0.8,
  csize = 2, clabel.row = 0.7, clabel.col = 0.7)

Faunistic Communities and Sampling Experiment

Description

This data set gives the abundance of 32 mollusk species in 163 samples. For each sample, 4 informations are known : the sampling sites, the seasons, the sampler types and the time of exposure.

Usage

data(mollusc)

Format

mollusc is a list of 2 objects.

fau

is a data frame with 163 samples and 32 mollusk species (abundance).

plan

contains the 163 samples and 4 variables.

Source

Richardot-Coulet, M., Chessel D. and Bournaud M. (1986) Typological value of the benthos of old beds of a large river. Methodological approach. Archiv fùr Hydrobiologie, 107, 363–383.

Examples

data(mollusc)
coa1 <- dudi.coa(log(mollusc$fau + 1), scannf = FALSE, nf = 3)

if(adegraphicsLoaded()) {
  g1 <- s.class(coa1$li, mollusc$plan$site, ellipseSize = 0, starSize = 0, chullSize = 1, 
    xax = 2, yax = 3, plot = FALSE)
  g2 <- s.class(coa1$li, mollusc$plan$season, ellipseSize = 0, starSize = 0, chullSize = 1, 
    xax = 2, yax = 3, plot = FALSE)
  g3 <- s.class(coa1$li, mollusc$plan$method, ellipseSize = 0, starSize = 0, chullSize = 1, 
    xax = 2, yax = 3, plot = FALSE)
  g4 <- s.class(coa1$li, mollusc$plan$duration, ellipseSize = 0, starSize = 0, chullSize = 1, 
    xax = 2, yax = 3, plot = FALSE)
  G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))
  
} else {
  par(mfrow = c(2, 2))
  s.chull(coa1$li, mollusc$plan$site, 2, 3, opt = 1, cpoi = 1)
  s.chull(coa1$li, mollusc$plan$season, 2, 3, opt = 1, cpoi = 1)
  s.chull(coa1$li, mollusc$plan$method, 2, 3, opt = 1, cpoi = 1)
  s.chull(coa1$li, mollusc$plan$duration, 2, 3, opt = 1, cpoi = 1)
  par(mfrow = c(1, 1))
}

Global State of the World in 1984

Description

The monde84 data frame gives five demographic variables for 48 countries in the world.

Usage

data(monde84)

Format

This data frame contains the following columns:

  1. pib: Gross Domestic Product

  2. croipop: Growth of the population

  3. morta: Infant Mortality

  4. anal: Literacy Rate

  5. scol: Percentage of children in full-time education

Source

Geze, F. and Coll., eds. (1984) L'état du Monde 1984 : annuaire économique et géopolitique mondial. La Découverte, Paris.

Examples

data(monde84)
X <- cbind.data.frame(lpib = log(monde84$pib), monde84$croipop)
Y <- cbind.data.frame(lmorta = log(monde84$morta), 
    lanal = log(monde84$anal + 1), rscol = sqrt(100 - monde84$scol))
pcaY <- dudi.pca(Y, scan = FALSE)
pcaiv1 <- pcaiv(pcaY, X0 <- scale(X), scan = FALSE)
sum(cor(pcaiv1$l1[,1], Y0 <- scale(Y))^2)
pcaiv1$eig[1] #the same

Athletes' Morphology

Description

This data set gives a morphological description of 153 athletes split in five different sports.

Usage

data(morphosport)

Format

morphosport is a list of 2 objects.

tab

is a data frame with 153 athletes and 5 variables.

sport

is a factor with 6 items

Details

Variables of morphosport$tab are the following ones: dbi (biacromial diameter (cm)), tde (height (cm)), tas (distance from the buttocks to the top of the head (cm)), lms (length of the upper limbs (cm)), poids (weigth (kg)).

The levels of morphosport$sport are: athl (athletics), foot (football), hand (handball), judo, nata (swimming), voll (volleyball).

Source

Mimouni , N. (1996) Contribution de méthodes biométriques à l'analyse de la morphotypologie des sportifs. Thèse de doctorat. Université Lyon 1.

Examples

data(morphosport)
plot(discrimin(dudi.pca(morphosport$tab, scan = FALSE), 
    morphosport$sport, scan = FALSE))

Minimal Spanning Tree

Description

Minimal Spanning Tree

Usage

mstree(xdist, ngmax = 1)

Arguments

xdist

an object of class dist containing an observed dissimilarity

ngmax

a component number (default=1). Select 1 for getting classical MST. To add n supplementary edges k times: select k+1.

Value

returns an object of class neig

Author(s)

Daniel Chessel

Examples

data(mafragh)
maf.coa <- dudi.coa(mafragh$flo, scan = FALSE)
maf.mst <- ade4::mstree(dist.dudi(maf.coa), 1)

if(adegraphicsLoaded()) {
  g0 <- s.label(maf.coa$li, plab.cex = 0, ppoints.cex = 2, nb = neig2nb(maf.mst))
} else {
  s.label(maf.coa$li, clab = 0, cpoi = 2, neig = maf.mst, cnei = 1)
}

xy <- data.frame(x = runif(20), y = runif(20))

if(adegraphicsLoaded()) {
  g1 <- s.label(xy, xlim = c(0, 1), ylim = c(0, 1), 
    nb = neig2nb(ade4::mstree(dist.quant(xy, 1), 1)), plot = FALSE)
  g2 <- s.label(xy, xlim = c(0, 1), ylim = c(0, 1), 
    nb = neig2nb(ade4::mstree(dist.quant(xy, 1), 2)), plot = FALSE)
  g3 <- s.label(xy, xlim = c(0, 1), ylim = c(0, 1), 
    nb = neig2nb(ade4::mstree(dist.quant(xy, 1), 3)), plot = FALSE)
  g4 <- s.label(xy, xlim = c(0, 1), ylim = c(0, 1), 
    nb = neig2nb(ade4::mstree(dist.quant(xy, 1), 4)), plot = FALSE)
  G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))

} else {
  par(mfrow = c(2, 2))
  for(k in 1:4) {
    neig <- mstree(dist.quant(xy, 1), k)
    s.label(xy, xlim = c(0, 1), ylim = c(0, 1), addax = FALSE, neig = neig)
  }
}

Display and summarize multiblock objects

Description

Generic methods print and summary for mulitblock objects

Usage

## S3 method for class 'multiblock'
summary(object, ...)
## S3 method for class 'multiblock'
print(x, ...)

Arguments

object

an object of class multiblock created by mbpls or mbpcaiv
x

an object of class multiblock created by mbpls or mbpcaiv
...

other arguments to be passed to methods

Author(s)

Stéphanie Bougeard ([email protected]) and Stéphane Dray ([email protected])

References

Bougeard, S. and Dray S. (2018) Supervised Multiblock Analysis in R with the ade4 Package. Journal of Statistical Software, 86 (1), 1-17. doi:10.18637/jss.v086.i01

See Also

mbpls, mbpcaiv

Multivariate spatial analysis

Description

These functions are deprecated. See the function multispati and the methods plot.multispati, summary.multispati and print.multispati in the package adespatial.

This function ensures a multivariate extension of the univariate method of spatial autocorrelation analysis. By accounting for the spatial dependence of data observations and their multivariate covariance simultaneously, complex interactions among many variables are analysed. Using a methodological scheme borrowed from duality diagram analysis, a strategy for the exploratory analysis of spatial pattern in the multivariate is developped.

Usage

multispati(dudi, listw, scannf = TRUE, nfposi = 2, nfnega = 0)
## S3 method for class 'multispati'
plot(x, xax = 1, yax = 2, ...) 
## S3 method for class 'multispati'
summary(object, ...) 
## S3 method for class 'multispati'
print(x, ...)

Arguments

dudi

an object of class dudi for the duality diagram analysis
listw

an object of class listw for the spatial dependence of data observations
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed
nfposi

an integer indicating the number of kept positive axes
nfnega

an integer indicating the number of kept negative axes
x, object

an object of class multispati
xax, yax

the numbers of the x-axis and the y-axis
...

further arguments passed to or from other methods

Details

This analysis generalizes the Wartenberg's multivariate spatial correlation analysis to various duality diagrams created by the functions (dudi.pca, dudi.coa, dudi.acm, dudi.mix...) If dudi is a duality diagram created by the function dudi.pca and listw gives spatial weights created by a row normalized coding scheme, the analysis is equivalent to Wartenberg's analysis.

We note X the data frame with the variables, Q the column weights matrix and D the row weights matrix associated to the duality diagram dudi. We note L the neighbouring weights matrix associated to listw. Then, the 'multispati' analysis gives principal axes v that maximize the product of spatial autocorrelation and inertia of row scores :

I(XQv)∗∥XQv∥2=vtQtXtDLXQvI(XQv)*\|XQv\|^2 = v^{t}Q^{t}X^{t}DLXQv

Value

Returns an object of class multispati, which contains the following elements :

eig

a numeric vector containing the eigenvalues
nfposi

integer, number of kept axes associated to positive eigenvalues
nfnega

integer, number of kept axes associated to negative eigenvalues
c1

principle axes (v), data frame with p rows and (nfposi + nfnega) columns
li

principal components (XQv), data frame with n rows and (nfposi + nfnega) columns
ls

lag vector onto the principal axes (LXQv), data frame with n rows and (nfposi + nfnega) columns
as

principal axes of the dudi analysis (u) onto principal axes of multispati (t(u)Qv), data frame with nf rows and (nfposi + nfnega) columns

Author(s)

Daniel Chessel
Sebastien Ollier [email protected]
Thibaut Jombart [email protected]

References

Dray, S., Said, S. and Debias, F. (2008) Spatial ordination of vegetation data using a generalization of Wartenberg's multivariate spatial correlation. Journal of vegetation science, 19, 45–56.

Grunsky, E. C. and Agterberg, F. P. (1988) Spatial and multivariate analysis of geochemical data from metavolcanic rocks in the Ben Nevis area, Ontario. Mathematical Geology, 20, 825–861.

Switzer, P. and Green, A.A. (1984) Min/max autocorrelation factors for multivariate spatial imagery. Tech. rep. 6, Stanford University.

Thioulouse, J., Chessel, D. and Champely, S. (1995) Multivariate analysis of spatial patterns: a unified approach to local and global structures. Environmental and Ecological Statistics, 2, 1–14.

Wartenberg, D. E. (1985) Multivariate spatial correlation: a method for exploratory geographical analysis. Geographical Analysis, 17, 263–283.

Jombart, T., Devillard, S., Dufour, A.-B. and Pontier, D. A spatially explicit multivariate method to disentangle global and local patterns of genetic variability. Submitted to Genetics.

See Also

dudi,mat2listw

Examples

## Not run: 
if (requireNamespace("spdep", quietly = TRUE)) {
    data(mafragh)
    maf.xy <- mafragh$xy
    maf.flo <- mafragh$flo
    maf.listw <- spdep::nb2listw(neig2nb(mafragh$neig))
    if(adegraphicsLoaded()) {
      g1 <- s.label(maf.xy, nb = neig2nb(mafragh$neig), plab.cex = 0.75)
    } else {
      s.label(maf.xy, neig = mafragh$neig, clab = 0.75)
    }
    maf.coa <- dudi.coa(maf.flo,scannf = FALSE)
    maf.coa.ms <- multispati(maf.coa, maf.listw, scannf = FALSE, nfposi = 2, nfnega = 2)
    maf.coa.ms
    
    ### detail eigenvalues components
    fgraph <- function(obj){
      # use multispati summary
      sum.obj <- summary(obj)
      # compute Imin and Imax
      L <- spdep::listw2mat(eval(as.list(obj$call)$listw))
      Imin <- min(eigen(0.5*(L+t(L)))$values)
      Imax <- max(eigen(0.5*(L+t(L)))$values)
      I0 <- -1/(nrow(obj$li)-1)
      # create labels
      labels <- lapply(1:length(obj$eig),function(i) bquote(lambda[.(i)]))
      # draw the plot
      xmax <- eval(as.list(obj$call)$dudi)$eig[1]*1.1
      par(las=1)
      var <- sum.obj[,2]
      moran <- sum.obj[,3]
      plot(x=var,y=moran,type='n',xlab='Inertia',ylab="Spatial autocorrelation (I)",
           xlim=c(0,xmax),ylim=c(Imin*1.1,Imax*1.1),yaxt='n')
      text(x=var,y=moran,do.call(expression,labels))
      ytick <- c(I0,round(seq(Imin,Imax,le=5),1))
      ytlab <- as.character(round(seq(Imin,Imax,le=5),1))
      ytlab <- c(as.character(round(I0,1)),as.character(round(Imin,1)),
           ytlab[2:4],as.character(round(Imax,1)))
      axis(side=2,at=ytick,labels=ytlab)
      rect(0,Imin,xmax,Imax,lty=2)
      segments(0,I0,xmax,I0,lty=2)
      abline(v=0)
      title("Spatial and inertia components of the eigenvalues")
    }
    fgraph(maf.coa.ms)
    ## end eigenvalues details


    if(adegraphicsLoaded()) {
      g2 <- s1d.barchart(maf.coa$eig, p1d.hori = FALSE, plot = FALSE)
      g3 <- s1d.barchart(maf.coa.ms$eig, p1d.hori = FALSE, plot = FALSE) 
      g4 <- s.corcircle(maf.coa.ms$as, plot = FALSE)
      G1 <- ADEgS(list(g2, g3, g4), layout = c(1, 3))
    } else {
      par(mfrow = c(1, 3))
      barplot(maf.coa$eig)
      barplot(maf.coa.ms$eig) 
      s.corcircle(maf.coa.ms$as)
      par(mfrow = c(1, 1))
    }
 
 
    if(adegraphicsLoaded()) {
      g5 <- s.value(maf.xy, -maf.coa$li[, 1], plot = FALSE)
      g6 <- s.value(maf.xy, -maf.coa$li[, 2], plot = FALSE)
      g7 <- s.value(maf.xy, maf.coa.ms$li[, 1], plot = FALSE)
      g8 <- s.value(maf.xy, maf.coa.ms$li[, 2], plot = FALSE)
      G2 <- ADEgS(list(g5, g6, g7, g8), layout = c(2, 2))
    } else {
      par(mfrow = c(2, 2))
      s.value(maf.xy, -maf.coa$li[, 1])
      s.value(maf.xy, -maf.coa$li[, 2])
      s.value(maf.xy, maf.coa.ms$li[, 1])
      s.value(maf.xy, maf.coa.ms$li[, 2])
      par(mfrow = c(1, 1))
    }


    w1 <- -maf.coa$li[, 1:2]
    w1m <- apply(w1, 2, spdep::lag.listw, x = maf.listw)
    w1.ms <- maf.coa.ms$li[, 1:2]
    w1.msm <- apply(w1.ms, 2, spdep::lag.listw, x = maf.listw)
    if(adegraphicsLoaded()) {
      g9 <- s.match(w1, w1m, plab.cex = 0.75, plot = FALSE)
      g10 <- s.match(w1.ms, w1.msm, plab.cex = 0.75, plot = FALSE)
      G3 <- cbindADEg(g9, g10, plot = TRUE)
    } else {
      par(mfrow = c(1,2))
      s.match(w1, w1m, clab = 0.75)
      s.match(w1.ms, w1.msm, clab = 0.75)
      par(mfrow = c(1, 1))
    }

    maf.pca <- dudi.pca(mafragh$env, scannf = FALSE)
    multispati.randtest(maf.pca, maf.listw)
    maf.pca.ms <- multispati(maf.pca, maf.listw, scannf=FALSE)
    plot(maf.pca.ms)
}

## End(Not run)

Multivariate spatial autocorrelation test (in C)

Description

This function performs a multivariate autocorrelation test.

Usage

multispati.randtest(dudi, listw, nrepet = 999, ...)

Arguments

dudi

an object of class dudi for the duality diagram analysis
listw

an object of class listw for the spatial dependence of data observations
nrepet

the number of permutations
...

further arguments passed to or from other methods

Details

We note X the data frame with the variables, Q the column weights matrix and D the row weights matrix associated to the duality diagram dudi. We note L the neighbouring weights matrix associated to listw. This function performs a Monte-Carlo Test on the multivariate spatial autocorrelation index :

r=trace(XtDLXQ)trace(XtDXQ)r = \frac{trace(X^{t}DLXQ)}{trace(X^{t}DXQ)}

Value

Returns an object of class randtest (randomization tests).

Author(s)

Daniel Chessel
Sébastien Ollier [email protected]

References

Smouse, P. E. and Peakall, R. (1999) Spatial autocorrelation analysis of individual multiallele and multilocus genetic structure. Heredity, 82, 561–573.

See Also

dudi,mat2listw

Examples

if (requireNamespace("spdep", quietly = TRUE)) {
    data(mafragh)
    maf.listw <- spdep::nb2listw(neig2nb(mafragh$neig))
    maf.pca <- dudi.pca(mafragh$env, scannf = FALSE)
    multispati.randtest(maf.pca, maf.listw)
    maf.pca.ms <- multispati(maf.pca, maf.listw, scannf = FALSE)
    plot(maf.pca.ms)
}

Multivariate spatial autocorrelation test

Description

This function performs a multivariate autocorrelation test.

Usage

multispati.rtest(dudi, listw, nrepet = 99, ...)

Arguments

dudi

an object of class dudi for the duality diagram analysis
listw

an object of class listw for the spatial dependence of data observations
nrepet

the number of permutations
...

further arguments passed to or from other methods

Details

We note X the data frame with the variables, Q the column weight matrix and D the row weight matrix associated to the duality diagram dudi. We note L the neighbouring weights matrix associated to listw. This function performs a Monte-Carlo Test on the multivariate spatial autocorrelation index :

r=XtDLXQXtDXQr = \frac{X^{t}DLXQ}{X^{t}DXQ}

Value

Returns an object of class randtest (randomization tests).

Author(s)

Daniel Chessel
Sébastien Ollier [email protected]

References

Smouse, P. E. and Peakall, R. (1999) Spatial autocorrelation analysis of individual multiallele and multilocus genetic structure. Heredity, 82, 561–573.

See Also

dudi,mat2listw

Examples

if (requireNamespace("spdep", quietly = TRUE)) {
    data(mafragh)
    maf.listw <- spdep::nb2listw(neig2nb(mafragh$neig))
    maf.pca <- dudi.pca(mafragh$env, scannf = FALSE)
    multispati.rtest(maf.pca, maf.listw)
    maf.pca.ms <- multispati(maf.pca, maf.listw, scannf = FALSE)
    plot(maf.pca.ms)
}

Neighbourhood Graphs

Description

neig creates objects of class neig with :
a list of edges
a binary square matrix
a list of vectors of neighbours
an integer (linear and circular graphs)
a data frame of polygons (area)

scores.neig returns the eigenvectors of neighbouring,
orthonormalized scores (null average, unit variance 1/n and null covariances) of maximal autocorrelation.

nb2neig returns an object of class neig using an object of class nb in the library 'spdep'

neig2nb returns an object of class nb using an object of class neig

neig2mat returns the incidence matrix between edges (1 = neighbour ; 0 = no neighbour)

neig.util.GtoL and neig.util.LtoG are utilities.

Usage

neig(list = NULL, mat01 = NULL, edges = NULL,
    n.line = NULL, n.circle = NULL, area = NULL)

scores.neig  (obj) 
## S3 method for class 'neig'
print(x, ...) 
## S3 method for class 'neig'
summary(object, ...)
nb2neig (nb)
neig2nb (neig)
neig2mat (neig)

Arguments

list

a list which each component gives the number of neighbours
mat01

a symmetric square matrix of 0-1 values
edges

a matrix of 2 columns with integer values giving a list of edges
n.line

the number of points for a linear plot
n.circle

the number of points for a circular plot
area

a data frame containing a polygon set (see area.plot)
nb

an object of class 'nb'
neig, x, obj, object

an object of class 'neig'
...

further arguments passed to or from other methods

Author(s)

Daniel Chessel

References

Thioulouse, J., D. Chessel, and S. Champely. 1995. Multivariate analysis of spatial patterns: a unified approach to local and global structures. Environmental and Ecological Statistics, 2, 1–14.

Examples

if(!adegraphicsLoaded()) {
  
  if(requireNamespace("deldir", quietly = TRUE)) {
  
    data(mafragh)
    par(mfrow = c(2, 1))
    provi <- deldir::deldir(mafragh$xy)
    provi.neig <- neig(edges = as.matrix(provi$delsgs[, 5:6]))
    
    s.label(mafragh$xy, neig = provi.neig, inc = FALSE, 
      addax = FALSE, clab = 0, cnei = 2)
    dist <- apply(provi.neig, 1, function(x) 
      sqrt(sum((mafragh$xy[x[1], ] - mafragh$xy[x[2], ]) ^ 2)))
    #hist(dist, nclass = 50)
    mafragh.neig <- neig(edges = provi.neig[dist < 50, ])
    s.label(mafragh$xy, neig = mafragh.neig, inc = FALSE, 
      addax = FALSE, clab = 0, cnei = 2)
    par(mfrow = c(1, 1))
    
    data(irishdata)
    irish.neig <- neig(area = irishdata$area)
    summary(irish.neig)
    print(irish.neig)
    s.label(irishdata$xy, neig = irish.neig, cneig = 3,
      area = irishdata$area, clab = 0.8, inc = FALSE)
    
    irish.scores <- scores.neig(irish.neig)
    par(mfrow = c(2, 3))
    for(i in 1:6)
      s.value(irishdata$xy, irish.scores[, i], inc = FALSE, grid = FALSE, addax = FALSE,
        neig = irish.neig, csi = 2, cleg = 0, sub = paste("Eigenvector ",i), csub = 2)
    par(mfrow = c(1, 1))
    
    a.neig <- neig(n.circle = 16)
    a.scores <- scores.neig(a.neig)
    xy <- cbind.data.frame(cos((1:16) * pi / 8), sin((1:16) * pi / 8))
    par(mfrow = c(4, 4))
    for(i in 1:15)
      s.value(xy, a.scores[, i], neig = a.neig, csi = 3, cleg = 0)
    par(mfrow = c(1, 1))
    
    a.neig <- neig(n.line = 28)
    a.scores <- scores.neig(a.neig)
    par(mfrow = c(7, 4))
    par(mar = c(1.1, 2.1, 0.1, 0.1))
    for(i in 1:27)
      barplot(a.scores[, i], col = grey(0.8))
    par(mfrow = c(1, 1))
  }

  if(requireNamespace("spdep", quietly = TRUE)) {
    
    data(mafragh)
    maf.rel <- spdep::relativeneigh(as.matrix(mafragh$xy))
    maf.rel <- spdep::graph2nb(maf.rel)
    s.label(mafragh$xy, neig = neig(list = maf.rel), inc = FALSE,
      clab = 0, addax = FALSE, cne = 1, cpo = 2)
    
    par(mfrow = c(2, 2))
    w <- matrix(runif(100), 50, 2)
    x.gab <- spdep::gabrielneigh(w)
    x.gab <- spdep::graph2nb(x.gab)
    s.label(data.frame(w), neig = neig(list = x.gab), inc = FALSE,
      clab = 0, addax = FALSE, cne = 1, cpo = 2, sub = "relative")
    x.rel <- spdep::relativeneigh(w)
    x.rel <- spdep::graph2nb(x.rel)
    s.label(data.frame(w), neig = neig(list = x.rel), inc = FALSE,
      clab = 0, addax = FALSE, cne = 1, cpo = 2, sub = "Gabriel")
    k1 <- spdep::knn2nb(spdep::knearneigh(w))
    s.label(data.frame(w), neig = neig(list = k1), inc = FALSE,
      clab = 0, addax = FALSE, cne = 1, cpo = 2, sub = "k nearest neighbours")
    
    all.linked <- max(unlist(spdep::nbdists(k1, w)))
    z <- spdep::dnearneigh(w, 0, all.linked)
    s.label(data.frame(w), neig = neig(list = z), inc = FALSE, clab = 0, 
      addax = FALSE, cne = 1, cpo = 2, sub = "Neighbourhood contiguity by distance")
    par(mfrow = c(1, 1))
  }
  
}

Phylogenetic trees in Newick format

Description

This data set contains various exemples of phylogenetic trees in Newick format.

Usage

data(newick.eg)

Format

newick.eg is a list containing 14 character strings in Newick format.

Source

Trees 1 to 7 were obtained from the URL
http://evolution.genetics.washington.edu/phylip/newicktree.html.

Trees 8 and 9 were obtained by Clémentine Carpentier-Gimaret.

Tree 10 was obtained from Treezilla Data Sets .

Trees 11 and 12 are taken from Bauwens and Díaz-Uriarte (1997).

Tree 13 is taken from Cheverud and Dow (1985).

Tree 13 is taken from Martins and Hansen (1997).

References

Bauwens, D. and Díaz-Uriarte, R. (1997) Covariation of life-history traits in lacertid lizards: a comparative study. American Naturalist, 149, 91–111.

Cheverud, J. and Dow, M.M. (1985) An autocorrelation analysis of genetic variation due to lineal fission in social groups of rhesus macaques. American Journal of Physical Anthropology, 67, 113–122.

Martins, E. P. and Hansen, T.F. (1997) Phylogenies and the comparative method: a general approach to incorporating phylogenetic information into the analysis of interspecific data. American Naturalist, 149, 646–667.

Examples

data(newick.eg)
newick2phylog(newick.eg[[11]])
radial.phylog(newick2phylog(newick.eg[[7]]), circ = 1,
 clabel.l = 0.75)

Create phylogeny

Description

The first three functions ensure to create object of class phylog from either a character string in Newick format (newick2phylog) or an object of class 'hclust' (hclust2phylog) or a taxonomy (taxo2phylog). The function newick2phylog.addtools is an internal function called by newick2phylog, hclust2phylog and taxo2phylog when newick2phylog.addtools = TRUE. It adds some items in 'phylog' objects.

Usage

newick2phylog(x.tre, add.tools = TRUE, call = match.call())
hclust2phylog(hc, add.tools = TRUE)
taxo2phylog(taxo, add.tools = FALSE, root="Root", abbrev=TRUE)
newick2phylog.addtools(res, tol = 1e-07)

Arguments

x.tre

a character string corresponding to a phylogenetic tree in Newick format
(http://evolution.genetics.washington.edu/phylip/newicktree.html)
add.tools

if TRUE, executes the function newick2phylog.addtools
call

call
hc

an object of class hclust
taxo

an object of class taxo
res

an object of class phylog (an internal argument of the function newick2phylog)
tol

used in case 3 of method as a tolerance threshold for null eigenvalues
root

a character string for the root of the tree
abbrev

logical : if TRUE levels are abbreviated by column and two characters are added before

Value

Return object of class phylog.

Author(s)

Daniel Chessel
Sébastien Ollier [email protected]

See Also

phylog, plot.phylog, as.taxo

Examples

w <- "((((,,),,(,)),),(,));"
 w.phy <- newick2phylog(w)
 print(w.phy)
 plot(w.phy)

## Not run: 
# newick2phylog
data(newick.eg)
radial.phylog(newick2phylog(newick.eg[[8]], FALSE), cnode = 1,
 clabel.l = 0.8)

w <- NULL
w[1] <- "(,((((((((((((((((,,(,(,))),),(((,(,)),(,)),),(,(,)),(,)),((((("
w[2] <- ",(,)),),),(,)),((((,((,),((,(,)),))),(,)),(,(,),,((,),(,)),)),("
w[3] <- "(((((,),),(,(,))),),(,)),(((,),),)))),((,,((,),)),(,)),((,),(,)"
w[4] <- ")),(((((((((,,),),,),),((,),)),(,),((,),)),),(((((,),),),((,),)"
w[5] <- "),(((,(,(,(,)))),(,)),(((,),(((((((,),),),,),(,)),(,)),)),((,)"
w[6] <- ",))))),(,((,),(,)),((,(,)),)))),((((,(,(,))),((,(,)),,((,(,)),)"
w[7] <- ",)),(((,),),(((,),),))),((,),))),((((((((((,,,,(,)),),((,),)),("
w[8] <- ",(,))),(((((((((,(,)),(,)),((((,((,),(,(,(,))))),((,),(,(,)))),"
w[9] <- "),((,),))),(((((((((,(,)),((,),(,))),),),),(((,((,),)),),((,((,"
w[10] <- "),)),)),(,)),(,(,(,)))),((((,(,)),(,)),(((,),(,)),(,),,(,))),(,"
w[11] <- "))),(,,,))),((((,),),),(((,(,(,))),((,),)),(,)))),(,)),),(,((,("
w[12] <- ",)),),(((,),),))),),(((,),),(,),(,(,))),(((,),(,)),((,),(,)))),"
w[13] <- "(((,),((,),)),(((((,,,,,),(,)),(,)),(,((,),))),))),(,(((((,(((("
w[14] <- ",(,)),),),)),),((,((,),((,((,),(,))),))),)),((((,),(((,),(,(,))"
w[15] <- "),)),),)),((,),)))),(((,((,,((,),)),)),),((,),))),((,),(,))),(("
w[16] <- ",),)),(((((,),((,(,)),(((,(,)),(,(((,),),))),))),(,),,),),),,(,"
w[17] <- ")),((((,),,),),((,,,),((,),((,),))))),((((((,(,)),,(,)),,(,),(,"
w[18] <- "),),(((((,(,(,),)),(((,),,),(,))),),),),,,((,),)),),)),(((((,),"
w[19] <- "(,(,)),),((,((,),),,),)),(((((((,),((((,,,),(,(,))),(((,(,)),),"
w[20] <- "(,))),)),),),),(,)),),),((,),))),((,),)),(((((((((((,),),(((((("
w[21] <- ",),),((,),)),(,)),),)),(,)),),((((((,),),(((,),),)),(,)),),(,))"
w[22] <- ",),),),),(,)),),((,),(,),,,)),(,(,(,)))),),(,)),),);"
phy1 <- newick2phylog(w,FALSE)
phy1
radial.phylog(phy1, clabel.l = 0, circle = 2.2, clea = 0.5,
 cnod = 0.5)
data(newick.eg)
radial.phylog(newick2phylog(newick.eg[[8]], FALSE), cnode = 1,
 clabel.l = 0.8)

# hclust2phylog
data(USArrests)
hc <- hclust(dist(USArrests), "ave")
par(mfrow = c(1,2))
plot(hc, hang = -1)
phy <- hclust2phylog(hc)
plot(phy, clabel.l = 0.75, clabel.n = 0.6, f = 0.75)

par(mfrow = c(1,1))
row.names(USArrests) 
names(phy$leaves) #WARNING not the same for two reasons
row.names(USArrests) <- gsub(" ","_",row.names(USArrests))
row.names(USArrests) 
names(phy$leaves) #WARNING not the same for one reason
USArrests <- USArrests[names(phy$leaves),]
row.names(USArrests) 
names(phy$leaves) #the same
table.phylog(data.frame(scalewt(USArrests)), phy, csi = 2.5,
 clabel.r = 0.75, f = 0.7)

#taxo2phylog
data(taxo.eg)
tax <- as.taxo(taxo.eg[[1]])
tax.phy <- taxo2phylog(as.taxo(taxo.eg[[1]]))
par(mfrow = c(1,2))
plot(tax.phy, clabel.l = 1.25, clabel.n = 1.25, f = 0.75)
plot(taxo2phylog(as.taxo(taxo.eg[[1]][sample(15),])),
 clabel.l = 1.25, clabel.n = 1.25, f = 0.75)

par(mfrow=c(1,1))
plot(taxo2phylog(as.taxo(taxo.eg[[2]])), clabel.l = 1,
 clabel.n = 0.75, f = 0.65)

## End(Not run)

Method to Analyse a pair of tables : Environmental and Faunistic Data

Description

performs a special multivariate analysis for ecological data.

Usage

niche(dudiX, Y, scannf = TRUE, nf = 2)
## S3 method for class 'niche'
print(x, ...) 
## S3 method for class 'niche'
plot(x, xax = 1, yax = 2, ...)
niche.param(x)
## S3 method for class 'niche'
rtest(xtest,nrepet=99, ...)

Arguments

dudiX

a duality diagram providing from a function dudi.coa, dudi.pca, ... using an array sites-variables
Y

a data frame sites-species according to dudiX$tab with no columns of zero
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes
x

an object of class niche
...

further arguments passed to or from other methods
xax, yax

the numbers of the x-axis and the y-axis
xtest

an object of class niche
nrepet

the number of permutations for the testing procedure

Value

Returns a list of the class niche (sub-class of dudi) containing :

rank

an integer indicating the rank of the studied matrix
nf

an integer indicating the number of kept axes
RV

a numeric value indicating the RV coefficient
eig

a numeric vector with the all eigenvalues
lw

a data frame with the row weigths (crossed array)
tab

a data frame with the crossed array (averaging species/sites)
li

a data frame with the species coordinates
l1

a data frame with the species normed scores
co

a data frame with the variable coordinates
c1

a data frame with the variable normed scores
ls

a data frame with the site coordinates
as

a data frame with the axis upon niche axis

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]
Stéphane Dray [email protected]

References

Dolédec, S., Chessel, D. and Gimaret, C. (2000) Niche separation in community analysis: a new method. Ecology, 81, 2914–1927.

Examples

data(doubs)
dudi1 <- dudi.pca(doubs$env, scale = TRUE, scan = FALSE, nf = 3)
nic1 <- niche(dudi1, doubs$fish, scann = FALSE)

if(adegraphicsLoaded()) {
  g1 <- s.traject(dudi1$li, plab.cex = 0, plot = FALSE)
  g2 <- s.traject(nic1$ls, plab.cex = 0, plot = FALSE)
  g3 <- s.corcircle(nic1$as, plot = FALSE)
  g4 <- s.arrow(nic1$c1, plot = FALSE)
  G1 <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))
  
  glist <- list()
  for(i in 1:ncol(doubs$fish))
    glist[[i]] <- s.distri(nic1$ls, dfdistri = doubs$fish[, i], psub.text = names(doubs$fish)[i], 
      plot = FALSE, storeData = TRUE)
  G2 <- ADEgS(glist, layout = c(5, 6))
  
  G3 <- s.arrow(nic1$li, plab.cex = 0.7)  
    
} else {
  par(mfrow = c(2, 2))
  s.traject(dudi1$li, clab = 0)
  s.traject(nic1$ls, clab = 0)
  s.corcircle(nic1$as)
  s.arrow(nic1$c1)

  par(mfrow = c(5, 6))
  for (i in 1:27) s.distri(nic1$ls, as.data.frame(doubs$fish[,i]),
    csub = 2, sub = names(doubs$fish)[i])
    
  par(mfrow = c(1, 1))
  s.arrow(nic1$li, clab = 0.7)

}

data(trichometeo)
pca1 <- dudi.pca(trichometeo$meteo, scan = FALSE)
nic1 <- niche(pca1, log(trichometeo$fau + 1), scan = FALSE)
plot(nic1)
niche.param(nic1)
rtest(nic1,19)

data(rpjdl)
plot(niche(dudi.pca(rpjdl$mil, scan = FALSE), rpjdl$fau, scan = FALSE))

Non-linear Iterative Partial Least Squares (NIPALS) algorithm

Description

This function performs NIPALS algorithm, i.e. a principal component analysis of a data table that can contain missing values.

Usage

nipals(df, nf = 2, rec = FALSE, niter = 100, tol = 1e-09)
## S3 method for class 'nipals'
scatter(x, xax = 1, yax = 2, clab.row = 0.75, clab.col
= 1, posieig = "top", sub = NULL, ...)
## S3 method for class 'nipals'
print(x, ...)

Arguments

df

a data frame that can contain missing values
nf

an integer, the number of axes to keep
rec

a logical that specify if the functions must perform the reconstitution of the data using the nf axes
niter

an integer, the maximum number of iterations
tol

a real, the tolerance used in the iterative algorithm
x

an object of class nipals
xax

the column number for the x-axis
yax

the column number for the y-axis
clab.row

a character size for the rows
clab.col

a character size for the columns
posieig

if "top" the eigenvalues bar plot is upside, if "bottom" it is downside, if "none" no plot
sub

a string of characters to be inserted as legend
...

further arguments passed to or from other methods

Details

Data are scaled (mean 0 and variance 1) prior to the analysis.

Value

Returns a list of classes nipals:

tab

the scaled data frame
eig

the pseudoeigenvalues
rank

the rank of the analyzed matrice
nf

the number of factors
c1

the column normed scores
co

the column coordinates
li

the row coordinates
call

the call function
nb

the number of iterations for each axis
rec

a data frame obtained by the reconstitution of the scaled data using the nf axes

Author(s)

Stéphane Dray [email protected]

References

Wold, H. (1966) Estimation of principal components and related models by iterative least squares. In P. Krishnaiah, editors.Multivariate Analysis, Academic Press, 391–420.

Wold, S., Esbensen, K. and Geladi, P. (1987) Principal component analysis Chemometrics and Intelligent Laboratory Systems, 2, 37–52.

See Also

dudi.pca

Examples

data(doubs)
## nipals is equivalent to dudi.pca when there are no NA
acp1 <- dudi.pca(doubs$env, scannf = FALSE, nf = 2)
nip1 <- nipals(doubs$env)


if(adegraphicsLoaded()) {
  if(requireNamespace("lattice", quietly = TRUE)) {
    g1 <- s1d.barchart(acp1$eig, psub.text = "dudi.pca", p1d.horizontal = FALSE, plot = FALSE)
    g2 <- s1d.barchart(nip1$eig, psub.text = "nipals", p1d.horizontal = FALSE, plot = FALSE)
    g3 <- lattice::xyplot(nip1$c1[, 1] ~ acp1$c1[, 1], main = "col scores", xlab = "dudi.pca", 
      ylab = "nipals")
    g4 <- lattice::xyplot(nip1$li[, 1] ~ acp1$li[, 1], main = "row scores", xlab = "dudi.pca", 
      ylab = "nipals")
    G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))
  }
  
} else {
  par(mfrow = c(2, 2))
  barplot(acp1$eig, main = "dudi.pca")
  barplot(nip1$eig, main = "nipals")
  plot(acp1$c1[, 1], nip1$c1[, 1], main = "col scores", xlab = "dudi.pca", ylab = "nipals")
  plot(acp1$li[, 1], nip1$li[, 1], main = "row scores", xlab = "dudi.pca", ylab = "nipals")
}

## Not run: 
## with NAs:
doubs$env[1, 1] <- NA
nip2 <- nipals(doubs$env)
cor(nip1$li, nip2$li)
nip1$eig
nip2$eig

## End(Not run)

Phylogeny and trait of bacteria

Description

This data set describes the phylogeny of 36 bacteria as reported by Perrière and Gouy (1996). It also gives the GC rate corresponding to these 36 species.

Usage

data(njplot)

Format

njplot is a list containing the 2 following objects:

tre

is a character string giving the fission tree in Newick format.

tauxcg

is a numeric vector that gives the CG rate of the 36 species.

Source

Data were obtained by Manolo Gouy [email protected]

References

Perrière, G. and Gouy, M. (1996) WWW-Query : an on-line retrieval system for biological sequence banks. Biochimie, 78, 364–369.

Examples

data(njplot)
njplot.phy <- newick2phylog(njplot$tre)
par(mfrow = c(2,1))
tauxcg0 <- njplot$tauxcg - mean(njplot$tauxcg)
symbols.phylog(njplot.phy, squares = tauxcg0)
symbols.phylog(njplot.phy, circles = tauxcg0)
par(mfrow = c(1,1))

Olympic Decathlon

Description

This data set gives the performances of 33 men's decathlon at the Olympic Games (1988).

Usage

data(olympic)

Format

olympic is a list of 2 components.

tab

is a data frame with 33 rows and 10 columns events of the decathlon: 100 meters (100), long jump (long), shotput (poid), high jump (haut), 400 meters (400), 110-meter hurdles (110), discus throw (disq), pole vault (perc), javelin (jave) and 1500 meters (1500).

score

is a vector of the final points scores of the competition.

Source

Example 357 in:
Hand, D.J., Daly, F., Lunn, A.D., McConway, K.J. and Ostrowski, E. (1994) A handbook of small data sets, Chapman & Hall, London. 458 p.

Lunn, A. D. and McNeil, D.R. (1991) Computer-Interactive Data Analysis, Wiley, New York

Examples

data(olympic)
pca1 <- dudi.pca(olympic$tab, scan = FALSE)

if(adegraphicsLoaded()) {
  if(requireNamespace("lattice", quietly = TRUE)) {
    g1 <- s1d.barchart(pca1$eig, p1d.hori = FALSE, plot = FALSE)
    g2 <- s.corcircle(pca1$co, plot = FALSE)
    g3 <- lattice::xyplot(pca1$l1[, 1] ~ olympic$score, type = c("p", "r"))
    g41 <- s.label(pca1$l1, plab.cex = 0.5, plot = FALSE)
    g42 <- s.arrow(2 * pca1$co, plot = FALSE)
    g4 <- superpose(g41, g42)
    G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))
  }
  
} else {
  par(mfrow = c(2, 2))
  barplot(pca1$eig)
  s.corcircle(pca1$co)
  plot(olympic$score, pca1$l1[, 1])
  abline(lm(pca1$l1[, 1] ~ olympic$score))
  s.label(pca1$l1, clab = 0.5)
  s.arrow(2 * pca1$co, add.p = TRUE)
  par(mfrow = c(1, 1))
}

Oribatid mite

Description

This data set contains informations about environmental control and spatial structure in ecological communities of Oribatid mites.

Usage

data(oribatid)

Format

oribatid is a list containing the following objects :

fau

: a data frame with 70 rows (sites) and 35 columns (Oribatid species)

envir

: a data frame with 70 rows (sites) and 5 columns (environmental variables)

xy

: a data frame that contains spatial coordinates of the 70 sites

Details

Variables of oribatid$envir are the following ones :
substrate: a factor with seven levels that describes the nature of the substratum
shrubs: a factor with three levels that describes the absence/presence of shrubs
topo: a factor with two levels that describes the microtopography
density: substratum density (g.L−1g.L^{-1})
water: water content of the substratum (g.L−1g.L^{-1})

Source

Data prepared by P. Legendre [email protected] and D. Borcard [email protected]

References

Borcard, D., and Legendre, P. (1994) Environmental control and spatial structure in ecological communities: an example using Oribatid mites (Acari Oribatei). Environmental and Ecological Statistics, 1, 37–61.

Borcard, D., Legendre, P., and Drapeau, P. (1992) Partialling out the spatial component of ecological variation. Ecology, 73, 1045–1055.

See a data description at http://pbil.univ-lyon1.fr/R/pdf/pps039.pdf (in French).

Examples

data(oribatid)
ori.xy <- oribatid$xy[, c(2, 1)]
names(ori.xy) <- c("x","y")
plot(ori.xy,pch = 20, cex = 2, asp = 1)

if(requireNamespace("deldir", quietly = TRUE) & requireNamespace("spdep", quietly = TRUE)) {
  plot(deldir::deldir(ori.xy), add = TRUE)
  if(adegraphicsLoaded()) {
    s.label(ori.xy, nb = spdep::knn2nb(spdep::knearneigh(as.matrix(ori.xy), 3)), plab.cex = 0)
  } else {
    s.label(ori.xy, add.p = TRUE, clab = 0, 
      neig = nb2neig(spdep::knn2nb(spdep::knearneigh(as.matrix(ori.xy), 3))))
  }
}

Originality of a species

Description

computes originality values for species from an ultrametric phylogenetic tree.

Usage

originality(phyl, method = 5)

Arguments

phyl

an object of class phylog
method

a vector containing integers between 1 and 7.

Details

1 = Vane-Wright et al.'s (1991) node-counting index 2 = May's (1990) branch-counting index 3 = Nixon and Wheeler's (1991) unweighted index, based on the sum of units in binary values 4 = Nixon and Wheeler's (1991) weighted index 5 = QE-based index 6 = Isaac et al. (2007) ED index 7 = Redding et al. (2006) Equal-split index

Value

Returns a data frame with species in rows, and the selected indices of originality in columns. Indices are expressed as percentages.

Author(s)

Sandrine Pavoine [email protected]

References

Isaac, N.J.B., Turvey, S.T., Collen, B., Waterman, C. and Baillie, J.E.M. (2007) Mammals on the EDGE: conservation priorities based on threat and phylogeny. PloS ONE, 2, e–296.

Redding, D. and Mooers, A. (2006) Incorporating evolutionary measures into conservation prioritization. Conservation Biology, 20, 1670–1678.

Pavoine, S., Ollier, S. and Dufour, A.-B. (2005) Is the originality of a species measurable? Ecology Letters, 8, 579–586.

Vane-Wright, R.I., Humphries, C.J. and Williams, P.H. (1991). What to protect? Systematics and the agony of choice. Biological Conservation, 55, 235–254.

May, R.M. (1990). Taxonomy as destiny. Nature, 347, 129–130.

Nixon, K.C. and Wheeler, Q.D. (1992). Measures of phylogenetic diversity. In: Extinction and Phylogeny (eds. Novacek, M.J. and Wheeler, Q.D.), 216–234, Columbia University Press, New York.

Examples

data(carni70)
carni70.phy <- newick2phylog(carni70$tre)
ori.tab <- originality(carni70.phy, 1:7)
names(ori.tab)
dotchart.phylog(carni70.phy, ori.tab, scaling = FALSE, yjoining = 0, 
    ranging = FALSE, cleaves = 0, ceti = 0.5, csub = 0.7, cdot = 0.5)

Orthonormal basis for orthonormal transform

Description

These functions returns object of class 'orthobasis' that contains data frame defining an orthonormal basis.

orthobasic.neig returns the eigen vectors of the matrix N-M where M is the symmetric n by n matrix of the between-sites neighbouring graph and N is the diagonal matrix of neighbour numbers.
orthobasis.line returns the analytical solution for the linear neighbouring graph.
orthobasic.circ returns the analytical solution for the circular neighbouring graph.
orthobsic.mat returns the eigen vectors of the general link matrix M.
orthobasis.haar returns wavelet haar basis.

Usage

orthobasis.neig(neig)
orthobasis.line(n)
orthobasis.circ(n)
orthobasis.mat(mat, cnw=TRUE)
orthobasis.haar(n)
## S3 method for class 'orthobasis'
print(x,..., nr = 6, nc = 4)
## S3 method for class 'orthobasis'
plot(x,...)
## S3 method for class 'orthobasis'
summary(object,...)
is.orthobasis(x)

Arguments

neig

is an object of class neig
n

is an integer that defines length of vectors
mat

is a n by n phylogenetic or spatial link matrix
cnw

if TRUE, the matrix of the neighbouring graph is modified to give Constant Neighbouring Weights
x, object

is an object of class orthobasis
nr, nc

the number of rows and columns to be printed
...

: further arguments passed to or from other methods

Value

All the functions return an object of class orthobasis containing a data frame. This data frame defines an orthonormal basis with various attributes:

names

names of the vectors
row.names

row names of the data frame
class

class
values

optional associated eigenvalues
weights

weights for the rows
call

: call

Note

the function orthobasis.haar uses function wavelet.filter from package waveslim.

Author(s)

Sébastien Ollier [email protected]
Daniel Chessel

References

Misiti, M., Misiti, Y., Oppenheim, G. and Poggi, J.M. (1993) Analyse de signaux classiques par décomposition en ondelettes. Revue de Statistique Appliquée, 41, 5–32.

Cornillon, P.A. (1998) Prise en compte de proximités en analyse factorielle et comparative. Thèse, Ecole Nationale Supérieure Agronomique, Montpellier.

See Also

gridrowcol that defines an orthobasis for square grid, phylog that defines an orthobasis for phylogenetic tree, orthogram and mld

Examples

# a 2D spatial orthobasis
w <- gridrowcol(8, 8)
if(adegraphicsLoaded()) {
  g1 <- s.value(w$xy, w$orthobasis[, 1:16], pleg.drawKey = FALSE, pgri.text.cex = 0, 
    ylim = c(0, 10), porigin.include = FALSE, paxes.draw = FALSE)
  g2 <- s1d.barchart(attr(w$orthobasis, "values"), p1d.horizontal = FALSE, 
    labels = names(attr(w$orthobasis, "values")), plabels.cex = 0.7)

} else {
  par(mfrow = c(4, 4))
  for(k in 1:16)
    s.value(w$xy, w$orthobasis[, k], cleg = 0, csi = 2, incl = FALSE,
      addax = FALSE, sub = k, csub = 4, ylim = c(0, 10), cgri = 0)
  par(mfrow = c(1, 1))
  barplot(attr(w$orthobasis, "values"))
}


# Haar 1D orthobasis
w <- orthobasis.haar(32)
par(mfrow = c(8, 4))
par(mar = c(0.1, 0.1, 0.1, 0.1))
 for (k in 1:31) {
    plot(w[, k], type = "S", xlab = "", ylab = "", xaxt = "n",
     yaxt = "n", xaxs = "i", yaxs = "i", ylim = c(-4.5, 4.5))
    points(w[, k], type = "p", pch = 20, cex = 1.5)
}

# a 1D orthobasis
w <- orthobasis.line(n = 33)
par(mfrow = c(8, 4))
par(mar = c(0.1, 0.1, 0.1, 0.1))
 for (k in 1:32) {
    plot(w[, k], type = "l", xlab = "", ylab = "", xaxt = "n",
     yaxt = "n", xaxs = "i", yaxs = "i", ylim = c(-1.5, 1.5))
    points(w[, k], type = "p", pch = 20, cex = 1.5)
}

if(adegraphicsLoaded()) {
  s1d.barchart(attr(w, "values"), p1d.horizontal = FALSE, labels = names(attr(w, "values")), 
    plab.cex = 0.7)
} else {
  par(mfrow = c(1, 1))
  barplot(attr(w, "values"))
}

w <- orthobasis.circ(n = 26)
#par(mfrow = c(5, 5))
#par(mar = c(0.1, 0.1, 0.1, 0.1))
# for (k in 1:25) 
#    dotcircle(w[, k], xlim = c(-1.5, 1.5), cleg = 0)

par(mfrow = c(1, 1))
#barplot(attr(w, "values"))

## Not run: 
# a spatial orthobasis
data(mafragh)
w <- orthobasis.neig(mafragh$neig)
if(adegraphicsLoaded()) {
  s.value(mafragh$xy, w[, 1:8], plegend.drawKey = FALSE)
  s1d.barchart(attr(w, "values"), p1d.horizontal = FALSE)
} else {
  par(mfrow = c(4, 2))
  for(k in 1:8)
    s.value(mafragh$xy, w[, k], cleg = 0, sub = as.character(k), csub = 3)
  par(mfrow = c(1, 1))
  barplot(attr(w, "values"))
}

# a phylogenetic orthobasis
data(njplot)
phy <- newick2phylog(njplot$tre)
wA <- phy$Ascores
wW <- phy$Wscores
table.phylog(phylog = phy, wA, clabel.row = 0, clabel.col  = 0.5)
table.phylog(phylog = phy, wW, clabel.row = 0, clabel.col  = 0.5)


## End(Not run)

A table of Qualitative Variables

Description

The ours (bears) data frame has 38 rows, areas of the "Inventaire National Forestier", and 10 columns.

Usage

data(ours)

Format

This data frame contains the following columns:

  1. altit: importance of the altitudinal area inhabited by bears, a factor with levels:

    • 1 less than 50% of the area between 800 and 2000 meters

    • 2 between 50 and 70%

    • 3 more than 70%

  2. deniv: importance of the average variation in level by square of 50 km2, a factor with levels:

    • 1 less than 700m

    • 2 between 700 and 900 m

    • 3 more than 900 m

  3. cloiso: partitioning of the massif, a factor with levels:

    • 1 a great valley or a ridge isolates at least a quarter of the massif

    • 2 less than a quarter of the massif is isolated

    • 3 the massif has no split

  4. domain: importance of the national forests on contact with the massif, a factor with levels:

    • 1 less than 400 km2

    • 2 between 400 and 1000 km2

    • 3 more than 1000 km2

  5. boise: rate of afforestation, a factor with levels:

    • 1 less than 30%

    • 2 between 30 and 50%

    • 3 more than 50%

  6. hetra: importance of plantations and mixed forests, a factor with levels:

    • 1 less than 5%

    • 2 between 5 and 10%

    • 3 more than 10% of the massif

  7. favor: importance of favorable forests, plantations, mixed forests, fir plantations, a factor with levels:

    • 1 less than 5%

    • 2 between 5 and 10%

    • 3 more than 10% of the massif

  8. inexp: importance of unworked forests, a factor with levels:

    • 1 less than 4%

    • 2 between 4 and 8%

    • 3 more than 8% of the total area

  9. citat: presence of the bear before its disappearance, a factor with levels:

    • 1 no quotation since 1840

    • 2 1 to 3 quotations before 1900 and none after

    • 3 4 quotations before 1900 and none after

    • 4 at least 4 quotations before 1900 and at least 1 quotation between 1900 and 1940

  10. depart: district, a factor with levels:

    • AHP Alpes-de-Haute-Provence

    • AM Alpes-Maritimes

    • D Drôme

    • HP Hautes-Alpes

    • HS Haute-Savoie

    • I Isère

    • S Savoie

Source

Erome, G. (1989) L'ours brun dans les Alpes françaises. Historique de sa disparition. Centre Ornithologique Rhône-Alpes, Villeurbanne. 120 p.

Examples

data(ours)
if(adegraphicsLoaded()) {
  s1d.boxplot(dudi.acm(ours, scan = FALSE)$l1[, 1], ours)
} else {
  boxplot(dudi.acm(ours, scan = FALSE))
}

Phylogenetic and quantitative traits of amazonian palm trees

Description

This data set describes the phylogeny of 66 amazonian palm trees. It also gives 7 traits corresponding to these 66 species.

Usage

data(palm)

Format

palm is a list containing the 2 following objects:

tre

is a character string giving the phylogenetic tree in Newick format.

traits

is a data frame with 66 species (rows) and 7 traits (columns).

Details

Variables of palm$traits are the following ones:
rord: specific richness with five ordered levels
h: height in meter (squared transform)
dqual: diameter at breast height in centimeter with five levels sout : subterranean, d1(0, 5 cm), d2(5, 15 cm), d3(15, 30 cm) and d4(30, 100 cm)
vfruit: fruit volume in mm3mm^{3} (logged transform)
vgrain: seed volume in mm3mm^{3} (logged transform)
aire: spatial distribution area (km2km^{2})
alti: maximum altitude in meter (logged transform)

Source

This data set was obtained by Clémentine Gimaret-Carpentier.

Examples

## Not run: 
data(palm)
palm.phy <- newick2phylog(palm$tre)
radial.phylog(palm.phy,clabel.l=1.25)

if (requireNamespace("adephylo", quietly = TRUE) & requireNamespace("ape", quietly = TRUE)) {
  tre <- ape::read.tree(text = palm$tre)
  adephylo::orthogram(palm$traits[, 4], tre)
}
dotchart.phylog(palm.phy,palm$traits[,4], clabel.l = 1,
 labels.n = palm.phy$Blabels, clabel.n = 0.75)
w <- cbind.data.frame(palm.phy$Bscores[,c(3,4,6,13,21)],
 scalewt((palm$traits[,4])))
names(w)[6] <- names(palm$traits[4])
table.phylog(w, palm.phy, clabel.r = 0.75, f = 0.5)

gearymoran(palm.phy$Amat, palm$traits[,-c(1,3)])

## End(Not run)

Taxonomy and quantitative traits of carnivora

Description

This data set describes the taxonomy of 39 carnivora. It also gives life-history traits corresponding to these 39 species.

Usage

data(pap)

Format

pap is a list containing the 2 following objects :

taxo

is a data frame with 39 species and 3 columns.

tab

is a data frame with 39 species and 4 traits.

Details

Variables of pap$tab are the following ones : genre (genus with 30 levels), famille (family with 6 levels), superfamille (superfamily with 2 levels).

Variables of pap$tab are Group Size, Body Weight, Brain Weight, Litter Size.

Source

Data taken from the phylogenetic autocorrelation package

Examples

data(pap)
taxo <- taxo2phylog(as.taxo(pap$taxo))
table.phylog(as.data.frame(scalewt(pap$tab)), taxo, csi = 2, clabel.nod = 0.6,
 f.phylog = 0.6)

Principal component analysis with respect to instrumental variables

Description

performs a principal component analysis with respect to instrumental variables.

Usage

pcaiv(dudi, df, scannf = TRUE, nf = 2)
## S3 method for class 'pcaiv'
plot(x, xax = 1, yax = 2, ...) 
## S3 method for class 'pcaiv'
print(x, ...)
## S3 method for class 'pcaiv'
summary(object, ...)

Arguments

dudi

a duality diagram, object of class dudi
df

a data frame with the same rows
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes


x, object

an object of class pcaiv
xax

the column number for the x-axis
yax

the column number for the y-axis
...

further arguments passed to or from other methods

Value

returns an object of class pcaiv, sub-class of class dudi

tab

a data frame with the modified array (projected variables)
cw

a numeric vector with the column weigths (from dudi)
lw

a numeric vector with the row weigths (from dudi)
eig

a vector with the all eigenvalues
rank

an integer indicating the rank of the studied matrix
nf

an integer indicating the number of kept axes
c1

a data frame with the Pseudo Principal Axes (PPA)
li

a data frame dudi$ls with the predicted values by X
co

a data frame with the inner products between the CPC and Y
l1

data frame with the Constraint Principal Components (CPC)
call

the matched call
X

a data frame with the explanatory variables
Y

a data frame with the dependant variables
ls

a data frame with the projections of lines of dudi$tab on PPA
param

a table containing information about contributions of the analyses : absolute (1) and cumulative (2) contributions of the decomposition of inertia of the dudi object, absolute (3) and cumulative (4) variances of the projections, the ration (5) between the cumulative variances of the projections (4) and the cumulative contributions (2), the square coefficient of correlation (6) and the eigenvalues of the pcaiv (7)
as

a data frame with the Principal axes of dudi$tab on PPA
fa

a data frame with the loadings (Constraint Principal Components as linear combinations of X
cor

a data frame with the correlations between the CPC and X

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]
Stéphane Dray [email protected]

References

Rao, C. R. (1964) The use and interpretation of principal component analysis in applied research. Sankhya, A 26, 329–359.

Obadia, J. (1978) L'analyse en composantes explicatives. Revue de Statistique Appliquee, 24, 5–28.

Lebreton, J. D., Sabatier, R., Banco G. and Bacou A. M. (1991) Principal component and correspondence analyses with respect to instrumental variables : an overview of their role in studies of structure-activity and species- environment relationships. In J. Devillers and W. Karcher, editors. Applied Multivariate Analysis in SAR and Environmental Studies, Kluwer Academic Publishers, 85–114.

Ter Braak, C. J. F. (1986) Canonical correspondence analysis : a new eigenvector technique for multivariate direct gradient analysis. Ecology, 67, 1167–1179.

Ter Braak, C. J. F. (1987) The analysis of vegetation-environment relationships by canonical correspondence analysis. Vegetatio, 69, 69–77.

Chessel, D., Lebreton J. D. and Yoccoz N. (1987) Propriétés de l'analyse canonique des correspondances. Une utilisation en hydrobiologie. Revue de Statistique Appliquée, 35, 55–72.

Examples

# example for the pcaiv
data(rhone)
pca1 <- dudi.pca(rhone$tab, scan = FALSE, nf = 3)
iv1 <- pcaiv(pca1, rhone$disch, scan = FALSE)
summary(iv1)
plot(iv1)

# example for the caiv
data(rpjdl)
millog <- log(rpjdl$mil + 1)
coa1 <- dudi.coa(rpjdl$fau, scann = FALSE)
caiv1 <- pcaiv(coa1, millog, scan = FALSE)

if(adegraphicsLoaded()) {
  G1 <- plot(caiv1)
  
  # analysis with c1 - as - li -ls
  # projections of inertia axes on PCAIV axes
  G2 <- s.corcircle(caiv1$as)
  
  # Species positions
  g31 <- s.label(caiv1$c1, xax = 2, yax = 1, plab.cex = 0.5, xlim = c(-4, 4), plot = FALSE)
  # Sites positions at the weighted mean of present species
  g32 <- s.label(caiv1$ls, xax = 2, yax = 1, plab.cex = 0, plot = FALSE)
  G3 <- superpose(g31, g32, plot = TRUE)
  
  # Prediction of the positions by regression on environmental variables
  G4 <- s.match(caiv1$ls, caiv1$li, xax = 2, yax = 1, plab.cex = 0.5)
  
  # analysis with fa - l1 - co -cor
  # canonical weights giving unit variance combinations
  G5 <- s.arrow(caiv1$fa)
  
  # sites position by environmental variables combinations
  # position of species by averaging
  g61 <- s.label(caiv1$l1, xax = 2, yax = 1, plab.cex = 0, ppoi.cex = 1.5, plot = FALSE)
  g62 <- s.label(caiv1$co, xax = 2, yax = 1, plot = FALSE)
  G6 <- superpose(g61, g62, plot = TRUE)
  
  G7 <- s.distri(caiv1$l1, rpjdl$fau, xax = 2, yax = 1, ellipseSize = 0, starSize = 0.33)
  
  # coherence between weights and correlations
  g81 <- s.corcircle(caiv1$cor, xax = 2, yax = 1, plot = FALSE)
  g82 <- s.arrow(caiv1$fa, xax = 2, yax = 1, plot = FALSE)
  G8 <- cbindADEg(g81, g82, plot = TRUE)

} else {
  plot(caiv1)
  
  # analysis with c1 - as - li -ls
  # projections of inertia axes on PCAIV axes
  s.corcircle(caiv1$as)
  
  # Species positions
  s.label(caiv1$c1, 2, 1, clab = 0.5, xlim = c(-4, 4))
  # Sites positions at the weighted mean of present species
  s.label(caiv1$ls, 2, 1, clab = 0, cpoi = 1, add.p = TRUE)
  
  # Prediction of the positions by regression on environmental variables
  s.match(caiv1$ls, caiv1$li, 2, 1, clab = 0.5)
  
  # analysis with fa - l1 - co -cor
  # canonical weights giving unit variance combinations
  s.arrow(caiv1$fa)
  
  # sites position by environmental variables combinations
  # position of species by averaging
  s.label(caiv1$l1, 2, 1, clab = 0, cpoi = 1.5)
  s.label(caiv1$co, 2, 1, add.plot = TRUE)
  
  s.distri(caiv1$l1, rpjdl$fau, 2, 1, cell = 0, csta = 0.33)
  s.label(caiv1$co, 2, 1, clab = 0.75, add.plot = TRUE)
  
  # coherence between weights and correlations
  par(mfrow = c(1, 2))
  s.corcircle(caiv1$cor, 2, 1)
  s.arrow(caiv1$fa, 2, 1)
  par(mfrow = c(1, 1))
}

Principal Component Analysis with respect to orthogonal instrumental variables

Description

performs a Principal Component Analysis with respect to orthogonal instrumental variables.

Usage

pcaivortho(dudi, df, scannf = TRUE, nf = 2)
## S3 method for class 'pcaivortho'
summary(object, ...)

Arguments

dudi

a duality diagram, object of class dudi
df

a data frame with the same rows
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes
object

an object of class pcaiv
...

further arguments passed to or from other methods

Value

an object of class 'pcaivortho' sub-class of class dudi

rank

an integer indicating the rank of the studied matrix
nf

an integer indicating the number of kept axes
eig

a vector with the all eigenvalues
lw

a numeric vector with the row weigths (from dudi)
cw

a numeric vector with the column weigths (from dudi)
Y

a data frame with the dependant variables
X

a data frame with the explanatory variables
tab

a data frame with the modified array (projected variables)
c1

a data frame with the Pseudo Principal Axes (PPA)
as

a data frame with the Principal axis of dudi$tab on PAP
ls

a data frame with the projection of lines of dudi$tab on PPA
li

a data frame dudi$ls with the predicted values by X
l1

a data frame with the Constraint Principal Components (CPC)
co

a data frame with the inner product between the CPC and Y
param

a data frame containing a summary

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]
Stéphane Dray [email protected]

References

Rao, C. R. (1964) The use and interpretation of principal component analysis in applied research. Sankhya, A 26, 329–359.

Sabatier, R., Lebreton J. D. and Chessel D. (1989) Principal component analysis with instrumental variables as a tool for modelling composition data. In R. Coppi and S. Bolasco, editors. Multiway data analysis, Elsevier Science Publishers B.V., North-Holland, 341–352

Examples

## Not run: 
data(avimedi)
cla <- avimedi$plan$reg:avimedi$plan$str
# simple ordination
coa1 <- dudi.coa(avimedi$fau, scan = FALSE, nf = 3)
# within region
w1 <- wca(coa1, avimedi$plan$reg, scan = FALSE)
# no region the same result
pcaivnonA <- pcaivortho(coa1, avimedi$plan$reg, scan = FALSE)
summary(pcaivnonA)
# region + strate
interAplusB <- pcaiv(coa1, avimedi$plan, scan = FALSE)

if(adegraphicsLoaded()) {
  g1 <- s.class(coa1$li, cla, psub.text = "Sans contrainte", plot = FALSE)
  g21 <- s.match(w1$li, w1$ls, plab.cex = 0, psub.text = "Intra Région", plot = FALSE)
  g22 <- s.class(w1$li, cla, plot = FALSE)
  g2 <- superpose(g21, g22)
  g31 <- s.match(pcaivnonA$li, pcaivnonA$ls, plab.cex = 0, psub.tex = "Contrainte Non A", 
    plot = FALSE)
  g32 <- s.class(pcaivnonA$li, cla, plot = FALSE)
  g3 <- superpose(g31, g32)
  g41 <- s.match(interAplusB$li, interAplusB$ls, plab.cex = 0, psub.text = "Contrainte A + B", 
    plot = FALSE)
  g42 <- s.class(interAplusB$li, cla, plot = FALSE)
  g4 <- superpose(g41, g42)
  G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))

} else {
  par(mfrow = c(2, 2))
  s.class(coa1$li, cla, sub = "Sans contrainte")
  s.match(w1$li, w1$ls, clab = 0, sub = "Intra Région")
  s.class(w1$li, cla, add.plot = TRUE)
  s.match(pcaivnonA$li, pcaivnonA$ls, clab = 0, sub = "Contrainte Non A")
  s.class(pcaivnonA$li, cla, add.plot = TRUE)
  s.match(interAplusB$li, interAplusB$ls, clab = 0, sub = "Contrainte A + B")
  s.class(interAplusB$li, cla, add.plot = TRUE)
  par(mfrow = c(1,1))
}
## End(Not run)

Simplified Analysis in Principal Coordinates

Description

performs a simplified analysis in principal coordinates, using an object of class dist.

Usage

pcoscaled(distmat, tol = 1e-07)

Arguments

distmat

an object of class dist
tol

a tolerance threshold, an eigenvalue is considered as positive if it is larger than -tol*lambda1 where lambda1 is the largest eigenvalue

Value

returns a data frame containing the Euclidean representation of the distance matrix with a total inertia equal to 1

Author(s)

Daniel Chessel

References

Gower, J. C. (1966) Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika, 53, 325–338.

Examples

a <- 1 / sqrt(3) - 0.2
    w <- matrix(c(0,0.8,0.8,a,0.8,0,0.8,a,
        0.8,0.8,0,a,a,a,a,0),4,4)
    w <- as.dist(w)
    w <- cailliez(w)
    w
    pcoscaled(w)
    dist(pcoscaled(w)) # w
    dist(pcoscaled(2 * w)) # the same
    sum(pcoscaled(w)^2) # unity

Distribution of of tropical trees along the Panama canal

Description

Abundance of tropical trees, environmental variables and spatial coordinates for 50 sites. Data are available at doi:10.1126/science.1066854 but plots from Barro Colorado Island were removed.

Usage

data(pcw)

Format

A list with 5 components.

spe

Distribution of the abundances of 778 species in 50 sites

env

Measurements of environmental variables for the 50 sites

xy

Spatial coordinates for the sites (decimal degrees)

xy.utm

Spatial coordinates for the sites (UTM)

map

Map of the study area stored as a SpatialPolygons object

Source

Condit, R., N. Pitman, E. G. Leigh, J. Chave, J. Terborgh, R. B. Foster, P. Núnez, S. Aguilar, R. Valencia, G. Villa, H. C. Muller-Landau, E. Losos, and S. P. Hubbell. (2002) Beta-diversity in tropical forest trees. Science, 295, 666-669.

Pyke, C. R., R. Condit, S. Aguilar, and S. Lao. (2001) Floristic composition across a climatic gradient in a neotropical lowland forest. Journal of Vegetation Science, 12, 553–566.

References

Dray, S., R. Pélissier, P. Couteron, M. J. Fortin, P. Legendre, P. R. Peres-Neto, E. Bellier, R. Bivand, F. G. Blanchet, M. De Caceres, A. B. Dufour, E. Heegaard, T. Jombart, F. Munoz, J. Oksanen, J. Thioulouse, and H. H. Wagner. (2012) Community ecology in the age of multivariate multiscale spatial analysis. Ecological Monographs, 82, 257–275.

Examples

if(adegraphicsLoaded()) {
  data(pcw)
  if(requireNamespace("spdep", quietly = TRUE)) {
    nb1 <- spdep::graph2nb(spdep::gabrielneigh(pcw$xy.utm), sym = TRUE) 
    s.label(pcw$xy, nb = nb1, Sp = pcw$map)
  }
}

Contingency Table with a partition in Molecular Biology

Description

This data set gives the amino acids of 904 proteins distributed in three classes.

Usage

data(perthi02)

Format

perthi02 is a list of 2 components.

tab

is a data frame 904 rows (proteins of 201 species) 20 columns (amino acids).

cla

is a factor of 3 classes of protein

The levels of perthi02$cla are cyto (cytoplasmic proteins) memb (integral membran proteins) peri (periplasmic proteins)

Source

Perriere, G. and Thioulouse, J. (2002) Use of Correspondence Discriminant Analysis to predict the subcellular location of bacterial proteins. Computer Methods and Programs in Biomedicine, 70, 2, 99–105.

Examples

data(perthi02)
plot(discrimin.coa(perthi02$tab, perthi02$cla, scan = FALSE))

Phylogeny

Description

Create and use objects of class phylog.
phylog.extract returns objects of class phylog. It extracts sub-trees from a tree.
phylog.permut returns objects of class phylog. It creates the different representations compatible with tree topology.

Usage

## S3 method for class 'phylog'
print(x, ...)
phylog.extract(phylog, node, distance = TRUE)
phylog.permut(phylog, list.nodes = NULL, distance = TRUE)

Arguments

x, phylog

: an object of class phylog
...

: further arguments passed to or from other methods
node

: a string of characters giving a node name. The functions extracts the tree rooted at this node.
distance

: if TRUE, both functions retain branch lengths. If FALSE, they returns tree with arbitrary branch lengths (each branch length equals one)
list.nodes

: a list which elements are vectors of string of character corresponding to direct descendants of nodes. This list defines one representation compatible with tree topology among the set of possibilities.

Value

Returns a list of class phylog :

tre

: a character string of the phylogenetic tree in Newick format whithout branch length values
leaves

: a vector which names corresponds to leaves and values gives the distance between leaves and nodes closest to these leaves
nodes

: a vector which names corresponds to nodes and values gives the distance between nodes and nodes closest to these leaves
parts

: a list which elements gives the direct descendants of each nodes
paths

: a list which elements gives the path leading from the root to taxonomic units (leaves and nodes)
droot

: a vector which names corresponds to taxonomic units and values gives distance between taxonomic units and the root
call

: call
Wmat

: a phylogenetic link matrix, generally called the covariance matrix. Matrix values WmatijWmat_{ij} correspond to path length that lead from root to the first common ancestor of the two leaves i and j
Wdist

: a phylogenetic distance matrix of class 'dist'. Matrix values WdistijWdist_{ij} correspond to dij\sqrt{d_{ij}} where dijd_{ij} is the classical distance between two leaves i and j
Wvalues

: a vector with the eigen values of Wmat
Wscores

: a data frame with eigen vectors of Wmat. This data frame defines an orthobasis that could be used to calculate the orthonormal decomposition of a biological trait on a tree.
Amat

: a phylogenetic link matrix stemed from Abouheif's test and defined in Ollier et al. (submited)
Avalues

: a vector with the eigen values of Amat
Adim

: number of positive eigen values
Ascores

: a data frame with eigen vectors of Amat. This data frame defines an orthobasis that could be used to calculate the orthonormal decomposition of a biological trait on a tree.
Aparam

: a data frame with attributes associated to nodes.
Bindica

: a data frame giving for some taxonomic units the partition of leaves that is associated to its
Bscores

: a data frame giving an orthobasis defined by Ollier et al. (submited) that could be used to calculate the orthonormal decomposition of a biological trait on a tree.
Bvalues

: a vector giving the degree of phylogenetic autocorrelation for each vectors of Bscores (Moran's form calculated with the matrix Wmat)
Blabels

: a vector giving for each nodes the name of the vector of Bscores that is associated to its

Author(s)

Daniel Chessel
Sébastien Ollier [email protected]

References

Ollier, S., Couteron, P. and Chessel, D. (2006) Orthonormal transform to decompose the variance of a life-history trait across a phylogenetic tree. Biometrics Biometrics, 62, 2, 471–477.

See Also

newick2phylog, plot.phylog

Examples

marthans.tre <- NULL
marthans.tre[1] <-"((((1:4,2:4)a:5,(3:7,4:7)b:2)c:2,5:11)d:2,"
marthans.tre[2] <- "((6:5,7:5)e:4,(8:4,9:4)f:5)g:4);"
marthans.phylog <- newick2phylog(marthans.tre)
marthans.phylog

if(requireNamespace("ape", quietly = TRUE)) {
  marthans.phylo <- ape::read.tree(text = marthans.tre)
  marthans.phylo

  par(mfrow = c(1, 2))
  plot(marthans.phylog, cnode = 3, f = 0.8, cle = 3)
  plot(marthans.phylo)
  par(mfrow = c(1, 1))
}

Import data files from Phylogenetic Independance Package

Description

This function ensures to transform a data set written for the Phylogenetic Independance package of Abouheif (1999) in a data set formatting for the functions of ade4.

Usage

PI2newick(x)

Arguments

x

is a data frame that contains information on phylogeny topology and trait values

Value

Returns a list containing :

tre

: a character string giving the phylogenetic tree in Newick format
trait

: a vector containing values of the trait

Author(s)

Sébastien Ollier [email protected]
Daniel Chessel

References

Abouheif, E. (1999) A method for testing the assumption of phylogenetic independence in comparative data. Evolutionary Ecology Research, 1, 895–909.

Examples

x <- c(2.0266, 0.5832, 0.2460, 1.2963, 0.2460, 0.1565, -99.0000,
        -99.0000, 10.1000, -99.0000,  20.2000,  28.2000, -99.0000, 
        14.1000, 11.2000, -99.0000, 21.3000, 27.5000, 1.0000, 2.0000,
        -1.0000, 4.0000, -1.0000, -1.0000, 3.0000, -1.0000, -1.0000,
        5.0000, -1.0000, -1.0000, 0.0000, 0.0000, 0.0000, 0.0000,
        0.0000, 0.0000)
x <- matrix(x, nrow = 6)
x <- as.data.frame(x)
res <- PI2newick(x)
dotchart.phylog(newick2phylog(res$tre), res$trait)

Plant traits response to grazing

Description

Plant species cover, traits and environmental parameters recorded around livestock watering points in different habitats of central Namibian farmlands. See the Wesuls et al. (2012) paper for a full description of the data set.

Usage

data(piosphere)

Format

piosphere is a list of 4 components.

veg

is a data frame containing plant species cover

traits

is a data frame with plant traits

env

is a data frame with environmental variables

habitat

is a factor describing habitat/years for each site

Source

Wesuls, D., Oldeland, J. and Dray, S. (2012) Disentangling plant trait responses to livestock grazing from spatio-temporal variation: the partial RLQ approach. Journal of Vegetation Science, 23, 98–113.

Examples

data(piosphere)
names(piosphere)
afcL <- dudi.coa(log(piosphere$veg + 1), scannf = FALSE)
acpR <- dudi.pca(piosphere$env, scannf = FALSE, row.w = afcL$lw)
acpQ <- dudi.hillsmith(piosphere$traits, scannf = FALSE, row.w = afcL$cw)
rlq1 <- rlq(acpR, afcL, acpQ, scannf = FALSE)
plot(rlq1)

Plot phylogenies

Description

plot.phylog draws phylogenetic trees as linear dendograms.
radial.phylog draws phylogenetic trees as circular dendograms.
enum.phylog enumerate all the possible representations for a phylogeny.

Usage

## S3 method for class 'phylog'
plot(x, y = NULL, f.phylog = 0.5, cleaves = 1, cnodes = 0,
 labels.leaves = names(x$leaves), clabel.leaves = 1,
 labels.nodes = names(x$nodes), clabel.nodes = 0, sub = "",
 csub = 1.25, possub = "bottomleft", draw.box = FALSE, ...)
radial.phylog(phylog, circle = 1, cleaves = 1, cnodes = 0,
 labels.leaves = names(phylog$leaves), clabel.leaves = 1,
 labels.nodes = names(phylog$nodes), clabel.nodes = 0,
 draw.box = FALSE)
enum.phylog(phylog, no.over = 1000)

Arguments

x, phylog

an object of class phylog
y

a vector which values correspond to leaves positions
f.phylog

a size coefficient for tree size (a parameter to draw the tree in proportion to leaves label)
circle

a size coefficient for the outer circle
cleaves

a character size for plotting the points that represent the leaves, used with par("cex")*cleaves. If zero, no points are drawn
cnodes

a character size for plotting the points that represent the nodes, used with par("cex")*cnodes. If zero, no points are drawn
labels.leaves

a vector of strings of characters for the leaves labels
clabel.leaves

a character size for the leaves labels, used with par("cex")*clabel.leaves. If zero, no leaves labels are drawn
labels.nodes

a vector of strings of characters for the nodes labels
clabel.nodes

a character size for the nodes labels, used with par("cex")*clabel.nodes. If zero, no nodes labels are drawn
sub

a string of characters to be inserted as legend
csub

a character size for the legend, used with par("cex")*csub
possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")
draw.box

if TRUE draws a box around the current plot with the function box()
...

further arguments passed to or from other methods
no.over

a size coefficient for the number of representations

Details

The vector y is an argument of the function plot.phylog that ensures to plot one of the possible representations of a phylogeny. The vector y is a permutation of the set of leaves {1,2,...,f} compatible with the phylogeny's topology.

Value

The function enum.phylog returns a matrix with as many columns as leaves. Each row gives a permutation of the set of leaves {1,2,...,f} compatible with the phylogeny's topology.

Author(s)

Daniel Chessel
Sébastien Ollier [email protected]

See Also

phylog

Examples

data(newick.eg)
par(mfrow = c(3,2))
for(i in 1:6) plot(newick2phylog(newick.eg[[i]], FALSE),
 clea = 2, clabel.l = 3, cnod = 2.5)
par(mfrow = c(1,1))

## Not run: 
par(mfrow = c(1,2))
plot(newick2phylog(newick.eg[[11]], FALSE), clea = 1.5,
 clabel.l = 1.5, clabel.nod = 0.75, f = 0.8)
plot(newick2phylog(newick.eg[[10]], FALSE), clabel.l = 0,
 clea = 0, cn = 0, f = 1)
par(mfrow = c(1,1))

## End(Not run)

par(mfrow = c(2,2))
w7 <- newick2phylog("(((((1,2,3)b),(6)c),(4,5)d,7)f);")
plot(w7,clabel.l = 1.5, clabel.n = 1.5, f = 0.8, cle = 2,
 cnod = 3, sub = "(((((1,2,3)b),(6)c),(4,5)d,7)f);", csub = 2)
w <- NULL
w[1] <- "((((e1:4,e2:4)a:5,(e3:7,e4:7)b:2)c:2,e5:11)d:2,"
w[2] <- "((e6:5,e7:5)e:4,(e8:4,e9:4)f:5)g:4);"
plot(newick2phylog(w), f = 0.8, cnod = 2, cleav = 2, clabel.l = 2)

data(taxo.eg)
w <- taxo2phylog(as.taxo(taxo.eg[[1]]))
plot(w, clabel.lea = 1.25, clabel.n = 1.25, sub = "Taxonomy",
 csub = 3, f = 0.8, possub = "topleft")

provi.tre <- "(((a,b,c,d,e)A,(f,g,h)B)C)D;"
provi.phy <- newick2phylog(provi.tre)
plot(provi.phy, clabel.l = 2, clabel.n = 2, f = 0.8)
par(mfrow = c(1,1))

## Not run: 
par(mfrow = c(3,3))
for (j in 1:6) radial.phylog(newick2phylog(newick.eg[[j]],
 FALSE), clabel.l = 2, cnodes = 2)
radial.phylog(newick2phylog(newick.eg[[7]],FALSE), clabel.l = 2)
radial.phylog(newick2phylog(newick.eg[[8]],FALSE), clabel.l = 0,
 circle = 1.8)
radial.phylog(newick2phylog(newick.eg[[9]],FALSE), clabel.l = 1,
 clabel.n = 1, cle = 0, cnode = 1)
par(mfrow = c(1,1))

data(bsetal97)
bsetal.phy = taxo2phylog(as.taxo(bsetal97$taxo[,1:3]), FALSE)
radial.phylog(bsetal.phy, cnod = 1, clea = 1, clabel.l = 0.75,
 draw.box = TRUE, cir = 1.1)
par(mfrow = c(1,1))

## End(Not run)

## Not run: 
# plot all the possible representations of a phylogenetic tree
a <- "((a,b)A,(c,d,(e,f)B)C)D;"
wa <- newick2phylog(a)
wx <- enum.phylog(wa)
dim(wx)

par(mfrow = c(6,8))
fun <- function(x) {
    w  <-NULL
    lapply(x, function(y) w<<-paste(w,as.character(y),sep=""))
    plot(wa, x, clabel.n = 1.25, f = 0.75, clabel.l = 2,
     box = FALSE, cle = 1.5, sub = w, csub = 2)
    invisible()}
apply(wx,1,fun)
par(mfrow = c(1,1))

## End(Not run)

Results of the French presidential elections of 2002

Description

presid2002 is a list of two data frames tour1 and tour2 with 93 rows (93 departments from continental Metropolitan France) and, 4 and 12 variables respectively .

Usage

data(presid2002)

Format

tour1 contains the following arguments:
the number of registered voters (inscrits); the number of abstentions (abstentions); the number of voters (votants); the number of expressed votes (exprimes) and, the numbers of votes for each candidate: Megret, Lepage, Gluksten, Bayrou, Chirac, Le_Pen, Taubira, Saint.josse, Mamere, Jospin, Boutin, Hue, Chevenement, Madelin, Besancenot.

tour2 contains the following arguments:
the number of registered voters (inscrits); the number of abstentions (abstentions); the number of voters (votants); the number of expressed votes (exprimes) and, the numbers of votes for each candidate: Chirac and Le_Pen.

Source

Site of the ministry of the Interior, of the Internal Security and of the local liberties
https://www.interieur.gouv.fr/Elections/Les-resultats/Presidentielles/elecresult__presidentielle_2002/(path)/presidentielle_2002/index.html

See Also

This dataset is compatible with elec88 and cnc2003

Examples

data(presid2002)
all((presid2002$tour2$Chirac + presid2002$tour2$Le_Pen) == presid2002$tour2$exprimes)

## Not run: 
data(elec88)
data(cnc2003)
w0 <- ade4:::area.util.class(elec88$area, cnc2003$reg)
w1 <- scale(elec88$tab$Chirac)
w2 <- scale(presid2002$tour1$Chirac / presid2002$tour1$exprimes)
w3 <- scale(elec88$tab$Mitterand)
w4 <- scale(presid2002$tour2$Chirac / presid2002$tour2$exprimes)

if(adegraphicsLoaded()) {
  g1 <- s.value(elec88$xy, w1, Sp = elec88$Spatial, pSp.col = "white", pgrid.draw = FALSE, 
    psub.text = "Chirac 1988 T1", plot = FALSE)
  g2 <- s.value(elec88$xy, w2, Sp = elec88$Spatial, pSp.col = "white", pgrid.draw = FALSE, 
    psub.text = "Chirac 2002 T1", plot = FALSE)
  g3 <- s.value(elec88$xy, w3, Sp = elec88$Spatial, pSp.col = "white", pgrid.draw = FALSE, 
    psub.text = "Mitterand 1988 T1", plot = FALSE)
  g4 <- s.value(elec88$xy, w4, Sp = elec88$Spatial, pSp.col = "white", pgrid.draw = FALSE, 
    psub.text = "Chirac 2002 T2", plot = FALSE)
  G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))
      
} else {
  par(mfrow = c(2, 2))
  par(mar = c(0.1, 0.1, 0.1, 0.1))

  area.plot(w0)
  s.value(elec88$xy, w1, add.plot = TRUE)
  scatterutil.sub("Chirac 1988 T1", csub = 2, "topleft")

  area.plot(w0)
  s.value(elec88$xy, w2, add.plot = TRUE)
  scatterutil.sub("Chirac 2002 T1", csub = 2, "topleft")
  
  area.plot(w0)
  s.value(elec88$xy, w3, add.plot = TRUE)
  scatterutil.sub("Mitterand 1988 T1", csub = 2, "topleft")
  
  area.plot(w0)
  s.value(elec88$xy, w4, add.plot = TRUE)
  scatterutil.sub("Chirac 2002 T2", csub = 2, "topleft")
}
## End(Not run)

Phylogeny and quantitative traits of birds

Description

This data set describes the phylogeny of 19 birds as reported by Bried et al. (2002). It also gives 6 traits corresponding to these 19 species.

Usage

data(procella)

Format

procella is a list containing the 2 following objects:

tre

is a character string giving the phylogenetic tree in Newick format.

traits

is a data frame with 19 species and 6 traits

Details

Variables of procella$traits are the following ones:
site.fid: a numeric vector that describes the percentage of site fidelity
mate.fid: a numeric vector that describes the percentage of mate fidelity
mass: an integer vector that describes the adult body weight (g)
ALE: a numeric vector that describes the adult life expectancy (years)
BF: a numeric vector that describes the breeding frequencies
col.size: an integer vector that describes the colony size (no nests monitored)

References

Bried, J., Pontier, D. and Jouventin, P. (2002) Mate fidelity in monogamus birds: a re-examination of the Procellariiformes. Animal Behaviour, 65, 235–246.

See a data description at http://pbil.univ-lyon1.fr/R/pdf/pps037.pdf (in French).

Examples

data(procella)
pro.phy <- newick2phylog(procella$tre)
plot(pro.phy,clabel.n = 1, clabel.l = 1)
wt <- procella$traits
wt$site.fid[is.na(wt$site.fid)] <- mean(wt$site.fid[!is.na(wt$site.fid)])
wt$site.fid <- asin(sqrt(wt$site.fid/100))
wt$ALE[is.na(wt$ALE)] <- mean(wt$ALE[!is.na(wt$ALE)])
wt$ALE <- sqrt(wt$ALE)
wt$BF[is.na(wt$BF)] <- mean(wt$BF[!is.na(wt$BF)])
wt$mass <- log(wt$mass)
wt <- wt[, -6]
table.phylog(scalewt(wt), pro.phy, csi = 2)
gearymoran(pro.phy$Amat,wt,9999)

Simple Procruste Rotation between two sets of points

Description

performs a simple procruste rotation between two sets of points.

Usage

procuste(dfX, dfY, scale = TRUE, nf = 4, tol = 1e-07) 
## S3 method for class 'procuste'
plot(x, xax = 1, yax = 2, ...)
## S3 method for class 'procuste'
print(x, ...)
## S3 method for class 'procuste'
randtest(xtest, nrepet = 999, ...)

Arguments

dfX, dfY

two data frames with the same rows
scale

a logical value indicating whether a transformation by the Gower's scaling (1971) should be applied
nf

an integer indicating the number of kept axes
tol

a tolerance threshold to test whether the distance matrix is Euclidean : an eigenvalue is considered positive if it is larger than -tol*lambda1 where lambda1 is the largest eigenvalue.


x, xtest

an objet of class procuste
xax

the column number for the x-axis
yax

the column number for the y-axis
nrepet

the number of repetitions to perform the randomization test
...

further arguments passed to or from other methods

Value

returns a list of the class procuste with 9 components

d

a numeric vector of the singular values
rank

an integer indicating the rank of the crossed matrix
nf

an integer indicating the number of kept axes
tabX

a data frame with the array X, possibly scaled
tabY

a data frame with the array Y, possibly scaled
rotX

a data frame with the result of the rotation from array X to array Y
rotY

a data frame with the result of the rotation from array Y to array X
loadX

a data frame with the loadings of array X
loadY

a data frame with the loadings of array Y
scorX

a data frame with the scores of array X
scorY

a data frame with the scores of array Y
call

a call order of the analysis

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

References

Digby, P. G. N. and Kempton, R. A. (1987) Multivariate Analysis of Ecological Communities. Population and Community Biology Series, Chapman and Hall, London.

Gower, J.C. (1971) Statistical methods of comparing different multivariate analyses of the same data. In Mathematics in the archaeological and historical sciences, Hodson, F.R, Kendall, D.G. & Tautu, P. (Eds.) University Press, Edinburgh, 138–149.

Schönemann, P.H. (1968) On two-sided Procustes problems. Psychometrika, 33, 19–34.

Torre, F. and Chessel, D. (1994) Co-structure de deux tableaux totalement appariés. Revue de Statistique Appliquée, 43, 109–121.

Dray, S., Chessel, D. and Thioulouse, J. (2003) Procustean co-inertia analysis for the linking of multivariate datasets. Ecoscience, 10, 1, 110-119.

Examples

data(macaca)
pro1 <- procuste(macaca$xy1, macaca$xy2, scal = FALSE)
pro2 <- procuste(macaca$xy1, macaca$xy2)
if(adegraphicsLoaded()) {
  g1 <- s.match(pro1$tabX, pro1$rotY, plab.cex = 0.7, plot = FALSE)
  g2 <- s.match(pro1$tabY, pro1$rotX, plab.cex = 0.7, plot = FALSE)
  g3 <- s.match(pro2$tabX, pro2$rotY, plab.cex = 0.7, plot = FALSE)
  g4 <- s.match(pro2$tabY, pro2$rotX, plab.cex = 0.7, plot = FALSE)
  G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))
} else {
  par(mfrow = c(2, 2))
  s.match(pro1$tabX, pro1$rotY, clab = 0.7)
  s.match(pro1$tabY, pro1$rotX, clab = 0.7)
  s.match(pro2$tabX, pro2$rotY, clab = 0.7)
  s.match(pro2$tabY, pro2$rotX, clab = 0.7)
  par(mfrow = c(1,1))
}

data(doubs)
pca1 <- dudi.pca(doubs$env, scal = TRUE, scann = FALSE)
pca2 <- dudi.pca(doubs$fish, scal = FALSE, scann = FALSE)
pro3 <- procuste(pca1$tab, pca2$tab, nf = 2)
if(adegraphicsLoaded()) {
  g11 <- s.traject(pro3$scorX, plab.cex = 0, plot = FALSE)
  g12 <- s.label(pro3$scorX, plab.cex = 0.8, plot = FALSE)
  g1 <- superpose(g11, g12)
  g21 <- s.traject(pro3$scorY, plab.cex = 0, plot = FALSE)
  g22 <- s.label(pro3$scorY, plab.cex = 0.8, plot = FALSE)
  g2 <- superpose(g21, g22)
  g3 <- s.arrow(pro3$loadX, plab.cex = 0.75, plot = FALSE)
  g4 <- s.arrow(pro3$loadY, plab.cex = 0.75, plot = FALSE)
  G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))

} else {
  par(mfrow = c(2, 2))
  s.traject(pro3$scorX, clab = 0)
  s.label(pro3$scorX, clab = 0.8, add.p = TRUE)
  s.traject(pro3$scorY, clab = 0)
  s.label(pro3$scorY, clab = 0.8, add.p = TRUE)
  s.arrow(pro3$loadX, clab = 0.75)
  s.arrow(pro3$loadY, clab = 0.75)
  par(mfrow = c(1, 1))
}

plot(pro3)
randtest(pro3)

data(fruits)
plot(procuste(scalewt(fruits$jug), scalewt(fruits$var)))

Monte-Carlo Test on the sum of the singular values of a procustean rotation (in C).

Description

performs a Monte-Carlo Test on the sum of the singular values of a procustean rotation.

Usage

procuste.randtest(df1, df2, nrepet = 999, ...)

Arguments

df1

a data frame
df2

a data frame
nrepet

the number of permutations
...

further arguments passed to or from other methods

Value

returns a list of class randtest

Author(s)

Jean Thioulouse [email protected]

References

Jackson, D.A. (1995) PROTEST: a PROcustean randomization TEST of community environment concordance. Ecosciences, 2, 297–303.

Examples

data(doubs)
pca1 <- dudi.pca(doubs$env, scal = TRUE, scann = FALSE)
pca2 <- dudi.pca(doubs$fish, scal = FALSE, scann = FALSE)
protest1 <- procuste.randtest(pca1$tab, pca2$tab, 999)
protest1
plot(protest1,main="PROTEST")

Monte-Carlo Test on the sum of the singular values of a procustean rotation (in R).

Description

performs a Monte-Carlo Test on the sum of the singular values of a procustean rotation.

Usage

procuste.rtest(df1, df2, nrepet = 99, ...)

Arguments

df1

a data frame
df2

a data frame
nrepet

the number of permutations
...

further arguments passed to or from other methods

Value

returns a list of class rtest

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

References

Jackson, D.A. (1995) PROTEST: a PROcustean randomization TEST of community environment concordance. Ecosciences, 2, 297–303.

Examples

data(doubs)
pca1 <- dudi.pca(doubs$env, scal = TRUE, scann = FALSE)
pca2 <- dudi.pca(doubs$fish, scal = FALSE, scann = FALSE)
proc1 <- procuste(pca1$tab, pca2$tab)
protest1 <- procuste.rtest(pca1$tab, pca2$tab, 999)
protest1
plot(protest1)

Partial Triadic Analysis of a K-tables

Description

performs a partial triadic analysis of a K-tables, using an object of class ktab.

Usage

pta(X, scannf = TRUE, nf = 2)
## S3 method for class 'pta'
plot(x, xax = 1, yax = 2, option = 1:4, ...)
## S3 method for class 'pta'
print(x, ...)

Arguments

X

an object of class ktab where the arrays have 1) the same dimensions 2) the same names for columns 3) the same column weightings
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes
x

an object of class 'pta'
xax, yax

the numbers of the x-axis and the y-axis
option

an integer between 1 and 4, otherwise the 4 components of the plot are displayed
...

further arguments passed to or from other methods

Value

returns a list of class 'pta', sub-class of 'dudi' containing :

RV

a matrix with the all RV coefficients
RV.eig

a numeric vector with the all eigenvalues (interstructure)
RV.coo

a data frame with the scores of the arrays
tab.names

a vector of characters with the array names
nf

an integer indicating the number of kept axes
rank

an integer indicating the rank of the studied matrix
tabw

a numeric vector with the array weights
cw

a numeric vector with the column weights
lw

a numeric vector with the row weights
eig

a numeric vector with the all eigenvalues (compromis)
cos2

a numeric vector with the cos⁡2\cos^2 between compromise and arrays
tab

a data frame with the modified array
li

a data frame with the row coordinates
l1

a data frame with the row normed scores
co

a data frame with the column coordinates
c1

a data frame with the column normed scores
Tli

a data frame with the row coordinates (each table)
Tco

a data frame with the column coordinates (each table)
Tcomp

a data frame with the principal components (each table)
Tax

a data frame with the principal axes (each table)
TL

a data frame with the factors for Tli
TC

a data frame with the factors for Tco
T4

a data frame with the factors for Tax and Tcomp

Author(s)

Pierre Bady [email protected]
Anne-Béatrice Dufour [email protected]

References

Blanc, L., Chessel, D. and Dolédec, S. (1998) Etude de la stabilité temporelle des structures spatiales par Analyse d'une série de tableaux faunistiques totalement appariés. Bulletin Français de la Pêche et de la Pisciculture, 348, 1–21.

Thioulouse, J., and D. Chessel. 1987. Les analyses multi-tableaux en écologie factorielle. I De la typologie d'état à la typologie de fonctionnement par l'analyse triadique. Acta Oecologica, Oecologia Generalis, 8, 463–480.

Examples

data(meaudret)
wit1 <- withinpca(meaudret$env, meaudret$design$season, scan = FALSE, scal = "partial")
kta1 <- ktab.within(wit1, colnames = rep(c("S1", "S2", "S3", "S4", "S5"), 4))
kta2 <- t(kta1)
pta1 <- pta(kta2, scann = FALSE)
pta1
plot(pta1)

Transformation of a distance matrice to a Euclidean one

Description

transforms a distance matrix in a Euclidean one.

Usage

quasieuclid(distmat)

Arguments

distmat

an object of class dist

Details

The function creates a distance matrice with the positive eigenvalues of the Euclidean representation.
Only for Euclidean distances which are not Euclidean for numeric approximations (for examples, in papers as the following example).

Value

object of class dist containing a Euclidean distance matrice

Author(s)

Daniel Chessel
Stéphane Dray [email protected]

Examples

data(yanomama)
geo <- as.dist(yanomama$geo)
is.euclid(geo) # FALSE
geo1 <- quasieuclid(geo)
is.euclid(geo1) # TRUE
par(mfrow = c(2,2))
lapply(yanomama, function(x) plot(as.dist(x), quasieuclid(as.dist(x))))

par(mfrow = c(1,1))

Bootstrap simulations

Description

Functions and classes to manage outputs of bootstrap simulations for one (class randboot) or several (class krandboot) statistics

Usage

as.krandboot(obs, boot, quantiles = c(0.025, 0.975), names =
colnames(boot), call = match.call())
## S3 method for class 'krandboot'
print(x, ...)
as.randboot(obs, boot, quantiles = c(0.025, 0.975), call = match.call())
## S3 method for class 'randboot'
print(x, ...)
randboot(object, ...)

Arguments

obs

a value (class randboot) or a vector (class krandboot) with observed statistics
boot

a vector (class randboot) or a matrix (class krandboot) with the bootstrap values of the statistics
quantiles

a vector indicating the lower and upper quantiles to compute
names

a vector of names for the statistics
call

the matching call
x

an object of class randboot or krandboot
object

an object on which bootstrap should be perform
...

other arguments to be passed to methods

Value

an object of class randboot or krandboot

Author(s)

Stéphane Dray ([email protected])

References

Carpenter, J. and Bithell, J. (2000) Bootstrap confidence intervals: when, which, what? A practical guide for medical statisticians.Statistics in medicine, 19, 1141-1164

See Also

randboot.multiblock

Examples

## an example corresponding to 10 statistics and 100 repetitions
bt <- as.krandboot(obs = rnorm(10), boot = matrix(rnorm(1000), nrow = 100))
bt
if(adegraphicsLoaded())
plot(bt)

Bootstraped simulations for multiblock methods

Description

Function to perform bootstraped simulations for multiblock principal component analysis with instrumental variables or multiblock partial least squares, in order to get confidence intervals for some parameters, i.e., regression coefficients, variable and block importances

Usage

## S3 method for class 'multiblock'
randboot(object, nrepet = 199, optdim, ...)

Arguments

object

an object of class multiblock created by mbpls or mbpcaiv
nrepet

integer indicating the number of repetitions
optdim

integer indicating the optimal number of dimensions, i.e., the optimal number of global components to be introduced in the model
...

other arguments to be passed to methods

Value

A list containing objects of class krandboot

Author(s)

Stéphanie Bougeard ([email protected]) and Stéphane Dray ([email protected])

References

Carpenter, J. and Bithell, J. (2000) Bootstrap confidence intervals: when, which, what? A practical guide for medical statisticians.Statistics in medicine, 19, 1141-1164.

Bougeard, S. and Dray S. (2018) Supervised Multiblock Analysis in R with the ade4 Package. Journal of Statistical Software, 86 (1), 1-17. doi:10.18637/jss.v086.i01

See Also

mbpcaiv, mbpls, testdim.multiblock, as.krandboot

Examples

data(chickenk)
Mortality <- chickenk[[1]]
dudiY.chick <- dudi.pca(Mortality, center = TRUE, scale = TRUE, scannf =
FALSE)
ktabX.chick <- ktab.list.df(chickenk[2:5])
resmbpcaiv.chick <- mbpcaiv(dudiY.chick, ktabX.chick, scale = TRUE,
option = "uniform", scannf = FALSE, nf = 4)
## nrepet should be higher for a real analysis
test <- randboot(resmbpcaiv.chick, optdim = 4, nrepet = 10)
test
if(adegraphicsLoaded())
plot(test$bipc)

Class of the Permutation Tests (in C).

Description

randtest is a generic function. It proposes methods for the following objects between, discrimin, coinertia ...

Usage

randtest(xtest, ...)
as.randtest(sim, obs, alter = c("greater", "less", "two-sided"), 
  output = c("light", "full"), call = match.call(), subclass = NULL)

## S3 method for class 'randtest'
plot(x, nclass = 10, coeff = 1, ...)
## S3 method for class 'randtest'
print(x, ...)

Arguments

xtest

an object used to select a method
x

an object of class randtest
...

further arguments passed to or from other methods; in plot.randtest to hist
output

a character string specifying if all simulations should be stored ("full"). This was the default until ade4 1.7-5. Now, by default ("light"), only the distribution of simulated values is stored in element plot as produced by the hist function.
nclass

a number of intervals for the histogram. Ignored if object output is "light"
coeff

to fit the magnitude of the graph. Ignored if object output is "light"
sim

a numeric vector of simulated values
obs

a numeric vector of an observed value
alter

a character string specifying the alternative hypothesis, must be one of "greater" (default), "less" or "two-sided"
call

a call order
subclass

a character vector indicating the subclasses associated to the returned object

Details

If the alternative hypothesis is "greater", a p-value is estimated as: (number of random values equal to or greater than the observed one + 1)/(number of permutations + 1). The null hypothesis is rejected if the p-value is less than the significance level. If the alternative hypothesis is "less", a p-value is estimated as: (number of random values equal to or less than the observed one + 1)/(number of permutations + 1). Again, the null hypothesis is rejected if the p-value is less than the significance level. Lastly, if the alternative hypothesis is "two-sided", the estimation of the p-value is equivalent to the one used for "greater" except that random and observed values are firstly centered (using the average of random values) and secondly transformed to their absolute values. Note that this is only suitable for symmetric random distribution.

Value

as.randtest returns a list of class randtest.
plot.randtest draws the simulated values histograms and the position of the observed value.

See Also

randtest.amova, randtest.between, randtest.coinertia, randtest.discrimin, randtest.dpcoa, randtest.pcaiv, rtest, rtest.between, rtest.discrimin, RV.rtest, RVdist.randtest, mantel.randtest, mantel.rtest, procuste.randtest, procuste.rtest

Examples

par(mfrow = c(2,2))
for (x0 in c(2.4,3.4,5.4,20.4)) {
  l0 <- as.randtest(sim = rnorm(200), obs = x0)
  print(l0)
  plot(l0,main=paste("p.value = ", round(l0$pvalue, dig = 5)))
}
par(mfrow = c(1,1))

Permutation tests on an analysis of molecular variance (in C).

Description

Tests the components of covariance with permutation processes described by Excoffier et al. (1992).

Usage

## S3 method for class 'amova'
randtest(xtest, nrepet = 99, ...)

Arguments

xtest

an object of class amova
nrepet

the number of permutations
...

further arguments passed to or from other methods

Value

returns an object of class krandtest or randtest

Author(s)

Sandrine Pavoine [email protected]

References

Excoffier, L., Smouse, P.E. and Quattro, J.M. (1992) Analysis of molecular variance inferred from metric distances among DNA haplotypes: application to human mitochondrial DNA restriction data. Genetics, 131, 479–491.

Examples

data(humDNAm)
amovahum <- amova(humDNAm$samples, sqrt(humDNAm$distances), humDNAm$structures)
amovahum
randtesthum <- randtest(amovahum, 49)
plot(randtesthum)

Monte-Carlo Test on the between-groups inertia percentage (in C).

Description

Performs a Monte-Carlo test on the between-groups inertia percentage.

Usage

## S3 method for class 'between'
randtest(xtest, nrepet = 999, ...)

Arguments

xtest

an object of class between
nrepet

the number of permutations
...

further arguments passed to or from other methods

Value

a list of the class randtest

Author(s)

Jean Thioulouse [email protected]

References

Romesburg, H. C. (1985) Exploring, confirming and randomization tests. Computers and Geosciences, 11, 19–37.

Examples

data(meaudret)
pca1 <- dudi.pca(meaudret$env, scan = FALSE, nf = 3)
rand1 <- randtest(bca(pca1, meaudret$design$season, scan = FALSE), 99)
rand1
plot(rand1, main = "Monte-Carlo test")

Monte-Carlo test on a Co-inertia analysis (in C).

Description

Performs a Monte-Carlo test on a Co-inertia analysis.

Usage

## S3 method for class 'coinertia'
randtest(xtest, nrepet = 999, fixed=0, ...)

Arguments

xtest

an object of class coinertia
nrepet

the number of permutations
fixed

when non uniform row weights are used in the coinertia analysis, this parameter must be the number of the table that should be kept fixed in the permutations
...

further arguments passed to or from other methods

Value

a list of the class randtest

Note

A testing procedure based on the total coinertia of the analysis is available by the function randtest.coinertia. The function allows to deal with various analyses for the two tables. The test is based on random permutations of the rows of the two tables. If the row weights are not uniform, mean and variances are recomputed for each permutation (PCA); for MCA, tables are recentred and column weights are recomputed. If weights are computed using the data contained in one table (e.g. COA), you must fix this table and permute only the rows of the other table. The case of decentred PCA (PCA where centers are entered by the user) is not yet implemented. If you want to use the testing procedure for this case, you must firstly center the table and then perform a non-centered PCA on the modified table. The case where one table is treated by hill-smith analysis (mix of quantitative and qualitative variables) will be soon implemented.

Author(s)

Jean Thioulouse [email protected] modified by Stéphane Dray [email protected]

References

Dolédec, S. and Chessel, D. (1994) Co-inertia analysis: an alternative method for studying species-environment relationships. Freshwater Biology, 31, 277–294.

Examples

data(doubs)
dudi1 <- dudi.pca(doubs$env, scale = TRUE, scan = FALSE, nf = 3)
dudi2 <- dudi.pca(doubs$fish, scale = FALSE, scan = FALSE, nf = 2)
coin1 <- coinertia(dudi1,dudi2, scan = FALSE, nf = 2)
plot(randtest(coin1))

Monte-Carlo Test on a Discriminant Analysis (in C).

Description

Test of the sum of a discriminant analysis eigenvalues (divided by the rank). Non parametric version of the Pillai's test. It authorizes any weighting.

Usage

## S3 method for class 'discrimin'
randtest(xtest, nrepet = 999, ...)

Arguments

xtest

an object of class discrimin
nrepet

the number of permutations
...

further arguments passed to or from other methods

Value

returns a list of class randtest

Author(s)

Jean Thioulouse [email protected]

Examples

data(meaudret)
pca1 <- dudi.pca(meaudret$env, scan = FALSE, nf = 3)
rand1 <- randtest(discrimin(pca1, meaudret$design$season, scan = FALSE), 99)
rand1
#Monte-Carlo test
#Observation: 0.3035 
#Call: as.randtest(sim = sim, obs = obs)
#Based on 999 replicates
#Simulated p-value: 0.001 
plot(rand1, main = "Monte-Carlo test")
summary.manova(manova(as.matrix(meaudret$env)~meaudret$design$season), "Pillai")
#                   Df Pillai approx F num Df den Df  Pr(>F)    
# meaudret$design$season  3   2.73    11.30     27     30 1.6e-09 ***
# Residuals         16                                          
# ---
# Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 
# 2.731/9 = 0.3034

Permutation test for double principal coordinate analysis (DPCoA)

Description

randtest.dpcoa calculates the ratio of beta to gamma diversity associated with DPCoA and compares the observed value to values obtained by permuting data.

Usage

## S3 method for class 'dpcoa'
randtest(xtest, model = c("1p","1s"), nrepet = 99,
alter = c("greater", "less", "two-sided"), ...)

Arguments

xtest

an object of class dpcoa
model

either "1p", "1s", or the name of a function, (see details)
nrepet

the number of permutations to perform, the default is 99
alter

a character string specifying the alternative hypothesis, must be one of "greater" (default), "less" or "two-sided"
...

further arguments passed to or from other methods

Details

Model 1p permutes the names of the columns of the abundance matrix. Model 1s permutes the abundances of the categories (columns of the abundance matrix, usually species) within collections (rows of the abundance matrix, usually communities). Only the categories with positive abundances are permuted. The null models were introduced in Hardy (2008).

Other null model can be used by entering the name of a function. For example, loading the picante package of R, if model=randomizeMatrix, then the permutations will follow function randomizeMatrix available in picante. Any function can be used provided it returns an abundance matrix of similar size as the observed abundance matrix. Parameters of the chosen function can be added to randtest.dpcoa. For example, using parameter null.model of randomizeMatrix, the following command can be used: randtest.dpcoa(xtest, model = randomizeMatrix, null.model = "trialswap")

Value

an object of class randtest

Author(s)

Sandrine Pavoine [email protected]

References

Hardy, O. (2008) Testing the spatial phylogenetic structure of local communities: statistical performances of different null models and test statistics on a locally neutral community. Journal of Ecology, 96, 914–926

See Also

dpcoa

Examples

data(humDNAm)
dpcoahum <- dpcoa(data.frame(t(humDNAm$samples)), sqrt(humDNAm$distances), scan = FALSE, nf = 2)
randtest(dpcoahum)

Monte-Carlo Test on the percentage of explained (i.e. constrained) inertia

Description

Performs a Monte-Carlo test on on the percentage of explained (i.e. constrained) inertia. The statistic is the ratio of the inertia (sum of eigenvalues) of the constrained analysis divided by the inertia of the unconstrained analysis.

Usage

## S3 method for class 'pcaiv'
randtest(xtest, nrepet = 99, ...)
## S3 method for class 'pcaivortho'
randtest(xtest, nrepet = 99, ...)

Arguments

xtest

an object of class pcaiv, pcaivortho or caiv
nrepet

the number of permutations
...

further arguments passed to or from other methods

Value

a list of the class randtest

Author(s)

Stéphane Dray [email protected], original code by Raphaël Pélissier

Examples

data(rpjdl)
millog <- log(rpjdl$mil + 1)
coa1 <- dudi.coa(rpjdl$fau, scann = FALSE)
caiv1 <- pcaiv(coa1, millog, scan = FALSE)
randtest(caiv1)

Two-fold cross-validation

Description

Functions and classes to manage outputs of two-fold cross-validation for one (class randxval) or several (class krandxval) statistics

Usage

as.krandxval(RMSEc, RMSEv, quantiles = c(0.25, 0.75), names =
colnames(RMSEc), call = match.call())
## S3 method for class 'krandxval'
print(x, ...)
as.randxval(RMSEc, RMSEv, quantiles = c(0.25, 0.75), call =
match.call())
## S3 method for class 'randxval'
print(x, ...)

Arguments

RMSEc

a vector (class randxval) or a matrix (class krandxval) with the root-mean-square error of calibration (statistics as columns and repetions as rows)
RMSEv

a vector (class randxval) or a matrix (class krandxval) with the root-mean-square error of validation (statistics as columns and repetions as rows)
quantiles

a vector indicating the lower and upper quantiles to compute
names

a vector of names for the statistics
call

the matching call
x

an object of class randxval or krandxval
...

other arguments to be passed to methods

Value

an object of class randxval or krandxval

Author(s)

Stéphane Dray ([email protected])

References

Stone M. (1974) Cross-validatory choice and assessment of statistical predictions. Journal of the Royal Statistical Society, 36, 111-147

See Also

testdim.multiblock

Examples

## an example corresponding to 10 statistics and 100 repetitions
cv <- as.krandxval(RMSEc = matrix(rnorm(1000), nrow = 100), RMSEv =
matrix(rnorm(1000, mean = 1), nrow = 100))
cv
if(adegraphicsLoaded())
plot(cv)

Ordination Table

Description

This data set gives the classification in order of preference of 10 music groups by 51 students.

Usage

data(rankrock)

Format

A data frame with 10 rows and 51 columns.
Each column contains the rank (1 for the favorite, ..., 10 for the less appreciated)
attributed to the group by a student.

Examples

data(rankrock)
dudi1 <- dudi.pca(rankrock, scannf = FALSE, nf = 3)
if(adegraphicsLoaded()) {
  g <- scatter(dudi1, row.plab.cex = 1.5)
} else {
  scatter(dudi1, clab.r = 1.5)
}

Reconstitution of Data from a Duality Diagram

Description

Generic Function for the reconstitution of data from a principal component analysis or a correspondence analysis

Usage

reconst (dudi, ...)
## S3 method for class 'pca'
reconst(dudi, nf = 1, ...) 
## S3 method for class 'coa'
reconst(dudi, nf = 1, ...)

Arguments

dudi

an object of class dudi used to select a method: pca or coa
nf

an integer indicating the number of kept axes for the reconstitution
...

further arguments passed to or from other methods

Value

returns a data frame containing the reconstituted data

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

References

Gabriel, K.R. (1978) Least-squares approximation of matrices by additive and multiplicative models. Journal of the Royal Statistical Society, B , 40, 186–196.

Examples

data(rhone)
dd1 <- dudi.pca(rhone$tab, nf = 2, scann = FALSE)
rh1 <- reconst(dd1, 1)
rh2 <- reconst(dd1, 2)
par(mfrow = c(4,4))
par(mar = c(2.6,2.6,1.1,1.1))
for (i in 1:15) {
    plot(rhone$date, rhone$tab[,i])
    lines(rhone$date, rh1[,i], lty = 2)
    lines(rhone$date, rh2[,i], lty = 1)
    ade4:::scatterutil.sub(names(rhone$tab)[i], 2, "topright")}

data(chats)
chatsw <- data.frame(t(chats))
chatscoa <- dudi.coa(chatsw, scann = FALSE)
model0 <- reconst(chatscoa, 0)
round(model0,3)
round(chisq.test(chatsw)$expected,3)
chisq.test(chatsw)$statistic
sum(((chatsw-model0)^2)/model0)
effectif <- sum(chatsw)
sum(chatscoa$eig)*effectif
model1 <- reconst(chatscoa, 1)
round(model1, 3)
sum(((chatsw-model1)^2)/model0)
sum(chatscoa$eig[-1])*effectif

Genetic structure of two nitrogen fixing bacteria influenced by geographical isolation and host specialization

Description

The data set concerns fixing bacteria belonging to the genus Sinorhizobium (Rhizobiaceae) associated with the plant genus Medicago (Fabaceae). It is a combination of two data sets fully available online from GenBank and published in two recent papers (see reference below). The complete sampling procedure is described in the Additional file 3 of the reference below. We delineated six populations according to geographical origin (France: F, Tunisia Hadjeb: TH, Tunisia Enfidha: TE), the host plant (M. truncatula or similar symbiotic specificity: T, M. laciniata: L), and the taxonomical status of bacteria (S. meliloti: mlt, S. medicae: mdc). Each population will be called hereafter according to the three above criteria, e.g. THLmlt is the population sampled in Tunisia at Hadjeb from M. laciniata nodules which include S. meliloti isolates. S. medicae interacts with M. truncatula while S. meliloti interacts with both M. laciniata (S. meliloti bv. medicaginis) and M. truncatula (S. meliloti bv. meliloti). The numbers of individuals are respectively 46 for FTmdc, 43 for FTmlt, 20 for TETmdc, 24 for TETmlt, 20 for TELmlt, 42 for THTmlt and 20 for THLmlt.

Four different intergenic spacers (IGS), IGSNOD, IGSEXO, IGSGAB, and IGSRKP, distributed on the different replication units of the model strain 1021 of S. meliloti bv. meliloti had been sequenced to characterize each bacterial isolate (DNA extraction and sequencing procedures are described in an additional file). It is noteworthy that the IGSNOD marker is located within the nod gene cluster and that specific alleles at these loci determine the ability of S. meliloti strains to interact with either M. laciniata or M. truncatula.

Usage

data(rhizobium)

Format

rhizobium is a list of 2 components.

  • dnaobj: list of dna lists. Each dna list corresponds to a locus. For a given locus, the dna list provides the dna sequences The ith sequences of all loci corresponds to the ith individual of the data set.

  • pop: The list of the populations which each individual sequence belongs to.

Source

Pavoine, S. and Bailly, X. (2007) New analysis for consistency among markers in the study of genetic diversity: development and application to the description of bacterial diversity. BMC Evolutionary Biology, 7, e156.

Examples

# The functions used below require the package ape
data(rhizobium)
if(requireNamespace("ape", quietly = TRUE)) {
dat <- prep.mdpcoa(rhizobium[[1]], rhizobium[[2]], 
    model = c("F84", "F84", "F84", "F81"),
    pairwise.deletion = TRUE)
sam <- dat$sam
dis <- dat$dis
# The distances should be Euclidean. 
# Several transformations exist to render a distance object Euclidean 
# (see functions cailliez, lingoes and quasieuclid in the ade4 package). 
# Here we use the quasieuclid function.
dis <- lapply(dis, quasieuclid)
mdpcoa1 <- mdpcoa(sam, dis, scann = FALSE, nf = 2)

# Reference analysis
plot(mdpcoa1)

# Differences between the loci
kplot(mdpcoa1)

# Alleles projected on the population maps.
kplotX.mdpcoa(mdpcoa1)
}

Physico-Chemistry Data

Description

This data set gives for 39 water samples a physico-chemical description with the number of sample date and the flows of three tributaries.

Usage

data(rhone)

Format

rhone is a list of 3 components.

tab

is a data frame with 39 water samples and 15 physico-chemical variables.

date

is a vector of the sample date (in days).

disch

is a data frame with 39 water samples and the flows of the three tributaries.

Source

Carrel, G., Barthelemy, D., Auda, Y. and Chessel, D. (1986) Approche graphique de l'analyse en composantes principales normée : utilisation en hydrobiologie. Acta Oecologica, Oecologia Generalis, 7, 189–203.

Examples

data(rhone)
pca1 <- dudi.pca(rhone$tab, nf = 2, scann = FALSE)
rh1 <- reconst(pca1, 1)
rh2 <- reconst(pca1, 2)
par(mfrow = c(4,4))
par(mar = c(2.6,2.6,1.1,1.1))
for (i in 1:15) {
    plot(rhone$date, rhone$tab[,i])
    lines(rhone$date, rh1[,i], lwd = 2)
    lines(rhone$date, rh2[,i])
    ade4:::scatterutil.sub(names(rhone$tab)[i], 2, "topright")
}
par(mfrow = c(1,1))

RLQ analysis

Description

RLQ analysis performs a double inertia analysis of two arrays (R and Q) with a link expressed by a contingency table (L). The rows of L correspond to the rows of R and the columns of L correspond to the rows of Q.

Usage

rlq(dudiR, dudiL, dudiQ, scannf = TRUE, nf = 2)
## S3 method for class 'rlq'
print(x, ...)
## S3 method for class 'rlq'
plot(x, xax = 1, yax = 2, ...)
## S3 method for class 'rlq'
summary(object, ...)
## S3 method for class 'rlq'
randtest(xtest,nrepet = 999, modeltype = 6,...)

Arguments

dudiR

a duality diagram providing from one of the functions dudi.hillsmith, dudi.pca, ...

dudiL

a duality diagram of the function dudi.coa

dudiQ

a duality diagram providing from one of the functions dudi.hillsmith, dudi.pca, ...

scannf

a logical value indicating whether the eigenvalues bar plot should be displayed

nf

if scannf FALSE, an integer indicating the number of kept axes

x

an rlq object

xax

the column number for the x-axis
yax

the column number for the y-axis
object

an rlq object

xtest

an rlq object

nrepet

the number of permutations

modeltype

the model used to permute data(2: permute rows of R, 4: permute rows of Q, 5: permute both, 6: sequential approach, see ter Braak et al. 2012)
...

further arguments passed to or from other methods

Value

Returns a list of class 'dudi', sub-class 'rlq' containing:

call

call
rank

rank
nf

a numeric value indicating the number of kept axes
RV

a numeric value, the RV coefficient
eig

a numeric vector with all the eigenvalues
lw

a numeric vector with the rows weigths (crossed array)
cw

a numeric vector with the columns weigths (crossed array)
tab

a crossed array (CA)
li

R col = CA row: coordinates
l1

R col = CA row: normed scores
co

Q col = CA column: coordinates
c1

Q col = CA column: normed scores
lR

the row coordinates (R)
mR

the normed row scores (R)
lQ

the row coordinates (Q)
mQ

the normed row scores (Q)
aR

the axis onto co-inertia axis (R)
aQ

the axis onto co-inertia axis (Q)

WARNING

IMPORTANT : row weights for dudiR and dudiQ must be taken from dudiL.

Note

A testing procedure based on the total coinertia of the RLQ analysis is available by the function randtest.rlq. The function allows to deal with various analyses for tables R and Q. Means and variances are recomputed for each permutation (PCA); for MCA, tables are recentred and column weights are recomputed.The case of decentred PCA (PCA where centers are entered by the user) for R or Q is not yet implemented. If you want to use the testing procedure for this case, you must firstly center the table and then perform a non-centered PCA on the modified table.

Author(s)

Stéphane Dray [email protected]

References

Doledec, S., Chessel, D., ter Braak, C.J.F. and Champely, S. (1996) Matching species traits to environmental variables: a new three-table ordination method. Environmental and Ecological Statistics, 3, 143–166.

Dray, S., Pettorelli, N., Chessel, D. (2002) Matching data sets from two different spatial samplings. Journal of Vegetation Science, 13, 867–874.

Dray, S. and Legendre, P. (2008) Testing the species traits-environment relationships: the fourth-corner problem revisited. Ecology, 89, 3400–3412.

ter Braak, C., Cormont, A., Dray, S. (2012) Improved testing of species traits-environment relationships in the fourth corner problem. Ecology, 93, 1525–1526.

See Also

coinertia, fourthcorner

Examples

data(aviurba)
   coa1 <- dudi.coa(aviurba$fau, scannf = FALSE, nf = 2)
   dudimil <- dudi.hillsmith(aviurba$mil, scannf = FALSE, nf = 2, row.w = coa1$lw)
   duditrait <- dudi.hillsmith(aviurba$traits, scannf = FALSE, nf = 2, row.w = coa1$cw)
   rlq1 <- rlq(dudimil, coa1, duditrait, scannf = FALSE, nf = 2)
   plot(rlq1)
   summary(rlq1)
   randtest(rlq1)
   fourthcorner.rlq(rlq1,type="Q.axes")
   fourthcorner.rlq(rlq1,type="R.axes")

Avifauna and Vegetation

Description

This data set gives the abundance of 51 species and 8 environmental variables in 182 sites.

Usage

data(rpjdl)

Format

rpjdl is a list of 5 components.

fau

is the faunistic array of 182 sites (rows) and 51 species (columns).

mil

is the array of environmental variables : 182 sites and 8 variables.

frlab

is a vector of the names of species in French.

lalab

is a vector of the names of species in Latin.

lab

is a vector of the simplified labels of species.

Source

Prodon, R. and Lebreton, J.D. (1981) Breeding avifauna of a Mediterranean succession : the holm oak and cork oak series in the eastern Pyrénées. 1 : Analysis and modelling of the structure gradient. Oïkos, 37, 21–38.

Lebreton, J. D., Chessel D., Prodon R. and Yoccoz N. (1988) L'analyse des relations espèces-milieu par l'analyse canonique des correspondances. I. Variables de milieu quantitatives. Acta Oecologica, Oecologia Generalis, 9, 53–67.

References

See a data description at http://pbil.univ-lyon1.fr/R/pdf/pps048.pdf (in French).

Examples

## Not run: 
data(rpjdl)
coa1 <- dudi.coa(rpjdl$fau, scann = FALSE)
pca1 <- dudi.pca(rpjdl$fau, scal = FALSE, scann = FALSE)

if(adegraphicsLoaded()) {
  g1 <- s.distri(coa1$l1, rpjdl$fau, xax = 2, yax = 1, starSize = 0.3, 
                 ellipseSize = 0, plab.cex = 0)
  g2 <- s.distri(pca1$l1, rpjdl$fau, xax = 2, yax = 1, starSize = 0.3, 
                 ellipseSize = 0, plab.cex = 0)
} else {
  s.distri(coa1$l1, rpjdl$fau, 2, 1, cstar = 0.3, cell = 0)
  s.distri(pca1$l1, rpjdl$fau, 2, 1, cstar = 0.3, cell = 0)
}

caiv1 <- pcaiv(coa1, rpjdl$mil, scan = FALSE)
plot(caiv1)

## End(Not run)

Class of the Permutation Tests (in R).

Description

rtest is a generic function. It proposes methods for the following objects between, discrimin, procuste ...

Usage

rtest(xtest, ...)

Arguments

xtest

an object used to select a method
...

further arguments passed to or from other methods; in plot.randtest to hist

Value

rtest returns an object of class randtest

Author(s)

Daniel Chessel

See Also

RV.rtest, mantel.rtest, procuste.rtest, randtest

Examples

par(mfrow = c(2, 2))
for (x0 in c(2.4, 3.4, 5.4, 20.4)) {
    l0 <- as.randtest(sim = rnorm(200), obs = x0)
    print(l0)
    plot(l0, main = paste("p.value = ", round(l0$pvalue, dig = 5)))
}
par(mfrow = c(1, 1))

Monte-Carlo Test on the between-groups inertia percentage (in R).

Description

Performs a Monte-Carlo test on the between-groups inertia percentage.

Usage

## S3 method for class 'between'
rtest(xtest, nrepet = 99, ...)

Arguments

xtest

an object of class between
nrepet

the number of permutations
...

further arguments passed to or from other methods

Value

a list of the class rtest

Author(s)

Daniel Chessel

References

Romesburg, H. C. (1985) Exploring, confirming and randomization tests. Computers and Geosciences, 11, 19–37.

Examples

data(meaudret)
pca1 <- dudi.pca(meaudret$env, scan = FALSE, nf = 3)
rand1 <- rtest(bca(pca1, meaudret$design$season, scan = FALSE), 99)
rand1
plot(rand1, main = "Monte-Carlo test")

Monte-Carlo Test on a Discriminant Analysis (in R).

Description

Test of the sum of a discriminant analysis eigenvalues (divided by the rank). Non parametric version of the Pillai's test. It authorizes any weighting.

Usage

## S3 method for class 'discrimin'
rtest(xtest, nrepet = 99, ...)

Arguments

xtest

an object of class discrimin
nrepet

the number of permutations
...

further arguments passed to or from other methods

Value

returns a list of class rtest

Author(s)

Daniel Chessel

Examples

data(meaudret)
pca1 <- dudi.pca(meaudret$env, scan = FALSE, nf = 3)
rand1 <- rtest(discrimin(pca1, meaudret$design$season, scan = FALSE), 99)
rand1
#Monte-Carlo test
#Observation: 0.3035 
#Call: as.rtest(sim = sim, obs = obs)
#Based on 999 replicates
#Simulated p-value: 0.001 
plot(rand1, main = "Monte-Carlo test")
summary.manova(manova(as.matrix(meaudret$env)~meaudret$design$season), "Pillai")
#                         Df Pillai approx F num Df den Df  Pr(>F)    
# meaudret$design$season  3   2.73    11.30     27     30 1.6e-09 ***
# Residuals         16                                          
# ---
# Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 
# 2.731/9 = 0.3034

Monte-Carlo Test on the sum of eigenvalues of a co-inertia analysis (in C++ with Rcpp).

Description

performs a Monte-Carlo Test on the sum of eigenvalues of a co-inertia analysis.

Usage

RV.randtest(df1, df2, nrepet = 999, ...)

Arguments

df1, df2

two data frames with the same rows
nrepet

the number of permutations
...

further arguments passed to or from other methods

Value

returns a list of class 'randtest'

Author(s)

Daniel Chessel and Jean Thioulouse

References

Heo, M. & Gabriel, K.R. (1997) A permutation test of association between configurations by means of the RV coefficient. Communications in Statistics - Simulation and Computation, 27, 843-856.

Examples

data(doubs)
pca1 <- dudi.pca(doubs$env, scal = TRUE, scann = FALSE)
pca2 <- dudi.pca(doubs$fish, scal = FALSE, scann = FALSE)
rv1 <- RV.randtest(pca1$tab, pca2$tab, 99)
rv1
plot(rv1)

Monte-Carlo Test on the sum of eigenvalues of a co-inertia analysis (in R).

Description

performs a Monte-Carlo Test on the sum of eigenvalues of a co-inertia analysis.

Usage

RV.rtest(df1, df2, nrepet = 99, ...)

Arguments

df1, df2

two data frames with the same rows
nrepet

the number of permutations
...

further arguments passed to or from other methods

Value

returns a list of class 'rtest'

Author(s)

Daniel Chessel

References

Heo, M. & Gabriel, K.R. (1997) A permutation test of association between configurations by means of the RV coefficient. Communications in Statistics - Simulation and Computation, 27, 843-856.

Examples

data(doubs)
pca1 <- dudi.pca(doubs$env, scal = TRUE, scann = FALSE)
pca2 <- dudi.pca(doubs$fish, scal = FALSE, scann = FALSE)
rv1 <- RV.rtest(pca1$tab, pca2$tab, 99)
rv1
plot(rv1)

Tests of randomization on the correlation between two distance matrices (in R).

Description

performs a RV Test between two distance matrices.

Usage

RVdist.randtest(m1, m2, nrepet = 999, ...)

Arguments

m1, m2

two Euclidean matrices
nrepet

the number of permutations
...

further arguments passed to or from other methods

Value

returns a list of class 'randtest'

Author(s)

Daniel Chessel

References

Heo, M. & Gabriel, K.R. (1997) A permutation test of association between configurations by means of the RV coefficient. Communications in Statistics - Simulation and Computation, 27, 843-856.

Monte-Carlo Test on the sum of eigenvalues of a within-class co-inertia analysis (in C++ with Rcpp).

Description

performs a Monte-Carlo Test on the sum of eigenvalues of a within-class co-inertia analysis.

Usage

RVintra.randtest(df1, df2, fac, nrepet = 999, ...)

Arguments

df1, df2

two data frames with the same rows
fac

the factor defining classes
nrepet

the number of permutations
...

further arguments passed to or from other methods

Value

returns a list of class 'randtest'

Author(s)

Daniel Chessel and Jean Thioulouse

References

Heo, M. & Gabriel, K.R. (1997) A permutation test of association between configurations by means of the RV coefficient. Communications in Statistics - Simulation and Computation, 27, 843-856.

Examples

data(meaudret)
pca1 <- dudi.pca(meaudret$env, scan = FALSE, nf = 4)
pca2 <- dudi.pca(meaudret$spe, scal = FALSE, scan = FALSE, nf = 4)
wit1 <- wca(pca1, meaudret$design$season, scan = FALSE, nf = 2)
wit2 <- wca(pca2, meaudret$design$season, scan = FALSE, nf = 2)
coiw <- coinertia(wit1, wit2, scann = FALSE)
rv1 <- RVintra.randtest(pca1$tab, pca2$tab, meaudret$design$season, nrep=999)
rv1
plot(rv1)

Plot of the factorial maps for the projection of a vector basis

Description

performs the scatter diagrams of the projection of a vector basis.

Usage

s.arrow(dfxy, xax = 1, yax = 2, label = row.names(dfxy), 
    clabel = 1, pch = 20, cpoint = 0, boxes = TRUE, edge = TRUE, origin = c(0,0), 
    xlim = NULL, ylim = NULL, grid = TRUE, addaxes = TRUE, cgrid = 1, 
    sub = "", csub = 1.25, possub = "bottomleft", pixmap = NULL, 
    contour = NULL, area = NULL, add.plot = FALSE)

Arguments

dfxy

a data frame containing the two columns for the axes
xax

the column number of x in dfxy
yax

the column number of y in dfxy
label

a vector of strings of characters for the point labels
clabel

if not NULL, a character size for the labels used with par("cex")*clabel
pch

if cpoint > 0, an integer specifying the symbol or the single character to be used in plotting points
cpoint

a character size for plotting the points, used with par("cex")*cpoint. If zero, no points are drawn.
boxes

if TRUE, labels are framed
edge

a logical value indicating whether the arrows should be plotted
origin

the fixed point in the graph space, by default c(0,0) the origin of axes. The arrows begin at cent.
xlim

the ranges to be encompassed by the x-axis, if NULL they are computed
ylim

the ranges to be encompassed by the y-axis, if NULL they are computed
grid

a logical value indicating whether a grid in the background of the plot should be drawn
addaxes

a logical value indicating whether the axes should be plotted
cgrid

a character size, parameter used with par("cex")*cgrid, to indicate the mesh of the grid
sub

a string of characters to be inserted as legend
csub

a character size for the legend, used with par("cex")*csub
possub

a string of characters indicating the legend position ("topleft", "topright", "bottomleft", "bottomright")
pixmap

an object 'pixmap' displayed in the map background
contour

a data frame with 4 columns to plot the contour of the map : each row gives a segment (x1,y1,x2,y2)
area

a data frame of class 'area' to plot a set of surface units in contour
add.plot

if TRUE uses the current graphics window

Value

The matched call.

Author(s)

Daniel Chessel

Examples

s.arrow(cbind.data.frame(runif(55,-2,3), runif(55,-3,2)))

Plot of the factorial maps with polygons of contour by level of a factor

Description

performs the scatter diagrams with polygons of contour by level of a factor.

Usage

s.chull(dfxy, fac, xax = 1, yax = 2, 
    optchull = c(0.25, 0.5, 0.75, 1), label = levels(fac), clabel = 1, 
    cpoint = 0, col = rep(1, length(levels(fac))), xlim = NULL, ylim = NULL,
    grid = TRUE, addaxes = TRUE, origin = c(0,0), include.origin = TRUE, 
    sub = "", csub = 1, possub = "bottomleft", cgrid = 1, pixmap = NULL, 
    contour = NULL, area = NULL, add.plot = FALSE)

Arguments

dfxy

a data frame containing the two columns for the axes
fac

a factor partioning the rows of the data frame in classes
xax

the column number of x in dfxy
yax

the column number of y in dfxy
optchull

the number of convex hulls and their interval
label

a vector of strings of characters for the point labels
clabel

if not NULL, a character size for the labels, used with par("cex")*clabel
cpoint

a character size for plotting the points, used with par("cex")*cpoint. If zero, no points are drawn
col

a vector of colors used to draw each class in a different color
xlim

the ranges to be encompassed by the x axis, if NULL, they are computed
ylim

the ranges to be encompassed by the y axis, if NULL they are computed
grid

a logical value indicating whether a grid in the background of the plot should be drawn
addaxes

a logical value indicating whether the axes should be plotted
origin

the fixed point in the graph space, for example c(0,0) the origin axes
include.origin

a logical value indicating whether the point "origin" should be belonged to the graph space
sub

a string of characters to be inserted as legend
csub

a character size for the legend, used with par("cex")*csub
possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")
cgrid

a character size, parameter used with par("cex")* cgrid to indicate the mesh of the grid
pixmap

an object 'pixmap' displayed in the map background
contour

a data frame with 4 columns to plot the contour of the map : each row gives a segment (x1,y1,x2,y2)
area

a data frame of class 'area' to plot a set of surface units in contour
add.plot

if TRUE uses the current graphics window

Value

The matched call.

Author(s)

Daniel Chessel

Examples

xy <- cbind.data.frame(x = runif(200,-1,1), y = runif(200,-1,1))
posi <- factor(xy$x > 0) : factor(xy$y > 0)
coul <- c("black", "red", "green", "blue")

if(adegraphicsLoaded()) {
  s.class(xy, posi, ppoi.cex = 1.5, chullSize = c(0.25, 0.5, 0.75, 1), ellipseSize = 0, 
    starSize = 0, ppoly = list(col = "white", border = coul))
} else {
  s.chull(xy, posi, cpoi = 1.5, col = coul)
}

Plot of factorial maps with representation of point classes

Description

performs the scatter diagrams with representation of point classes.

Usage

s.class(dfxy, fac, wt = rep(1, length(fac)), xax = 1, 
    yax = 2, cstar = 1, cellipse = 1.5, axesell = TRUE, 
    label = levels(fac), clabel = 1, cpoint = 1, pch = 20, 
    col = rep(1, length(levels(fac))), xlim = NULL, ylim = NULL, 
    grid = TRUE, addaxes = TRUE, origin = c(0,0), 
    include.origin = TRUE, sub = "", csub = 1, possub = "bottomleft", 
    cgrid = 1, pixmap = NULL, contour = NULL, area = NULL, add.plot = FALSE)

Arguments

dfxy

a data frame containing the two columns for the axes
fac

a factor partitioning the rows of the data frame in classes
wt

a vector of the point weightings of the data frame used for computing the means (star centers) and the ellipses of dispersion
xax

the column number of x in dfxy
yax

the column number of y in dfxy
cstar

a number between 0 and 1 which defines the length of the star size
cellipse

a positive coefficient for the inertia ellipse size
axesell

a logical value indicating whether the ellipse axes should be drawn
label

a vector of strings of characters for the point labels
clabel

if not NULL, a character size for the labels, used with par("cex")*clabel
cpoint

a character size for plotting the points, used with par("cex")*cpoint. If zero, no points are drawn
pch

if cpoint > 0, an integer specifying the symbol or the single character to be used in plotting points
col

a vector of colors used to draw each class in a different color
xlim

the ranges to be encompassed by the x, if NULL they are computed
ylim

the ranges to be encompassed by the y, if NULL they are computed
grid

a logical value indicating whether a grid in the background of the plot should be drawn
addaxes

a logical value indicating whether the axes should be plotted
origin

the fixed point in the graph space, for example c(0,0) the origin axes
include.origin

a logical value indicating whether the point "origin" should be belonged to the graph space
sub

a string of characters to be inserted as legend
csub

a character size for the legend, used with par("cex")*csub
possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")
cgrid

a character size, parameter used with par("cex")* cgrid to indicate the mesh of the grid
pixmap

an object 'pixmap' displayed in the map background
contour

a data frame with 4 columns to plot the contour of the map : each row gives a segment (x1,y1,x2,y2)
area

a data frame of class 'area' to plot a set of surface units in contour
add.plot

if TRUE uses the current graphics window

Value

The matched call.

Author(s)

Daniel Chessel

Examples

if(!adegraphicsLoaded()) {
  xy <- cbind.data.frame(x = runif(200, -1, 1), y = runif(200, -1, 1))
  posi <- factor(xy$x > 0) : factor(xy$y > 0)
  coul <- c("black", "red", "green", "blue")
  par(mfrow = c(2, 2))
  s.class(xy, posi, cpoi = 2)
  s.class(xy, posi, cell = 0, cstar = 0.5)
  s.class(xy, posi, cell = 2, axesell = FALSE, csta = 0, col = coul)
  s.chull(xy, posi, cpoi = 1)
  par(mfrow = c(1, 1))
  
  ## Not run: 
  data(banque)
  dudi1 <- dudi.acm(banque, scannf = FALSE)
  coul = rainbow(length(levels(banque[, 20])))
  par(mfrow = c(2, 2))
  s.label(dudi1$li, sub = "Factorial map from ACM", csub = 1.5, 
    possub = "topleft")
  s.class(dudi1$li, banque[, 20], sub = names(banque)[20], 
    possub = "bottomright", cell = 0, cstar = 0.5, cgrid = 0, csub = 1.5)
  s.class(dudi1$li, banque[, 20], csta = 0, cell = 2, cgrid = 0, 
    clab = 1.5)
  s.class(dudi1$li, banque[, 20], sub = names(banque)[20], 
    possub = "topright", cgrid = 0, col = coul)
  par(mfrow = c(1, 1))
  
  par(mfrow = n2mfrow(ncol(banque)))
  for(i in 1:(ncol(banque)))
    s.class(dudi1$li, banque[, i], clab = 1.5, sub = names(banque)[i], 
      csub = 2, possub = "topleft", cgrid = 0, csta = 0, cpoi = 0)
  s.label(dudi1$li, clab = 0, sub = "Common background")
  par(mfrow = c(1, 1))

## End(Not run)
}

Plot of the factorial maps of a correlation circle

Description

performs the scatter diagram of a correlation circle.

Usage

s.corcircle(dfxy, xax = 1, yax = 2, label = row.names(df), 
    clabel = 1, grid = TRUE, sub = "", csub = 1, possub = "bottomleft", 
    cgrid = 0, fullcircle = TRUE, box = FALSE, add.plot = FALSE)

Arguments

dfxy

a data frame with two coordinates

xax

the column number for the x-axis
yax

the column number for the y-axis
label

a vector of strings of characters for the point labels
clabel

if not NULL, a character size for the labels, used with par("cex")*clabel
grid

a logical value indicating whether a grid in the background of the plot should be drawn
sub

a string of characters to be inserted as legend
csub

a character size for the legend, used with par("cex")*csub
possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")
cgrid

a character size, parameter used with par("cex")*cgrid to indicate the mesh of the grid
fullcircle

a logical value indicating whether the complete circle sould be drawn
box

a logical value indcating whether a box should be drawn
add.plot

if TRUE uses the current graphics window

Value

The matched call.

Author(s)

Daniel Chessel

Examples

if(!adegraphicsLoaded()) {
  data (olympic)
  dudi1 <- dudi.pca(olympic$tab, scan = FALSE) # a normed PCA
  par(mfrow = c(2, 2))
  s.corcircle(dudi1$co, lab = names(olympic$tab))
  s.corcircle(dudi1$co, cgrid = 0, full = FALSE, clab = 0.8)
  s.corcircle(dudi1$co, lab = as.character(1:11), cgrid = 2, 
    full = FALSE, sub = "Correlation circle", csub = 2.5, 
    possub = "bottomleft", box = TRUE)
  s.arrow(dudi1$co, clab = 1)
  par(mfrow = c(1, 1))
}

Plot of a frequency distribution

Description

performs the scatter diagram of a frequency distribution.

Usage

s.distri(dfxy, dfdistri, xax = 1, yax = 2, cstar = 1, 
    cellipse = 1.5, axesell = TRUE, label = names(dfdistri), 
    clabel = 0, cpoint = 1, pch = 20, xlim = NULL, ylim = NULL, 
    grid = TRUE, addaxes = TRUE, origin = c(0,0), 
    include.origin = TRUE, sub = "", csub = 1, possub = "bottomleft", 
    cgrid = 1, pixmap = NULL, contour = NULL, area = NULL, add.plot = FALSE)

Arguments

dfxy

a data frame containing two columns for the axes
dfdistri

a data frame containing the mass distributions in columns
xax

the column number for the x-axis
yax

the column number for the y-axis
cstar

a number between 0 and 1 which defines the length of the star size
cellipse

a positive coefficient for the inertia ellipse size
axesell

a logical value indicating whether the ellipse axes should be drawn
label

a vector of strings of characters for the distribution centers labels
clabel

if not NULL, a character size for the labels, used with par("cex")*clabel
cpoint

a character size for plotting the points, used with par("cex")*cpoint. If zero, no points are drawn
pch

if cpoint > 0, an integer specifying the symbol or the single character to be used in plotting points
xlim

the ranges to be encompassed by the x, if NULL they are computed
ylim

the ranges to be encompassed by the y, if NULL they are computed
grid

a logical value indicating whether a grid in the background of the plot should be drawn
addaxes

a logical value indicating whether the axes should be plotted
origin

the fixed point in the graph space, for example c(0,0) the origin axes
include.origin

a logical value indicating whether the point "origin" should be belonged to the graph space
sub

a string of characters to be inserted as legend
csub

a character size for the legend, used with par("cex")*csub
possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")
cgrid

a character size, parameter used with par("cex")* cgrid to indicate the mesh of the grid
pixmap

an object 'pixmap' displayed in the map background
contour

a data frame with 4 columns to plot the contour of the map : each row gives a segment (x1,y1,x2,y2)
area

a data frame of class 'area' to plot a set of surface units in contour
add.plot

if TRUE uses the current graphics window

Value

The matched call.

Author(s)

Daniel Chessel

Examples

if(!adegraphicsLoaded()) {
  xy <- cbind.data.frame(x = runif(200, -1, 1), y = runif(200, -1, 1))
  distri <- data.frame(w1 = rpois(200, xy$x * (xy$x > 0)))
  s.value(xy, distri$w1, cpoi = 1)
  s.distri(xy, distri, add.p = TRUE)
  
  w1 <- as.numeric((xy$x> 0) & (xy$y > 0))
  w2 <- ((xy$x > 0) & (xy$y < 0)) * (1 - xy$y) * xy$x
  w3 <- ((xy$x < 0) & (xy$y > 0)) * (1 - xy$x) * xy$y
  w4 <- ((xy$x < 0) & (xy$y < 0)) * xy$y * xy$x
  
  distri <- data.frame(a = w1 / sum(w1), b = w2 / sum(w2), 
    c = w3 / sum(w3), d = w4 / sum(w4))
  s.value(xy, unlist(apply(distri, 1, sum)), cleg = 0, csi = 0.75)
  s.distri(xy, distri, clab = 2, add.p = TRUE)
  
  data(rpjdl)
  xy <- dudi.coa(rpjdl$fau, scan = FALSE)$li
  par(mfrow = c(3, 4))
  for (i in c(1, 5, 8, 20, 21, 23, 26, 33, 36, 44, 47, 49)) {
    s.distri(xy, rpjdl$fau[, i], cell = 1.5, sub = rpjdl$frlab[i], 
      csub = 2, cgrid = 1.5)}
  par(mfrow = c(1, 1))
}

Display of a scatterplot and its two marginal histograms

Description

performs a scatterplot and the two marginal histograms of each axis.

Usage

s.hist(dfxy, xax = 1, yax = 2, cgrid = 1, cbreaks = 2, adjust = 1, ...)

Arguments

dfxy

a data frame with two coordinates

xax

column for the x axis

yax

column for the y axis

cgrid

a character size, parameter used with par("cex")*cgrid to indicate the mesh of the grid

cbreaks

a parameter used to define the numbers of cells for the histograms. By default, two cells are defined for each interval of the grid displayed in s.label. With an increase of the integer cbreaks, the number of cells increases as well.
adjust

a parameter passed to density to display a kernel density estimation
...

further arguments passed from the s.label for the scatter plot

Value

The matched call.

Author(s)

Daniel Chessel

Examples

data(rpjdl)
coa1 <- dudi.coa(rpjdl$fau, scannf = FALSE, nf = 4)
s.hist(coa1$li)
s.hist(coa1$li, cgrid = 2, cbr = 3, adj = 0.5, clab = 0)
s.hist(coa1$co, cgrid = 2, cbr = 3, adj = 0.5, clab = 0)

Graph of a variable using image and contour

Description

performs a scatterplot

Usage

s.image(dfxy, z, xax = 1, yax = 2, span = 0.5, xlim = NULL, ylim = NULL, 
  kgrid = 2, scale = TRUE, grid = FALSE, addaxes = FALSE, cgrid = 0, 
  include.origin = FALSE, origin = c(0, 0), sub = "", csub = 1, 
  possub = "topleft", neig = NULL, cneig = 1, image.plot = TRUE, 
  contour.plot = TRUE, pixmap = NULL, contour = NULL, area = NULL, 
  add.plot = FALSE)

Arguments

dfxy

a data frame containing the two columns for the axes

z

a vector of values on the dfxy rows

xax

the column number of x in dfxy

yax

the column number of y in dfxy

span

the parameter alpha which controls the degree of smoothing

xlim

the ranges to be encompassed by the x-axis, if NULL they are computed

ylim

the ranges to be encompassed by the y-axis, if NULL they are computed

kgrid

a number of points used to locally estimate the level line through the nodes of the grid, used by kgrid*sqrt(length(z))

scale

if TRUE, data are centered and reduced

grid

if TRUE, the background grid is traced

addaxes

a logical value indicating whether the axes should be plotted

cgrid

a character size, parameter used with par("cex")* cgrid to indicate the mesh of the grid

include.origin

a logical value indicating whether the point "origin" should be belonged to the graph space

origin

the fixed point in the graph space, for example c(0,0) the origin axes

sub

a string of characters to be inserted as legend

csub

a character size for the legend, used with par("cex")*csub

possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")

neig

an object of class neig

cneig

a size for the neighbouring graph lines used with par("lwd")*cneig

image.plot

if TRUE, the image is traced

contour.plot

if TRUE, the contour lines are plotted

pixmap

an object 'pixmap' displayed in the map background

contour

a data frame with 4 columns to plot the contour of the map : each row gives a segment (x1,y1,x2,y2)

area

a data frame of class 'area' to plot a set of surface units in contour

add.plot

if TRUE uses the current graphics window

Value

The matched call.

Author(s)

Daniel Chessel

Examples

if(!adegraphicsLoaded()) {
  if(requireNamespace("splancs", quietly = TRUE)) {
    wxy <- data.frame(expand.grid(-3:3, -3:3))
    names(wxy) <- c("x", "y")
    z <- (1 / sqrt(2)) * exp(-(wxy$x ^ 2 + wxy$y ^ 2) / 2)
    par(mfrow = c(2, 2))
    s.value(wxy, z)
    s.image(wxy, z)
    s.image(wxy, z, kgrid = 5)
    s.image(wxy, z, kgrid = 15)
    par(mfrow = c(1, 1))
  }
  
  ## Not run: 
  data(t3012)
  if(requireNamespace("splancs", quietly = TRUE)) {
    par(mfrow = c(3, 4))
    for(k in 1:12)
      s.image(t3012$xy, scalewt(t3012$temp[, k]), kgrid = 3)
    par(mfrow = c(1, 1))
  }
      
  data(elec88)
  if(requireNamespace("splancs", quietly = TRUE)) {
    par(mfrow = c(3,4))
    for(k in 1:12)
      s.image(t3012$xy, scalewt(t3012$temp[, k]), kgrid = 3, sub = names(t3012$temp)[k],
        csub = 3, area = elec88$area)
    par(mfrow = c(1, 1))
  }
  
## End(Not run)
}

Scatter Plot with Kernel Density Estimate

Description

performs a scatter of points without labels by a kernel Density Estimation in One or Two Dimensions

Usage

s.kde2d(dfxy, xax = 1, yax = 2, pch = 20, cpoint = 1, neig = NULL, cneig = 2, 
    xlim = NULL, ylim = NULL, grid = TRUE, addaxes = TRUE, cgrid = 1, 
    include.origin = TRUE, origin = c(0, 0), sub = "", csub = 1.25, 
    possub = "bottomleft", pixmap = NULL, contour = NULL, 
    area = NULL, add.plot = FALSE)

Arguments

dfxy

a data frame with at least two coordinates

xax

the column number for the x-axis

yax

the column number for the y-axis
pch

if cpoint > 0, an integer specifying the symbol or the single character to be used in plotting points

cpoint

a character size for plotting the points, used with par("cex")*cpoint. If zero, no points are drawn

neig

a neighbouring graph

cneig

a size for the neighbouring graph lines used with par("lwd")*cneig

xlim

the ranges to be encompassed by the x axis, if NULL, they are computed

ylim

the ranges to be encompassed by the y axis, if NULL, they are computed

grid

a logical value indicating whether a grid in the background of the plot should be drawn

addaxes

a logical value indicating whether the axes should be plotted

cgrid

a character size, parameter used with par("cex")* 'cgrid' to indicate the mesh of the grid

include.origin

a logical value indicating whether the point "origin" should be belonged to the graph space

origin

the fixed point in the graph space, for example c(0,0) the origin axes

sub

a string of characters to be inserted as legend

csub

a character size for the legend, used with par("cex")*csub

possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")

pixmap

an object pixmap displayed in the map background

contour

a data frame with 4 columns to plot the contour of the map : each row gives a segment (x1,y1,x2,y2)

area

a data frame of class 'area' to plot a set of surface units in contour

add.plot

if TRUE uses the current graphics window

Value

The matched call.

Author(s)

Daniel Chessel

Examples

# To recognize groups of points
if(!adegraphicsLoaded()) {
  data(rpjdl)
  coa1 <- dudi.coa(rpjdl$fau, scannf = FALSE, nf = 3)
  s.kde2d(coa1$li)
}

Scatter Plot

Description

performs the scatter diagrams with labels.

Usage

s.label(dfxy, xax = 1, yax = 2, label = row.names(dfxy), 
    clabel = 1, pch = 20, cpoint = if (clabel == 0) 1 else 0, boxes = TRUE,
    neig = NULL, cneig = 2, xlim = NULL, ylim = NULL, grid = TRUE, 
    addaxes = TRUE, cgrid = 1, include.origin = TRUE, origin = c(0,0), 
    sub = "", csub = 1.25, possub = "bottomleft", pixmap = NULL, 
    contour = NULL, area = NULL, add.plot = FALSE)

Arguments

dfxy

a data frame with at least two coordinates
xax

the column number for the x-axis
yax

the column number for the y-axis
label

a vector of strings of characters for the point labels
clabel

if not NULL, a character size for the labels, used with par("cex")*clabel
pch

if cpoint > 0, an integer specifying the symbol or the single character to be used in plotting points
cpoint

a character size for plotting the points, used with par("cex")*cpoint. If zero, no points are drawn
boxes

if TRUE, labels are framed
neig

a neighbouring graph
cneig

a size for the neighbouring graph lines used with par("lwd")*cneig
xlim

the ranges to be encompassed by the x axis, if NULL, they are computed
ylim

the ranges to be encompassed by the y axis, if NULL, they are computed
grid

a logical value indicating whether a grid in the background of the plot should be drawn
addaxes

a logical value indicating whether the axes should be plotted
cgrid

a character size, parameter used with par("cex")* cgrid to indicate the mesh of the grid
include.origin

a logical value indicating whether the point "origin" should be belonged to the graph space
origin

the fixed point in the graph space, for example c(0,0) the origin axes
sub

a string of characters to be inserted as legend
csub

a character size for the legend, used with par("cex")*csub
possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")
pixmap

an object 'pixmap' displayed in the map background
contour

a data frame with 4 columns to plot the contour of the map : each row gives a segment (x1,y1,x2,y2)
area

a data frame of class 'area' to plot a set of surface units in contour
add.plot

if TRUE uses the current graphics window

Value

The matched call.

Author(s)

Daniel Chessel

Examples

if(!adegraphicsLoaded()) {
  layout(matrix(c(1, 2, 3, 2), 2, 2))
  data(atlas)
  s.label(atlas$xy, lab = atlas$names.district, 
    area = atlas$area, inc = FALSE, addax = FALSE)
  data(mafragh)
  s.label(mafragh$xy, inc = FALSE, neig = mafragh$neig, addax = FALSE)
  data(irishdata)
  s.label(irishdata$xy, inc = FALSE, contour = irishdata$contour, 
    addax = FALSE)
  
  par(mfrow = c(2, 2))
  cha <- ls()
  s.label(cbind.data.frame(runif(length(cha)), 
    runif(length(cha))), lab = cha)
  x <- runif(50, -2, 2)
  y <- runif(50, -2, 2)
  z <- x^2 + y^2
  s.label(data.frame(x, y), lab = as.character(z < 1))
  s.label(data.frame(x, y), clab = 0, cpoi = 1, add.plot = TRUE)
  symbols(0, 0, circles = 1, add = TRUE, inch = FALSE)
  s.label(cbind.data.frame(runif(100, 0, 10), runif(100, 5, 12)), 
    incl = FALSE, clab = 0)
  s.label(cbind.data.frame(runif(100, -3, 12),
    runif(100, 2, 10)), cl = 0, cp = 2, include = FALSE)
}

Plot of Paired Coordinates

Description

performs the scatter diagram for a paired coordinates.

Usage

s.match(df1xy, df2xy, xax = 1, yax = 2, pch = 20, cpoint = 1, 
    label = row.names(df1xy), clabel=1, edge = TRUE, xlim = NULL, 
    ylim = NULL, grid = TRUE, addaxes = TRUE, cgrid = 1, 
    include.origin = TRUE, origin = c(0,0), sub = "", csub = 1.25, 
    possub = "bottomleft", pixmap = NULL, contour = NULL, area = NULL, 
    add.plot = FALSE)

Arguments

df1xy

a data frame containing two columns from the first system
df2xy

a data frame containing two columns from teh second system
xax

the column number for the x-axis of both the two systems
yax

the column number for the y-axis of both the two systems
pch

if cpoint > 0, an integer specifying the symbol or the single character to be used in plotting points
cpoint

a character size for plotting the points, used with par("cex")*cpoint. If zero, no points are drawn

label

a vector of strings of characters for the couple labels
clabel

if not NULL, a character size for the labels, used with par("cex")*clabel

edge

If TRUE the arrows are plotted, otherwise only the segments are drawn
xlim

the ranges to be encompassed by the x axis, if NULL they are computed
ylim

the ranges to be encompassed by the y axis, if NULL they are computed
grid

a logical value indicating whether a grid in the background of the plot should be drawn
addaxes

a logical value indicating whether the axes should be plotted
cgrid

a character size, parameter used with par("cex")* cgrid to indicate the mesh of the grid
include.origin

a logical value indicating whether the point "origin" should be belonged to the graph space
origin

the fixed point in the graph space, for example c(0,0) the origin axes
sub

a string of characters to be inserted as legend
csub

a character size for the legend, used with par("cex")*csub
possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")
pixmap

aan object pixmap displayed in the map background
contour

a data frame with 4 columns to plot the contour of the map : each row gives a segment (x1,y1,x2,y2)
area

a data frame of class 'area' to plot a set of surface units in contour
add.plot

if TRUE uses the current graphics window

Value

The matched call.

Author(s)

Daniel Chessel

Examples

if(!adegraphicsLoaded()) {
  X <- data.frame(x = runif(50, -1, 2), y = runif(50, -1, 2))
  Y <- X + rnorm(100, sd = 0.3)
  par(mfrow = c(2, 2))
  s.match(X, Y)
  s.match(X, Y, edge = FALSE, clab = 0)
  s.match(X, Y, edge = FALSE, clab = 0)
  s.label(X, clab = 1, add.plot = TRUE)
  s.label(Y, clab = 0.75, add.plot = TRUE)
  s.match(Y, X, clab = 0)
  par(mfrow = c(1, 1))
}

Scatterplot of two sets of coordinates and a partionning into classes

Description

Performs a graphical representation of two sets of coordinates (different colors and symbols) and a partitionning into classes

Usage

s.match.class(df1xy, df2xy, fac, wt = rep(1/nrow(df1xy), nrow(df1xy)),
xax = 1, yax = 2, pch1 = 16, pch2 = 15, col1 = rep("lightgrey",
nlevels(fac)), col2 = rep("darkgrey", nlevels(fac)), cpoint = 1, label =
levels(fac), clabel = 1, cstar = 1, cellipse = 0, axesell = TRUE, xlim =
NULL, ylim = NULL, grid = TRUE, addaxes = TRUE, cgrid = 1,
include.origin = TRUE, origin = c(0, 0), sub = "", csub = 1.25, possub =
"bottomleft", pixmap = NULL, contour = NULL, area = NULL, add.plot = FALSE)

Arguments

df1xy

a dataframe with the first system of coordinates
df2xy

a dataframe with the secocnd system of coordinates
fac

a factor partitioning the rows of the data frame in classes
wt

a vector of weights
xax

a number indicating which column should be plotted on the x-axis
yax

a number indicating which column should be plotted on the x-axis
pch1

if cpoint > 0, an integer specifying the symbol or the single character to be used for plotting points
pch2

if cpoint > 0, an integer specifying the symbol or the single character to be used for plotting points
col1

a color for symbols
col2

a color for symbols
cpoint

a character size for plotting the points, used with par("cex")*cpoint. If zero, no points are drawn
label

a vector of strings of characters for the couple labels
clabel

if not NULL, a character size for the labels, used with par("cex")*clabel
cstar

a number between 0 and 1 which defines the length of the star size
cellipse

a positive coefficient for the inertia ellipse size
axesell

a logical value indicating whether the ellipse axes should be drawn
xlim

the ranges to be encompassed by the x axis, if NULL they are computed
ylim

the ranges to be encompassed by the y axis, if NULL they are computed
grid

a logical value indicating whether a grid in the background of the plot should be drawn
addaxes

a logical value indicating whether the axes should be plotted
cgrid

a character size, parameter used with par("cex")* cgrid to indicate the mesh of the grid
include.origin

a logical value indicating whether the point "origin" should belong to the graph space
origin

a fixed point in the graph space, for example c(0,0) for the origin of axes
sub

a string of characters to be inserted as legend
csub

a character size for the legend, used with par("cex")*csub
possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")
pixmap

a pixmap object
contour

a dataframe with 4 columns to plot the contour of the map : each row gives a segment (x1,y1,x2,y2)
area

a dataframe of class 'area' to plot an areal map
add.plot

if TRUE, add the plot to the current graphic device

Value

The matched call.

Author(s)

Stéphane Dray [email protected]

See Also

s.class, s.match

Examples

xy <- data.frame(matrix(rnorm(100), 50, 2))
xy[, 1] <- xy[, 1] + rep(seq(0, 12, by = 3), rep(10, 5))
xy[, 2] <- xy[, 2] + rep(seq(0, 12, by = 3), rep(10, 5))
fac <- gl(5, 10)
xy2 <- xy + matrix(rnorm(100), 50, 2) + 1

if(adegraphicsLoaded()) {
  mat <- rbind(xy, xy2)
  minmat <- apply(mat, 2, min)
  maxmat <- apply(mat, 2, max)
  lag <- 0.1 * abs(minmat - maxmat)
  xli <- c(minmat[1] - lag[1], maxmat[1] + lag[1])
  yli <- c(minmat[2] - lag[2], maxmat[2] + lag[2])
  
  g1 <- s.class(xy, fac, ellipseSize = 0, col = rep("grey45", nlevels(fac)), xlim = xli, 
    ylim = yli, plabels.cex = 0, plot = FALSE)
  g2 <- s.class(xy2, fac, ellipseSize = 0, col = rep("grey75", nlevels(fac)), xlim = xli, 
    ylim = yli, plabels.cex = 0, plot = FALSE)
  g3 <- s.match(g1@stats$means, g2@stats$means, xlim = xli, ylim = yli, plines.lwd = 2, 
    psub.text = "xy -> xy2", plot = FALSE)
  
  g4 <- do.call("superpose", list(g1, g2))
  g4@Call <- call("superpose", g1@Call, g2@Call)
  g4 <- do.call("superpose", list(g4, g3))
  g4@Call <- call("superpose", g4@Call, g3@Call)
  g4
  
} else {
  s.match.class(xy, xy2, fac)
}

Graph of frequency profiles (useful for instance in genetic)

Description

The main purpose of this function is to draw categories using scores and profiles by their gravity center. Confidence intervals of the average position (issued from a multinomial distribution) can be superimposed.

Usage

s.multinom(dfxy, dfrowprof, translate = FALSE, xax = 1, yax = 2, 
   labelcat = row.names(dfxy), clabelcat = 1, cpointcat = if (clabelcat == 0) 2 else 0,
   labelrowprof = row.names(dfrowprof), clabelrowprof = 0.75, 
   cpointrowprof = if (clabelrowprof == 0) 2 else 0, pchrowprof = 20, 
   coulrowprof = grey(0.8), proba = 0.95, n.sample = apply(dfrowprof, 1, sum),
   axesell = TRUE, ...)

Arguments

dfxy

dfxy is a data frame containing at least two numerical variables. The rows of dfxy are categories such as 1,2 and 3 in the triangular plot.
dfrowprof

dfrowprof is a data frame whose the columns are the rows of dfxy. The rows of dfxy are profiles or frequency distributions on the categories. The column number of dfrowprof must be equal to the row number of dfxy. row.names(dfxy) and names(dfrowprof) must be identical.

translate

a logical value indicating whether the plot should be translated(TRUE) or not. The origin becomes the gravity center weighted by profiles.

xax

the column number of dfxy for the x-axis

yax

the column number of dfxy for the y-axis

labelcat

a vector of strings of characters for the labels of categories

clabelcat

an integer specifying the character size for the labels of categories, used with par("cex")*clabelcat

cpointcat

an integer specifying the character size for the points showing the categories, used with par("cex")*cpointcat

labelrowprof

a vector of strings of characters for the labels of profiles (rows of dfrowprof)

clabelrowprof

an integer specifying the character size for the labels of profiles used with par("cex")*clabelrowprof
cpointrowprof

an integer specifying the character size for the points representative of the profiles used with par("cex")*cpointrowprof

pchrowprof

either an integer specifying a symbol or a single character to be used for the profile labels

coulrowprof

a vector of colors used for ellipses, possibly recycled
proba

a value lying between 0.500 and 0.999 to draw a confidence interval

n.sample

a vector containing the sample size, possibly recycled. Used n.sample = 0 if the profiles are not issued from a multinomial distribution and that confidence intervals have no sense.

axesell

a logical value indicating whether the ellipse axes should be drawn
...

further arguments passed from the s.label for the initial scatter plot.

Value

Returns in a hidden way a list of three components :

tra

a vector with two values giving the done original translation.

ell

a matrix, with 5 columns and for rows the number of profiles, giving the means, the variances and the covariance of the profile for the used numerical codes (column of dfxy)
call

the matched call

Author(s)

Daniel Chessel

Examples

par(mfrow = c(2,2))
par(mar = c(0.1,0.1,0.1,0.1))
proba <- matrix(c(0.49,0.47,0.04,0.4,0.3,0.3,0.05,0.05,0.9,0.05,0.7,0.25), ncol = 3, byrow = TRUE)
proba.df <- as.data.frame (proba)
names(proba.df) <- c("A","B","C") ; row.names(proba.df) <- c("P1","P2","P3","P4")
w.proba <- triangle.plot(proba.df, clab = 2, show = FALSE)
box()

w.tri = data.frame(x = c(-sqrt(1/2),sqrt(1/2),0), y = c(-1/sqrt(6),-1/sqrt(6),2/sqrt(6)))
L3 <- c("A","B","C")
row.names(w.tri) <- L3
s.multinom(w.tri, proba.df, n.sample = 0, coulrowprof = "black", clabelrowprof = 1.5)
s.multinom(w.tri, proba.df, n.sample = 30, coul = palette()[5])
s.multinom(w.tri, proba.df, n.sample = 60, coul = palette()[6], add.p = TRUE)
s.multinom(w.tri, proba.df, n.sample = 120, coul = grey(0.8), add.p = TRUE)

print(s.multinom(w.tri, proba.df[-3,], n.sample = 0, translate = TRUE)$tra)

Trajectory Plot

Description

performs the scatter diagram with trajectories.

Usage

s.traject(dfxy, fac = factor(rep(1, nrow(dfxy))), 
    ord = (1:length(fac)),  xax = 1, yax = 2, label = levels(fac), 
    clabel = 1, cpoint = 1, pch = 20, xlim = NULL, ylim = NULL, 
    grid = TRUE, addaxes = TRUE, edge = TRUE, origin = c(0,0), 
    include.origin = TRUE, sub = "", csub = 1, possub = "bottomleft", 
    cgrid = 1, pixmap = NULL, contour = NULL, area = NULL, add.plot = FALSE)

Arguments

dfxy

a data frame containing two columns for the axes
fac

a factor partioning the rows of the data frame in classes
ord

a vector of length equal to fac. The trajectory is drawn in an ascending order of the ord values
xax

the column number for the x-axis
yax

the column number for the y-axis
label

a vector of strings of characters for the point labels
clabel

if not NULL, a character size for the labels, used with par("cex")*clabel
cpoint

a character size for plotting the points, used with par("cex")*cpoint. If zero, no points are drawn
pch

if cpoint > 0, an integer specifying the symbol or the single character to be used in plotting points
xlim

the ranges to be encompassed by the x, if NULL they are computed
ylim

the ranges to be encompassed by the y, if NULL they are computed
grid

a logical value indicating whether a grid in the background of the plot should be drawn
addaxes

a logical value indicating whether the axes should be plotted
edge

if TRUE the arrows are plotted, otherwhise only the segments
origin

the fixed point in the graph space, for example c(0,0) the origin axes
include.origin

a logical value indicating whether the point "origin" should be belonged to the graph space
sub

a string of characters to be inserted as legend
csub

a character size for the legend, used with par("cex")*csub
possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")
cgrid

a character size, parameter used with par("cex")*cgrid to indicate the mesh of the grid
pixmap

aan object 'pixmap' displayed in the map background
contour

a data frame with 4 columns to plot the contour of the map : each row gives a segment (x1,y1,x2,y2)
area

a data frame of class 'area' to plot a set of surface units in contour
add.plot

if TRUE uses the current graphics window

Value

The matched call.

Author(s)

Daniel Chessel

Examples

if(!adegraphicsLoaded()) {
  rw <- function(a) {
    x <- 0
    for(i in 1:49) x <- c(x, x[length(x)] + runif(1, -1, 1))
    x
  }
  y <- unlist(lapply(1:5, rw))
  x <- unlist(lapply(1:5, rw))
  z <- gl(5, 50)
  s.traject(data.frame(x, y), z, edge = FALSE)
}

Representation of a value in a graph

Description

performs the scatter diagram with the representation of a value for a variable

Usage

s.value(dfxy, z, xax = 1, yax = 2, method = c("squaresize", "greylevel"), 
    zmax=NULL, csize = 1, cpoint = 0, pch = 20, clegend = 0.75, neig = NULL, 
    cneig = 1, xlim = NULL, ylim = NULL, grid = TRUE, addaxes = TRUE, 
    cgrid = 0.75, include.origin = TRUE, origin = c(0,0), sub = "", 
    csub = 1, possub = "topleft", pixmap = NULL, contour = NULL, 
    area = NULL, add.plot = FALSE)

Arguments

dfxy

a data frame with two coordinates
z

a vector of the values corresponding to the rows of dfxy
xax

column for the x axis
yax

column for the y axis
method

a string of characters
"squaresize" gives black squares for positive values and white for negative values with a proportional area equal to the absolute value.
"greylevel" gives squares of equal size with a grey level proportional to the value. By default the first choice
zmax

a numeric value, equal by default to max(abs(z)), can be used to impose a common scale of the size of the squares to several drawings in the same device
csize

a size coefficient for symbols
cpoint

a character size for plotting the points, used with par("cex")*cpoint. If zero, no points are drawn
pch

if cpoint > 0, an integer specifying the symbol or the single character to be used in plotting points
clegend

a character size for the legend used by par("cex")*clegend
neig

a neighbouring graph
cneig

a size for the neighbouring graph lines used with par("lwd")*cneig
xlim

the ranges to be encompassed by the x, if NULL they are computed
ylim

the ranges to be encompassed by the y, if NULL they are computed
grid

a logical value indicating whether a grid in the background of the plot should be drawn
addaxes

a logical value indicating whether the axes should be plotted
cgrid

a character size, parameter used with par("cex")*cgrid to indicate the mesh of the grid
include.origin

a logical value indicating whether the point "origin" should be belonged to the graph space
origin

the fixed point in the graph space, for example c(0,0) the origin axes
sub

a string of characters to be inserted as legend
csub

a character size for the legend, used with par("cex")*csub
possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")
pixmap

an object 'pixmap' displayed in the map background
contour

a data frame with 4 columns to plot the contour of the map : each row gives a segment (x1,y1,x2,y2)
area

a data frame of class 'area' to plot a set of surface units in contour
add.plot

if TRUE uses the current graphics window

Value

The matched call.

Author(s)

Daniel Chessel

Examples

if(!adegraphicsLoaded()) {
  xy <- cbind.data.frame(x = runif(500), y = runif(500))
  z <- rnorm(500)
  s.value(xy, z)
  
  s.value(xy, z, method = "greylevel")
  
  data(rpjdl)
  fau.coa <- dudi.coa(rpjdl$fau, scan = FALSE, nf = 3)
  s.value(fau.coa$li, fau.coa$li[,3], csi = 0.75, cleg = 0.75)
  
  data(irishdata)
  par(mfrow = c(3, 4))
  irq0 <- data.frame(scale(irishdata$tab, scale = TRUE))
  for (i in 1:12) {
    z <- irq0[, i]
    nam <- names(irq0)[i]
    s.value(irishdata$xy, z, area = irishdata$area, csi = 3,
      csub = 2, sub = nam, cleg = 1.5, cgrid = 0, inc = FALSE,
      xlim = c(16, 205), ylim = c(-50, 268), adda = FALSE, grid = FALSE)
  }
}

Indirect Ordination

Description

This data set gives the densities per hectare of 11 species of trees for 10 transects of topographic moisture values (mean of several stations per class).

Usage

data(santacatalina)

Format

a data frame with 11 rows and 10 columns

Source

Gauch, H. G. J., Chase, G. B. and Whittaker R. H. (1974) Ordination of vegetation samples by Gaussian species distributions. Ecology, 55, 1382–1390.

Examples

data(santacatalina)
coa1 <- dudi.coa(log(santacatalina + 1), scan = FALSE) # 2 factors

if(adegraphicsLoaded()) {
  g1 <- table.value(log(santacatalina + 1), plot = FALSE)
  g2 <- table.value(log(santacatalina + 1)[, sample(10)], plot = FALSE)
  g3 <- table.value(log(santacatalina + 1)[order(coa1$li[, 1]), order(coa1$co[, 1])], plot = FALSE)
  g4 <- scatter(coa1, posi = "bottomright", plot = FALSE)
  G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))
} else {
  par(mfrow = c(2, 2))
  table.value(log(santacatalina + 1))
  table.value(log(santacatalina + 1)[, sample(10)])
  table.value(log(santacatalina + 1)[order(coa1$li[, 1]), order(coa1$co[, 1])]) 
  scatter(coa1, posi = "bottomright")
  par(mfrow = c(1, 1))
}

Array of Recapture of Rings

Description

The data frame sarcelles$tab contains the number of the winter teals (Anas C. Crecca) for which the ring was retrieved in the area i during the month j (n=3049).

Usage

data(sarcelles)

Format

sarcelles is a list with the following components:

tab

a data frame with 14 rows-areas and 12 columns-months

xy

a data frame with the 2 spatial coordinates of the 14 region centers

neig

the neighbouring graph between areas, object of the class neig

col.names

a vector containing the month items

nb

a neighborhood object (class nb defined in package spdep)

Source

Lebreton, J.D. (1973). Etude des déplacements saisonniers des Sarcelles d'hiver, Anas c. crecca L., hivernant en Camargue à l'aide de l'analyse factorielle des correspondances. Compte rendu hebdomadaire des séances de l'Académie des sciences, Paris, D, III, 277, 2417–2420.

Examples

## Not run: 
if(!adegraphicsLoaded()) {
  # depends of pixmap
  if(requireNamespace("pixmap", quietly = TRUE)) {
    bkgnd.pnm <- pixmap::read.pnm(system.file("pictures/sarcelles.pnm", package = "ade4"))
    data(sarcelles)
    par(mfrow = c(4, 3))
    for(i in 1:12) {
      s.distri(sarcelles$xy, sarcelles$tab[, i], pixmap = bkgnd.pnm, 
       sub = sarcelles$col.names[i], clab = 0, csub = 2)
      s.value(sarcelles$xy, sarcelles$tab[, i], add.plot = TRUE, cleg = 0)
    }
    par(mfrow = c(1, 1))
  }
}
## End(Not run)

Compute or scale data using (weighted) means, variances and covariances (possibly for the levels of a factor)

Description

These utility functions compute (weighted) means, variances and covariances for dataframe partitioned by a factor. The scale transforms a numeric matrix in a centred and scaled matrix for any weighting.

Usage

covwt(x, wt, na.rm = FALSE)
varwt(x, wt, na.rm = FALSE)
scalewt(df, wt = rep(1/nrow(df), nrow(df)), center = TRUE, scale = TRUE)
meanfacwt(df, fac = NULL, wt = rep(1/nrow(df), nrow(df)), drop = FALSE)
varfacwt(df, fac = NULL, wt = rep(1/nrow(df), nrow(df)), drop = FALSE)
covfacwt(df, fac = NULL, wt = rep(1/nrow(df), nrow(df)), drop = FALSE)
scalefacwt(df, fac = NULL, wt = rep(1/nrow(df), nrow(df)), scale = TRUE, drop = FALSE)

Arguments

x

a numeric vector (varwt) or a matrix (covwt) containg the data.
na.rm

a logical value indicating whether NA values should be stripped before the computation proceeds.
df

a matrix or a dataframe containing the data.
fac

a factor partitioning the data.
wt

a numeric vector of weights.
drop

a logical value indicating whether unused levels should be kept.
scale

a logical value indicating whether data should be scaled or not.
center

a logical value indicating whether data should be centered or not.

Details

Functions returns biased estimates of variances and covariances (i.e. divided by n and not n-1)

Value

For varwt, the weighted variance. For covwt, the matrix of weighted co-variances. For scalewt, the scaled dataframe. For other function a list (if fac is not null) of dataframes with approriate values

Author(s)

Stéphane Dray [email protected]

Examples

data(meau)
w <- rowSums(meau$spe)
varwt(meau$env, w)
varfacwt(meau$env, wt = w)
varfacwt(meau$env, wt = w, fac = meau$design$season)
covfacwt(meau$env, wt = w, fac = meau$design$season)
scalewt(meau$env, wt = w)

Graphical representation of the outputs of a multivariate analysis

Description

scatter is a generic function that has methods for the classes coa, dudi, fca, acm and pco. It plots the outputs of a multivariate analysis by representing simultaneously the rows and the colums of the original table (biplot). The function biplot returns exactly the same representation.
The function screeplot represents the amount of inertia (usually variance) associated to each dimension.

Usage

scatter(x, ...)
## S3 method for class 'dudi'
biplot(x, ...)
## S3 method for class 'dudi'
screeplot(x, npcs = length(x$eig), type = c("barplot", "lines"), 
    main = deparse(substitute(x)), col = c(rep("black", x$nf),
rep("grey", npcs - x$nf)), ...)

Arguments

x

an object of the class dudi containing the outputs of a multivariate analysis
npcs

the number of components to be plotted
type

the type of plot
main

the title of the plot
col

a vector of colors
...

further arguments passed to or from other methods

Author(s)

Daniel Chessel
Stéphane Dray [email protected]

See Also

s.arrow, s.chull, s.class, s.corcircle, s.distri, s.label, s.match, s.traject, s.value, add.scatter

Examples

data(rpjdl)
rpjdl.coa <- dudi.coa(rpjdl$fau, scannf = FALSE, nf = 4)
screeplot(rpjdl.coa)
biplot(rpjdl.coa)

Plot of the factorial maps in a Multiple Correspondence Analysis

Description

performs the scatter diagrams of a Multiple Correspondence Analysis.

Usage

## S3 method for class 'acm'
scatter(x, xax = 1, yax = 2, mfrow=NULL, csub = 2, possub = "topleft", ...)

Arguments

x

an object of class acm
xax

the column number for the x-axis
yax

the column number for the y-axis
mfrow

a vector of the form "c(nr,nc)", if NULL (the default) is computed by n2mfrow
csub

a character size for the legend, used with par("cex")*csub
possub

a string of characters indicating the legend position ("topleft", "topright", "bottomleft", "bottomright") in a array of figures
...

further arguments passed to or from other methods

Author(s)

Daniel Chessel

Examples

data(lascaux)
if(adegraphicsLoaded()) {
  plot(dudi.acm(lascaux$ornem, sca = FALSE))
} else {
  scatter(dudi.acm(lascaux$ornem, sca = FALSE), csub = 3)
}

Plot of the factorial maps for a correspondence analysis

Description

performs the scatter diagrams of a correspondence analysis.

Usage

## S3 method for class 'coa'
scatter(x, xax = 1, yax = 2, method = 1:3, clab.row = 0.75, 
    clab.col = 1.25, posieig = "top", sub = NULL, csub = 2, ...)

Arguments

x

an object of class coa
xax

the column number for the x-axis
yax

the column number for the y-axis
method

an integer between 1 and 3
1 Rows and columns with the coordinates of lambda variance
2 Columns variance 1 and rows by averaging
3 Rows variance 1 and columns by averaging
clab.row

a character size for the rows
clab.col

a character size for the columns
posieig

if "top" the eigenvalues bar plot is upside,vif "bottom" it is downside, if "none" no plot
sub

a string of characters to be inserted as legend
csub

a character size for the legend, used with par("cex")*csub
...

further arguments passed to or from other methods

Author(s)

Daniel Chessel

References

Oksanen, J. (1987) Problems of joint display of species and site scores in correspondence analysis. Vegetatio, 72, 51–57.

Examples

data(housetasks)
w <- dudi.coa(housetasks, scan = FALSE)
if(adegraphicsLoaded()) {
  g1 <- scatter(w, method = 1, psub.text = "1 / Standard", posieig = "none", plot = FALSE)
  g2 <- scatter(w, method = 2, psub.text = "2 / Columns -> averaging -> Rows", 
    posieig = "none", plot = FALSE)
  g3 <- scatter(w, method = 3, psub.text = "3 / Rows -> averaging -> Columns ", 
    posieig = "none", plot = FALSE)
  G <- ADEgS(list(g1, g2, g3), layout = c(2, 2))
  
} else {
  par(mfrow = c(2, 2))
  scatter(w, method = 1, sub = "1 / Standard", posieig = "none")
  scatter(w, method = 2, sub = "2 / Columns -> averaging -> Rows", posieig = "none")
  scatter(w, method = 3, sub = "3 / Rows -> averaging -> Columns ", posieig = "none")
  par(mfrow = c(1, 1))
}

Plot of the Factorial Maps

Description

performs the scatter diagrams of objects of class dudi.

Usage

## S3 method for class 'dudi'
scatter(x, xax = 1, yax = 2, clab.row = 0.75, clab.col = 1, 
    permute = FALSE, posieig = "top", sub = NULL, ...)

Arguments

x

an object of class dudi
xax

the column number for the x-axis
yax

the column number for the y-axis
clab.row

a character size for the rows
clab.col

a character size for the columns
permute

if FALSE, the rows are plotted by points and the columns by arrows. If TRUE it is the opposite.
posieig

if "top" the eigenvalues bar plot is upside, if "bottom" it is downside, if "none" no plot
sub

a string of characters to be inserted as legend
...

further arguments passed to or from other methods

Details

scatter.dudi is a factorial map of individuals and the projection of the vectors of the canonical basis multiplied by a constante of rescaling. In the eigenvalues bar plot,the used axes for the plot are in black, the other kept axes in grey and the other in white.

The permute argument can be used to choose between the distance biplot (default) and the correlation biplot (permute = TRUE).

Author(s)

Daniel Chessel

Examples

data(deug)
scatter(dd1 <- dudi.pca(deug$tab, scannf = FALSE, nf = 4), 
    posieig = "bottomright")

data(rhone)
dd1 <- dudi.pca(rhone$tab, nf = 4, scann = FALSE)
if(adegraphicsLoaded()) {
  scatter(dd1, row.psub.text = "Principal component analysis")
} else {
  scatter(dd1, sub = "Principal component analysis")
}

Plot of the factorial maps for a fuzzy correspondence analysis

Description

performs the scatter diagrams of a fuzzy correspondence analysis.

Usage

## S3 method for class 'fca'
scatter(x, xax = 1, yax = 2, clab.moda = 1, labels = names(x$tab), 
    sub = NULL, csub = 2, ...)

Arguments

x

an object of class fca
xax

the column number for the x-axis
yax

the column number for the y-axis
clab.moda

the character size to write the modalities
labels

a vector of strings of characters for the labels of the modalities
sub

a vector of strings of characters to be inserted as legend in each figure
csub

a character size for the legend, used with par("cex")*csub
...

further arguments passed to or from other methods

Author(s)

Daniel Chessel

References

Chevenet, F., Dolédec, S. and Chessel, D. (1994) A fuzzy coding approach for the analysis of long-term ecological data. Freshwater Biology, 31, 295–309.

Examples

data(coleo)
coleo.fuzzy <- prep.fuzzy.var(coleo$tab, coleo$col.blocks)
fca1 <- dudi.fca(coleo.fuzzy, sca = FALSE, nf = 3)

if(adegraphicsLoaded()) {
  plot(fca1)
} else {
  scatter(fca1, labels = coleo$moda.names, clab.moda = 1.5,
    sub = names(coleo$col.blocks), csub = 3)
}

Graphical utility functions

Description

These are utilities used in graphical functions.

Details

The functions scatter use some utilities functions :

scatterutil.base

defines the layer of the plot for all scatters

scatterutil.sco

defines the layer of the plot for sco functions

scatterutil.chull

plots the polygons of the external contour

scatterutil.eigen

plots the eigenvalues bar plot

scatterutil.ellipse

plots an inertia ellipse for a weighting distribution

scatterutil.eti.circ

puts labels on a correlation circle

scatterutil.eti

puts labels centred on the points

scatterutil.grid

plots a grid and adds a legend

scatterutil.legend.bw.square

puts a legend of values by square size

scatterutil.legend.square.grey

puts a legend by squares and grey levels

scatterutil.legendgris

adds a legend of grey levels for the areas

scatterutil.scaling

to fit a plot on a background bipmap

scatterutil.star

plots a star for a weighting distribution

scatterutil.sub

adds a string of characters in sub-title of a graph

scatterutil.convrot90

is used to rotate labels

Author(s)

Daniel Chessel, Stéphane Dray [email protected]

See Also

s.arrow, s.chull, s.class, s.corcircle, s.distri, s.label, s.match, s.traject, s.value, add.scatter

Examples

par(mfrow = c(3,3))
plot.new()
ade4:::scatterutil.legendgris(1:20, 4, 1.6) 

plot.new()
ade4:::scatterutil.sub("lkn5555555555lkn", csub = 2, possub = "bottomleft")
ade4:::scatterutil.sub("lkn5555555555lkn", csub = 1, possub = "topleft")
ade4:::scatterutil.sub("jdjjl", csub = 3, possub = "topright")
ade4:::scatterutil.sub("**", csub = 2, possub = "bottomright")

x <- c(0.5,0.2,-0.5,-0.2) ; y <- c(0.2,0.5,-0.2,-0.5)
eti <- c("toto", "kjbk", "gdgiglgl", "sdfg")
plot(x, y, xlim = c(-1,1), ylim = c(-1,1))
ade4:::scatterutil.eti.circ(x, y, eti, 2.5)
abline(0, 1, lty = 2) ; abline(0, -1, lty = 2)

x <- c(0.5,0.2,-0.5,-0.2) ; y <- c(0.2,0.5,-0.2,-0.5)
eti <- c("toto", "kjbk", "gdgiglgl", "sdfg")
plot(x, y, xlim = c(-1,1), ylim = c(-1,1))
ade4:::scatterutil.eti(x, y, eti, 1.5)

plot(runif(10,-3,5), runif(10,-1,1), asp = 1)
ade4:::scatterutil.grid(2)
abline(h = 0, v = 0, lwd = 3)

x <- runif(10,0,1) ; y <- rnorm(10) ; z <- rep(1,10)
plot(x,y) ; ade4:::scatterutil.star(x, y, z, 0.5)
plot(x,y) ; ade4:::scatterutil.star(x, y, z, 1)

x <- c(runif(10,0,0.5), runif(10,0.5,1))
y <- runif(20)
plot(x, y, asp = 1) # asp=1 is essential to have perpendicular axes
ade4:::scatterutil.ellipse(x, y, rep(c(1,0), c(10,10)), cell = 1.5, ax = TRUE)
ade4:::scatterutil.ellipse(x, y, rep(c(0,1), c(10,10)), cell = 1.5, ax = TRUE)

x <- c(runif(100,0,0.75), runif(100,0.25,1))
y <- c(runif(100,0,0.75), runif(100,0.25,1))
z <- factor(rep(c(1,2), c(100,100)))
plot(x, y, pch = rep(c(1,20), c(100,100)))
ade4:::scatterutil.chull(x, y, z, opt = c(0.25,0.50,0.75,1))
par(mfrow = c(1,1))

Representation of the link between a variable and a set of qualitative variables

Description

represents the link between a variable and a set of qualitative variables.

Usage

sco.boxplot(score, df, labels = names(df), clabel = 1, xlim = NULL, 
    grid = TRUE, cgrid = 0.75, include.origin = TRUE, origin = 0, 
    sub = NULL, csub = 1)

Arguments

score

a numeric vector
df

a data frame with only factors
labels

a vector of strings of characters for the labels of variables
clabel

if not NULL, a character size for the labels, used with par("cex")*clabel
xlim

the ranges to be encompassed by the x axis, if NULL they are computed
grid

a logical value indicating whether the scale vertical lines should be drawn
cgrid

a character size, parameter used with par("cex")*cgrid to indicate the mesh of the scale
include.origin

a logical value indicating whether the point "origin" should be belonged to the graph space
origin

the fixed point in the graph space, for example 0 the origin axis
sub

a string of characters to be inserted as legend
csub

a character size for the legend, used with par("cex")*csub

Author(s)

Daniel Chessel

Examples

w1 <- rnorm(100,-1)
w2 <- rnorm(100)
w3 <- rnorm(100,1)
f1 <- gl(3,100)
f2 <- gl(30,10)
sco.boxplot(c(w1,w2,w3), data.frame(f1,f2))

data(banque)
banque.acm <- dudi.acm(banque, scan = FALSE, nf = 4)
par(mfrow = c(1,3))
sco.boxplot(banque.acm$l1[,1], banque[,1:7], clab = 1.8)
sco.boxplot(banque.acm$l1[,1], banque[,8:14], clab = 1.8)
sco.boxplot(banque.acm$l1[,1], banque[,15:21], clab = 1.8)
par(mfrow = c(1,1))

1D plot of a numeric score and a factor with labels

Description

Draws evenly spaced labels, each label linked to the corresponding values of the levels of a factor.

Usage

sco.class(score, fac, label = levels(fac), clabel = 1, horizontal = TRUE, 
    reverse = FALSE, pos.lab = 0.5, pch = 20, cpoint = 1, boxes = TRUE, 
    col = rep(1, length(levels(fac))), lim = NULL, grid = TRUE, 
    cgrid = 1, include.origin = TRUE, origin = c(0, 0), sub = "", 
    csub = 1.25, possub = "bottomleft")

Arguments

score

a numeric vector
fac

a factor
label

labels for the levels of the factor
clabel

a character size for the labels, used with par("cex")*clabel
horizontal

logical. If TRUE, the plot is horizontal
reverse

logical. If horizontal = TRUE and reverse=TRUE, the plot is at the bottom, if reverse = FALSE, the plot is at the top. If horizontal = FALSE, the plot is at the right (TRUE) or at the left (FALSE).
pos.lab

a values between 0 and 1 to manage the position of the labels.
pch

an integer specifying the symbol or the single character to be used in plotting points
cpoint

a character size for plotting the points, used with par("cex")*cpoint. If zero, no points are drawn
boxes

if TRUE, labels are framed
col

a vector of colors used to draw each class in a different color
lim

the range for the x axis or y axis (if horizontal = FALSE), if NULL, they are computed
grid

a logical value indicating whether a grid in the background of the plot should be drawn
cgrid

a character size, parameter used with par("cex")* cgrid to indicate the mesh of the grid
include.origin

a logical value indicating whether the point "origin" should belong to the plot
origin

the fixed point in the graph space, for example c(0,0) the origin axes
sub

a string of characters to be inserted as legend
csub

a character size for the legend, used with par("cex")*csub
possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")

Value

The matched call.

Author(s)

Stéphane Dray [email protected]

Examples

data(meau)
envpca <- dudi.pca(meau$env, scannf=FALSE)
par(mfrow=c(2,1))
sco.class(envpca$li[,1],meau$design$season, col = 1:6)
sco.class(envpca$li[,1],meau$design$season, col = 1:4, reverse = TRUE)

Representation by mean- standard deviation of a set of weight distributions on a numeric score

Description

represents the mean- standard deviation of a set of weight distributions on a numeric score.

Usage

sco.distri(score, df, y.rank = TRUE, csize = 1, labels = names(df), 
    clabel = 1, xlim = NULL, grid = TRUE, cgrid = 0.75,
    include.origin = TRUE, origin = 0, sub = NULL, csub = 1)

Arguments

score

a numeric vector
df

a data frame with only positive or null values
y.rank

a logical value indicating whether the means should be classified in ascending order
csize

an integer indicating the size segment
labels

a vector of strings of characters for the labels of the variables
clabel

if not NULL, a character size for the labels, used with par("cex")*clabel
xlim

the ranges to be encompassed by the x axis, if NULL they are computed
grid

a logical value indicating whether the scale vertical lines should be drawn
cgrid

a character size, parameter used with par("cex")*cgrid to indicate the mesh of the scale
include.origin

a logical value indicating whether the point "origin" should be belonged to the graph space
origin

the fixed point in the graph space, for example c(0,0) the origin axes
sub

a string of characters to be inserted as legend
csub

a character size for the legend, used with par("cex")*csub

Value

returns an invisible data.frame with means and variances

Author(s)

Daniel Chessel

Examples

if(!adegraphicsLoaded()) {
  w <- seq(-1, 1, le = 200)
  distri <- data.frame(lapply(1:50, 
    function(x) sample((200:1)) * ((w >= (- x / 50)) & (w <= x / 50))))
  names(distri) <- paste("w", 1:50, sep = "")
  par(mfrow = c(1, 2))
  sco.distri(w, distri, csi = 1.5)
  sco.distri(w, distri, y.rank = FALSE, csi = 1.5)
  par(mfrow = c(1, 1))
  
  data(rpjdl)
  coa2 <- dudi.coa(rpjdl$fau, FALSE)
  sco.distri(coa2$li[, 1], rpjdl$fau, lab = rpjdl$frlab, clab = 0.8)
  
  data(doubs)
  par(mfrow = c(2, 2))
  poi.coa <- dudi.coa(doubs$fish, scann = FALSE)
  sco.distri(poi.coa$l1[, 1], doubs$fish)
  poi.nsc <- dudi.nsc(doubs$fish, scann = FALSE)
  sco.distri(poi.nsc$l1[, 1], doubs$fish)
  s.label(poi.coa$l1)
  s.label(poi.nsc$l1)
  
  data(rpjdl)
  fau.coa <- dudi.coa(rpjdl$fau, scann = FALSE)
  sco.distri(fau.coa$l1[,1], rpjdl$fau)
  fau.nsc <- dudi.nsc(rpjdl$fau, scann = FALSE)
  sco.distri(fau.nsc$l1[,1], rpjdl$fau)
  s.label(fau.coa$l1)
  s.label(fau.nsc$l1)
  
  par(mfrow = c(1, 1))
}

Relationships between one score and qualitative variables

Description

Draws Gauss curves with the same mean and variance as the scores of indivivuals belonging to categories of several qualitative variables.

Usage

sco.gauss(score, df, xlim = NULL, steps = 200, ymax = NULL, sub =
names(df), csub = 1.25, possub = "topleft", legen =TRUE, label = row.names(df),
clabel = 1, grid = TRUE, cgrid = 1, include.origin = TRUE, origin = c(0, 0))

Arguments

score

a numeric vector
df

a dataframe containing only factors, number of rows equal to the length of the score vector
xlim

starting point and end point for drawing the Gauss curves
steps

number of segments for drawing the Gauss curves
ymax

max ordinate for all Gauss curves. If NULL, ymax is computed and different for each factor
sub

vector of strings of characters for the lables of qualitative variables
csub

character size for the legend
possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")
legen

if TRUE, the first graphic of the series displays the score with evenly spaced labels (see sco.label)
label

labels for the score
clabel

a character size for the labels, used with par("cex")*clabel
grid

a logical value indicating whether a grid in the background of the plot should be drawn
cgrid

a character size, parameter used with par("cex")*cgrid to indicate the mesh of the grid
include.origin

a logical value indicating whether the point "origin" should belong to the plot
origin

the fixed point in the graph space, for example c(0,0) the origin axes

Details

Takes one vector containing quantitative values (score) and one dataframe containing only factors that give categories to wich the quantitative values belong. Computes the mean and variance of the values in each category of each factor, and draws a Gauss curve with the same mean and variance for each category of each factor. Can optionaly set the start and end point of the curves and the number of segments. The max ordinate (ymax) can also be set arbitrarily to set a common max for all factors (else the max is different for each factor).

Value

The matched call.

Author(s)

Jean Thioulouse, Stéphane Dray [email protected]

Examples

data(meau)
envpca <- dudi.pca(meau$env, scannf=FALSE)
dffac <- cbind.data.frame(meau$design$season, meau$design$site)
sco.gauss(envpca$li[,1], dffac, clabel = 2, csub = 2)

1D plot of a numeric score with labels

Description

Draws evenly spaced labels, each label linked to the corresponding value of a numeric score.

Usage

sco.label(score, label = names(score), clabel = 1, horizontal = TRUE,
reverse = FALSE, pos.lab = 0.5, pch = 20, cpoint = 1, boxes = TRUE, lim
= NULL, grid = TRUE, cgrid = 1, include.origin = TRUE, origin = c(0, 0),
sub = "", csub = 1.25, possub = "bottomleft")

Arguments

score

a numeric vector
label

labels for the score
clabel

a character size for the labels, used with par("cex")*clabel
horizontal

logical. If TRUE, the plot is horizontal
reverse

logical. If horizontal = TRUE and reverse=TRUE, the plot is at the bottom, if reverse = FALSE, the plot is at the top. If horizontal = FALSE, the plot is at the right (TRUE) or at the left (FALSE).
pos.lab

a values between 0 and 1 to manage the position of the labels.
pch

an integer specifying the symbol or the single character to be used in plotting points
cpoint

a character size for plotting the points, used with par("cex")*cpoint. If zero, no points are drawn
boxes

if TRUE, labels are framed
lim

the range for the x axis or y axis (if horizontal = FALSE), if NULL, they are computed
grid

a logical value indicating whether a grid in the background of the plot should be drawn
cgrid

a character size, parameter used with par("cex")* cgrid to indicate the mesh of the grid
include.origin

a logical value indicating whether the point "origin" should belong to the plot
origin

the fixed point in the graph space, for example c(0,0) the origin axes
sub

a string of characters to be inserted as legend
csub

a character size for the legend, used with par("cex")*csub
possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")

Value

The matched call.

Author(s)

Stéphane Dray [email protected], Jean Thioulouse

Examples

data(meau)
envpca <- dudi.pca(meau$env, scannf=FALSE)
par(mfrow=c(2,1))
sco.label(envpca$l1[,1], row.names(envpca$l1), lim=c(-1,3.5))
sco.label(envpca$co[,1], row.names(envpca$co), reverse = TRUE, lim=c(-1,3.5))

1D plot of a pair of numeric scores with labels

Description

Draws evenly spaced labels, each label linked to the corresponding values of two numeric score.

Usage

sco.match(score1, score2, label = names(score1), clabel = 1, 
    horizontal = TRUE, reverse = FALSE, pos.lab = 0.5, wmatch = 3, 
    pch = 20, cpoint = 1, boxes = TRUE, lim = NULL, grid = TRUE, 
    cgrid = 1, include.origin = TRUE, origin = c(0, 0), sub = "", 
    csub = 1.25, possub = "bottomleft")

Arguments

score1

a numeric vector
score2

a numeric vector
label

labels for the score
clabel

a character size for the labels, used with par("cex")*clabel
horizontal

logical. If TRUE, the plot is horizontal
reverse

logical. If horizontal = TRUE and reverse=TRUE, the plot is at the bottom, if reverse = FALSE, the plot is at the top. If horizontal = FALSE, the plot is at the right (TRUE) or at the left (FALSE).
pos.lab

a values between 0 and 1 to manage the position of the labels.
wmatch

a numeric values to specify the width of the matching region in the plot. The width is equal to wmatch * the height of character
pch

an integer specifying the symbol or the single character to be used in plotting points
cpoint

a character size for plotting the points, used with par("cex")*cpoint. If zero, no points are drawn
boxes

if TRUE, labels are framed
lim

the range for the x axis or y axis (if horizontal = FALSE), if NULL, they are computed
grid

a logical value indicating whether a grid in the background of the plot should be drawn
cgrid

a character size, parameter used with par("cex")* cgrid to indicate the mesh of the grid
include.origin

a logical value indicating whether the point "origin" should belong to the plot
origin

the fixed point in the graph space, for example c(0,0) the origin axes
sub

a string of characters to be inserted as legend
csub

a character size for the legend, used with par("cex")*csub
possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")

Value

The matched call.

Author(s)

Stéphane Dray [email protected]

Examples

sco.match(-5:5,2*(-5:5))

Graph to Analyse the Relation between a Score and Quantitative Variables

Description

represents the graphs to analyse the relation between a score and quantitative variables.

Usage

sco.quant (score, df, fac = NULL, clabel = 1, abline = FALSE, 
    sub = names(df), csub = 2, possub = "topleft")

Arguments

score

a numeric vector
df

a data frame which rows equal to the score length
fac

a factor with the same length than the score
clabel

character size for the class labels (if any) used with par("cex")*clabel
abline

a logical value indicating whether a regression line should be added
sub

a vector of strings of characters for the labels of variables
csub

a character size for the legend, used with par("cex")*csub
possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")

Author(s)

Daniel Chessel

Examples

w <- runif(100, -5, 10)
fw <- cut (w, 5)
levels(fw) <- LETTERS[1:5]
wX <- data.frame(matrix(w + rnorm(900, sd = (1:900) / 100), 100, 9))
sco.quant(w, wX, fac = fw, abline = TRUE, clab = 2, csub = 3)

Graphs for One Dimension

Description

score is a generic function. It proposes methods for the objects 'coa', 'acm', 'mix', 'pca'.

Usage

score(x, ...)
scoreutil.base(y, xlim, grid, cgrid, include.origin, origin, sub, csub)

Arguments

x

an object used to select a method
...

further arguments passed to or from other methods
y

a numeric vector
xlim

the ranges to be encompassed by the x axis, if NULL they are computed
grid

a logical value indicating whether the scale vertical lines should be drawn
cgrid

a character size, parameter used with par("cex")*cgrid to indicate the mesh of the scale
include.origin

a logical value indicating whether the point "origin" should be belonged to the graph space
origin

the fixed point in the graph space, for example 0 the origin axis
sub

a string of characters to be inserted as legend
csub

a character size for the legend, used with par("cex")*csub

Details

scoreutil.base is a utility function - not for the user - to define the bottom of the layout of all score.

Author(s)

Daniel Chessel

See Also

sco.boxplot, sco.distri, sco.quant

Examples

## Not run: 
par(mar = c(1, 1, 1, 1))
ade4:::scoreutil.base (runif(20, 3, 7), xlim = NULL, grid = TRUE, cgrid = 0.8, 
  include.origin = TRUE, origin = 0, sub = "Uniform", csub = 1)
## End(Not run)
# returns the value of the user coordinate of the low line.  
# The user window id defined with c(0,1) in ordinate.
# box()

Graphs to study one factor in a Multiple Correspondence Analysis

Description

performs the canonical graph of a Multiple Correspondence Analysis.

Usage

## S3 method for class 'acm'
score(x, xax = 1, which.var = NULL, mfrow = NULL, 
    sub = names(oritab), csub = 2, possub = "topleft", ...)

Arguments

x

an object of class acm
xax

the column number for the used axis
which.var

the numbers of the kept columns for the analysis, otherwise all columns
mfrow

a vector of the form "c(nr,nc)", otherwise computed by a special own function n2mfrow
sub

a vector of strings of characters to be inserted as sub-titles, otherwise the variable names of the initial array
csub

a character size for the sub-titles
possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")
...

further arguments passed to or from other methods

Author(s)

Daniel Chessel

Examples

data(banque)
banque.acm <- dudi.acm(banque, scann = FALSE, nf = 3)
score(banque.acm, which = which(banque.acm$cr[, 1] > 0.2))

Reciprocal scaling after a correspondence analysis

Description

performs the canonical graph of a correspondence analysis.

Usage

## S3 method for class 'coa'
score(x, xax = 1, dotchart = FALSE, clab.r = 1, clab.c = 1, 
    csub = 1, cpoi = 1.5, cet = 1.5, ...)
reciprocal.coa(x)

Arguments

x

an object of class coa
xax

the column number for the used axis
dotchart

if TRUE the graph gives a "dual scaling", if FALSE a "reciprocal scaling"
clab.r

a character size for row labels
clab.c

a character size for column labels
csub

a character size for the sub-titles, used with par("cex")*csub
cpoi

a character size for the points
cet

a coefficient for the size of segments in standard deviation
...

further arguments passed to or from other methods

Details

In a "reciprocal scaling", the reference score is a numeric code centred and normalized of the non zero cells of the array which both maximizes the variance of means by row and by column. The bars are drawn with half the length of this standard deviation.

Value

return a data.frame with the scores, weights and factors of correspondences (non zero cells)

Author(s)

Daniel Chessel

References

Thioulouse, J. and Chessel D. (1992) A method for reciprocal scaling of species tolerance and sample diversity. Ecology, 73, 670–680.

Examples

layout(matrix(c(1,1,2,3), 2, 2), resp = FALSE)
data(aviurba)
dd1 <- dudi.coa(aviurba$fau, scan = FALSE)
score(dd1, clab.r = 0, clab.c = 0.75)
recscal <- reciprocal.coa(dd1)
head(recscal)
abline(v = 1, lty = 2, lwd = 3)
sco.distri(dd1$l1[,1], aviurba$fau)
sco.distri(dd1$c1[,1], data.frame(t(aviurba$fau)))

# 1 reciprocal scaling correspondence score -> species amplitude + sample diversity
# 2 sample score -> averaging -> species amplitude
# 3 species score -> averaging -> sample diversity

layout(matrix(c(1,1,2,3), 2, 2), resp = FALSE)
data(rpjdl)
rpjdl1 <- dudi.coa(rpjdl$fau, scan = FALSE)
score(rpjdl1, clab.r = 0, clab.c = 0.75)
if (requireNamespace("MASS", quietly = TRUE)) {
   data(caith, package = "MASS")
   score(dudi.coa(caith, scan = FALSE), clab.r = 1.5, clab.c = 1.5, cpoi = 3)
   data(housetasks)
   score(dudi.coa(housetasks, scan = FALSE), clab.r = 1.25, clab.c = 1.25, 
        csub = 0, cpoi = 3)
}
par(mfrow = c(1,1))
score(rpjdl1, dotchart = TRUE, clab.r = 0)

Graphs to Analyse a factor in a Mixed Analysis

Description

performs the canonical graph of a mixed analysis.

Usage

## S3 method for class 'mix'
score(x, xax = 1, csub = 2, mfrow = NULL, which.var = NULL, ...)

Arguments

x

an object of class mix
xax

the column number for the used axis
csub

a character size for the sub-titles, used with par("cex")*csub
mfrow

a vector of the form "c(nr,nc)", otherwise computed by a special own function n2mfrow
which.var

the numbers of the kept columns for the analysis, otherwise all columns

...

further arguments passed to or from other methods

Author(s)

Daniel Chessel

Examples

data(lascaux)
w <- cbind.data.frame(lascaux$colo, lascaux$ornem)
dd <- dudi.mix(w, scan = FALSE, nf = 4, add = TRUE)
score(dd, which = which(dd$cr[,1] > 0.3))

Graphs to Analyse a factor in PCA

Description

performs the canonical graph of a Principal Component Analysis.

Usage

## S3 method for class 'pca'
score(x, xax = 1, which.var = NULL, mfrow = NULL, csub = 2, 
    sub = names(x$tab), abline = TRUE, ...)

Arguments

x

an object of class pca
xax

the column number for the used axis
which.var

the numbers of the kept columns for the analysis, otherwise all columns
mfrow

a vector of the form "c(nr,nc)", otherwise computed by a special own function n2mfrow
csub

a character size for sub-titles, used with par("cex")*csub
sub

a vector of string of characters to be inserted as sub-titles, otherwise the names of the variables
abline

a logical value indicating whether a regression line should be added
...

further arguments passed to or from other methods

Author(s)

Daniel Chessel

Examples

data(deug)
dd1 <- dudi.pca(deug$tab, scan = FALSE)
score(dd1)
 
# The correlations are :
dd1$co[,1]
# [1] 0.7925 0.6532 0.7410 0.5287 0.5539 0.7416 0.3336 0.2755 0.4172

Students and Subjects

Description

The seconde data frame gives the marks of 22 students for 8 subjects.

Usage

data(seconde)

Format

This data frame (22,8) contains the following columns: - HGEO: History and Geography - FRAN: French literature - PHYS: Physics - MATH: Mathematics - BIOL: Biology - ECON: Economy - ANGL: English language - ESPA: Spanish language

Source

Personal communication

Examples

data(seconde)
if(adegraphicsLoaded()) {
  scatter(dudi.pca(seconde, scan = FALSE), row.plab.cex = 1, col.plab.cex = 1.5)
} else {
  scatter(dudi.pca(seconde, scan = FALSE), clab.r = 1, clab.c = 1.5)
}

Separated Analyses in a K-tables

Description

performs K separated multivariate analyses of an object of class ktab containing K tables.

Usage

sepan(X, nf = 2)
## S3 method for class 'sepan'
plot(x, mfrow = NULL, csub = 2, ...)
## S3 method for class 'sepan'
summary(object, ...)
## S3 method for class 'sepan'
print(x, ...)

Arguments

X

an object of class ktab
nf

an integer indicating the number of kept axes for each separated analysis
x, object

an object of class 'sepan'
mfrow

a vector of the form "c(nr,nc)", otherwise computed by a special own function n2mfrow
csub

a character size for the sub-titles, used with par("cex")*csub
...

further arguments passed to or from other methods

Details

The function plot on a sepan object allows to compare inertias and structures between arrays. In black, the eigenvalues of kept axes in the object 'sepan'.

Value

returns a list of class 'sepan' containing :

call

a call order
tab.names

a vector of characters with the names of tables
blo

a numeric vector with the numbers of columns for each table
rank

a numeric vector with the rank of the studied matrix for each table
Eig

a numeric vector with all the eigenvalues
Li

a data frame with the row coordinates
L1

a data frame with the row normed scores
Co

a data frame with the column coordinates
C1

a data frame with the column normed coordinates
TL

a data frame with the factors for Li L1
TC

a data frame with the factors for Co C1

Author(s)

Daniel Chessel

Examples

data(escopage)
w <- data.frame(scale(escopage$tab))
w <- ktab.data.frame(w, escopage$blo, tabnames = escopage$tab.names)
sep1 <- sepan(w)
sep1
summary(sep1)
plot(sep1)

Morphometric Evolution

Description

This data set gives four anthropometric measures of 150 Egyptean skulls belonging to five different historical periods.

Usage

data(skulls)

Format

The skulls data frame has 150 rows (egyptean skulls) and 4 columns (anthropometric measures). The four variables are the maximum breadth (V1), the basibregmatic height (V2), the basialveolar length (V3) and the nasal height (V4). All measurements were taken in millimeters.

Details

The measurements are made on 5 groups and 30 Egyptian skulls. The groups are defined as follows :
1 - the early predynastic period (circa 4000 BC)
2 - the late predynastic period (circa 3300 BC)
3 - the 12th and 13th dynasties (circa 1850 BC)
4 - the Ptolemiac period (circa 200 BC)
5 - the Roman period (circa 150 BC)

Source

Thompson, A. and Randall-Maciver, R. (1905) Ancient races of the Thebaid, Oxford University Press.

References

Manly, B.F. (1994) Multivariate Statistical Methods. A primer, Second edition. Chapman & Hall, London. 1–215.
The example is treated pp. 6, 13, 51, 64, 72, 107, 112 and 117.

Examples

data(skulls)
pca1 <- dudi.pca(skulls, scan = FALSE)
fac <- gl(5, 30)
levels(fac) <- c("-4000", "-3300", "-1850", "-200", "+150")
dis.skulls <- discrimin(pca1, fac, scan = FALSE)
if(!adegraphicsLoaded())
  plot(dis.skulls, 1, 1)

STATIS and Co-Inertia : Analysis of a series of paired ecological tables

Description

Does the analysis of a series of pairs of ecological tables. This function uses Partial Triadic Analysis (pta) and ktab.match2ktabs to do the computations.

Usage

statico(KTX, KTY, scannf = TRUE)

Arguments

KTX

an objet of class ktab
KTY

an objet of class ktab
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed

Details

This function takes 2 ktabs and crosses each pair of tables of these ktabs with the function ktab.match2ktabs. It then does a partial triadic analysis on this new ktab with pta.

Value

a list of class ktab, subclass kcoinertia. See ktab

WARNING

IMPORTANT : KTX and KTY must have the same k-tables structure, the same number of columns, and the same column weights.

Author(s)

Jean Thioulouse [email protected]

References

Thioulouse J. (2011). Simultaneous analysis of a sequence of paired ecological tables: a comparison of several methods. Annals of Applied Statistics, 5, 2300-2325. Thioulouse J., Simier M. and Chessel D. (2004). Simultaneous analysis of a sequence of paired ecological tables. Ecology 85, 272-283. Simier, M., Blanc L., Pellegrin F., and Nandris D. (1999). Approche simultanée de K couples de tableaux : Application a l'étude des relations pathologie végétale - environnement. Revue de Statistique Appliquée, 47, 31-46.

Examples

data(meau)
wit1 <- withinpca(meau$env, meau$design$season, scan = FALSE, scal = "total")
spepca <- dudi.pca(meau$spe, scale = FALSE, scan = FALSE, nf = 2)
wit2 <- wca(spepca, meau$design$season, scan = FALSE, nf = 2)
kta1 <- ktab.within(wit1, colnames = rep(c("S1","S2","S3","S4","S5","S6"), 4))
kta2 <- ktab.within(wit2, colnames = rep(c("S1","S2","S3","S4","S5","S6"), 4))
statico1 <- statico(kta1, kta2, scan = FALSE)
plot(statico1)
kplot(statico1)

Monte-Carlo test on a Statico analysis (in C).

Description

Performs the series of Monte-Carlo coinertia tests of a Statico analysis (one for each couple of tables).

Usage

statico.krandtest(KTX, KTY, nrepet = 999, ...)

Arguments

KTX

an objet of class ktab containing the environmental data
KTY

an objet of class ktab containing the species data
nrepet

the number of permutations
...

further arguments passed to or from other methods

Details

This function takes 2 ktabs and does a coinertia analysis with coinertia on each pair of tables. It then uses the randtest function to do a permutation test on each of these coinertia analyses.

Value

krandtest, a list of randtest objects. See krandtest

WARNING

IMPORTANT : KTX and KTY must have the same k-tables structure, the same number of columns, and the same column weights.

Author(s)

Jean Thioulouse [email protected]

References

Thioulouse J. (2011). Simultaneous analysis of a sequence of paired ecological tables: a comparison of several methods. Annals of Applied Statistics, 5, 2300-2325.

Examples

data(meau)
wit1 <- withinpca(meau$env, meau$design$season, scan = FALSE, scal = "total")
spepca <- dudi.pca(meau$spe, scale = FALSE, scan = FALSE, nf = 2)
wit2 <- wca(spepca, meau$design$season, scan = FALSE, nf = 2)
kta1 <- ktab.within(wit1, colnames = rep(c("S1","S2","S3","S4","S5","S6"), 4))
kta2 <- ktab.within(wit2, colnames = rep(c("S1","S2","S3","S4","S5","S6"), 4))
statico1 <- statico(kta1, kta2, scan = FALSE)
kr1 <- statico.krandtest(kta1, kta2)
plot(kr1)

STATIS, a method for analysing K-tables

Description

performs a STATIS analysis of a ktab object.

Usage

statis(X, scannf = TRUE, nf = 3, tol = 1e-07)
## S3 method for class 'statis'
plot(x, xax = 1, yax = 2, option = 1:4, ...) 
## S3 method for class 'statis'
print(x, ...)

Arguments

X

an object of class 'ktab'
scannf

a logical value indicating whether the number of kept axes for the compromise should be asked
nf

if scannf FALSE, an integer indicating the number of kept axes for the compromise
tol

a tolerance threshold to test whether the distance matrix is Euclidean : an eigenvalue is considered positive if it is larger than -tol*lambda1 where lambda1 is the largest eigenvalue
x

an object of class 'statis'
xax, yax

the numbers of the x-axis and the y-axis
option

an integer between 1 and 4, otherwise the 4 components of the plot are dispayed
...

further arguments passed to or from other methods

Value

statis returns a list of class 'statis' containing :

RV

a matrix with the all RV coefficients
RV.eig

a numeric vector with all the eigenvalues
RV.coo

a data frame with the array scores
tab.names

a vector of characters with the names of the arrays
RV.tabw

a numeric vector with the array weigths
C.nf

an integer indicating the number of kept axes
C.rank

an integer indicating the rank of the analysis
C.li

a data frame with the row coordinates
C.Co

a data frame with the column coordinates
C.T4

a data frame with the principal vectors (for each table)
TL

a data frame with the factors (not used)
TC

a data frame with the factors for Co
T4

a data frame with the factors for T4

Author(s)

Daniel Chessel

References

Lavit, C. (1988) Analyse conjointe de tableaux quantitatifs, Masson, Paris.

Lavit, C., Escoufier, Y., Sabatier, R. and Traissac, P. (1994) The ACT (Statis method). Computational Statistics and Data Analysis, 18, 97–119.

Examples

data(jv73)
kta1 <- ktab.within(withinpca(jv73$morpho, jv73$fac.riv, scann = FALSE))
statis1 <- statis(kta1, scann = FALSE)
plot(statis1)

dudi1 <- dudi.pca(jv73$poi, scann = FALSE, scal = FALSE)
wit1 <- wca(dudi1, jv73$fac.riv, scann = FALSE)
kta3 <- ktab.within(wit1)
data(jv73)
statis3 <- statis(kta3, scann = FALSE)
plot(statis3)

if(adegraphicsLoaded()) {
  s.arrow(statis3$C.li, pgrid.text.cex = 0)
  kplot(statis3, traj = TRUE, arrow = FALSE, plab.cex = 0, psub.cex = 3, ppoi.cex = 3)
} else {
  s.arrow(statis3$C.li, cgrid = 0)
  kplot(statis3, traj = TRUE, arrow = FALSE, unique = TRUE, 
    clab = 0, csub = 3, cpoi = 3)
}

statis3

Transect in the Vegetation

Description

This data set gives the presence-absence of 37 species on 515 sites.

Usage

data(steppe)

Format

steppe is a list of 2 components.

tab

is a data frame with 512 rows (sites) and 37 variables (species) in presence-absence.

esp.names

is a vector of the species names.

Source

Estève, J. (1978) Les méthodes d'ordination : éléments pour une discussion. in J. M. Legay and R. Tomassone, editors. Biométrie et Ecologie, Société Française de Biométrie, Paris, 223–250.

Examples

par(mfrow = c(3,1))
data(steppe)
w1 <- col(as.matrix(steppe$tab[,1:15]))
w1 <- as.numeric(w1[steppe$tab[,1:15] > 0])
w2 <- row(as.matrix(steppe$tab[,1:15]))
w2 <- as.numeric(w2[steppe$tab[,1:15] > 0])
plot(w2, w1, pch = 20)
plot(dudi.pca(steppe$tab, scan = FALSE, scale = FALSE)$li[,1],
    pch = 20, ylab = "PCA", xlab = "", type = "b")
plot(dudi.coa(steppe$tab, scan = FALSE)$li[,1], pch = 20, 
    ylab = "COA", xlab = "", type = "b")
par(mfrow = c(1,1))

Projections of Supplementary Columns

Description

performs projections of supplementary columns.

Usage

supcol(x, ...)
## S3 method for class 'dudi'
supcol(x, Xsup, ...) 
## S3 method for class 'coa'
supcol(x, Xsup, ...)

Arguments

x

an object used to select a method
Xsup

an array with the supplementary columns (Xsup and x$tab have the same row number)
...

further arguments passed to or from other methods

Details

If supcol.dudi is used, the column vectors of Xsup are projected without prior modification onto the principal components of dudi with the scalar product associated to the row weightings of dudi.

Value

A list of two components:

tabsup

data frame containing the array with the supplementary columns transformed or not
cosup

data frame containing the coordinates of the supplementary projections

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

Examples

data(rpjdl)
rpjdl.coa <- dudi.coa(rpjdl$fau, scan = FALSE, nf = 4)
rpjdl.coa$co[1:3, ]
supcol(rpjdl.coa, rpjdl$fau[, 1:3])$cosup  #the same

data(doubs)
dudi1 <- dudi.pca(doubs$fish, scal = FALSE, scan = FALSE)
if(adegraphicsLoaded()) {
  g1 <- s.arrow(dudi1$co, plot = FALSE)
  g2 <- s.arrow(supcol(dudi1, data.frame(scalewt(doubs$env)))$cosup, plab.cex = 2, plot = FALSE)
  G <- superpose(g1, g2, plot = TRUE)
  
} else {
  s.arrow(dudi1$co)
  s.arrow(supcol(dudi1, data.frame(scalewt(doubs$env)))$cosup, add.p = TRUE, clab = 2)
  symbols(0, 0, circles = 1, inches = FALSE, add = TRUE)
}

Projection of additional items in a PCO analysis

Description

This function takes the grand distance matrix between all items (Active + Supplementary). It computes the PCO of the distance matrix between Active items, and projects the distance matrix of Supplementary items in this PCO.

Usage

supdist(d, fsup, tol = 1e-07)

Arguments

d

Grand distance matrix between all (Active + Supplementary) items
fsup

A factor with two levels giving the Active (level ‘A’) or Supplementary (level ‘S’) status for each item in the distance matrix.
tol

Numeric tolerance used to evaluate zero eigenvalues

Value

coordSup

Coordinates of Supplementary items projected in the PCO of Active items
coordAct

Coordinates of Active item
coordTot

Coordinates of Active plus Supplementary items

Author(s)

Jean Thioulouse

References

Computations based on the Methods section of the following paper: Pele J, Abdi H, Moreau M, Thybert D, Chabbert M (2011) Multidimensional Scaling Reveals the Main Evolutionary Pathways of Class A G-Protein-Coupled Receptors. PLoS ONE 6(4): e19094. doi:10.1371/journal.pone.0019094

See Also

dudi.pco, suprow

Examples

data(meau)
## Case 1: Supplementary items = subset of Active items
## Supplementary coordinates should be equal to Active coordinates
## PCO of active items (meau dataset has 6 sites and 10 variables)
envpca1 <- dudi.pca(meau$env, scannf = FALSE)
dAct <- dist(envpca1$tab)
pco1 <- dudi.pco(dAct, scannf = FALSE)
## Projection of rows 19:24 (winter season for the 6 sites)
## Supplementary items must be normalized
f1 <- function(w) (w - envpca1$cent) / envpca1$norm
envSup <- t(apply(meau$env[19:24, ], 1, f1))
envTot <- rbind.data.frame(envpca1$tab, envSup)
dTot <- dist(envTot)
fSA1 <- as.factor(rep(c("A", "S"), c(24, 6)))
cSup1 <- supdist(dTot, fSA1)
## Comparison (coordinates should be equal)
cSup1$coordSup[, 1:2]
pco1$li[19:24, ]

data(meaudret)
## Case 2: Supplementary items = new items
## PCO of active items (meaudret dataset has only 5 sites and 9 variables)
envpca2 <- dudi.pca(meaudret$env, scannf = FALSE)
dAct <- dist(envpca2$tab)
pco2 <- dudi.pco(dAct, scannf = FALSE)
## Projection of site 6 (four seasons, without Oxyg variable)
## Supplementary items must be normalized
f1 <- function(w) (w - envpca2$cent) / envpca2$norm
envSup <- t(apply(meau$env[seq(6, 24, 6), -5], 1, f1))
envTot <- rbind.data.frame(envpca2$tab, envSup)
dTot <- dist(envTot)
fSA2 <- as.factor(rep(c("A", "S"), c(20, 4)))
cSup2 <- supdist(dTot, fSA2)
## Supplementary items vs. real items (both in red)
if(!adegraphicsLoaded()) {
 par(mfrow = c(2, 2))
 s.label(pco1$li, boxes = FALSE)
 s.label(rbind.data.frame(pco2$li, cSup2$coordSup[, 1:2]), boxes = FALSE)
} else {
 gl1 <- s.label(pco1$li, plabels.optim = TRUE, plabels.col=rep(c(rep("black", 5),"red"), 4))
 gl2 <- s.label(rbind.data.frame(pco2$li, cSup2$coordSup[, 1:2]),
  plabels.optim = TRUE, plabels.col=rep(c("black","red"),c(20, 4)))
 ADEgS(list(gl1, gl2))
}

Projections of Supplementary Rows

Description

This function performs a projection of supplementary rows (i.e. supplementary individuals).

Usage

## S3 method for class 'coa'
suprow(x, Xsup, ...) 
## S3 method for class 'dudi'
suprow(x, Xsup, ...) 
## S3 method for class 'dudi'
predict(object, newdata, ...) 
## S3 method for class 'pca'
suprow(x, Xsup, ...)
## S3 method for class 'acm'
suprow(x, Xsup, ...) 
## S3 method for class 'mix'
suprow(x, Xsup, ...)
## S3 method for class 'fca'
suprow(x, Xsup, ...)

Arguments

x, object

an object of class dudi
Xsup, newdata

an array with the supplementary rows
...

further arguments passed to or from other methods

Details

If suprow.dudi is used, the column vectors of Xsup are projected without prior modifications onto the principal components of dudi with the scalar product associated to the row weightings of dudi.

Value

predict returns a data frame containing the coordinates of the supplementary rows. suprow returns a list with the transformed table Xsup in tabsup and the coordinates of the supplementary rows in lisup.

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

References

Gower, J. C. (1967) Multivariate analysis and multivariate geometry. The statistician, 17, 13–28.

Examples

data(euro123)
par(mfrow = c(2, 2))
w <- euro123[[2]]
dudi1 <- dudi.pca(w, scal = FALSE, scan = FALSE)

if(adegraphicsLoaded()) {
  g11 <- s.arrow(dudi1$c1, psub.text = "Classical", psub.posi = "bottomright", plot = FALSE)
  g12 <- s.label(suprow(dudi1, w)$tabsup, plab.cex = 0.75, plot = FALSE)
  g1 <- superpose(g11, g12)
  
  g21 <- s.arrow(dudi1$c1, psub.text = "Without centring", psub.posi = "bottomright", plot = FALSE)
  g22 <- s.label(suprow(dudi1, w)$tabsup, plab.cex = 0.75, plot = FALSE)
  g2 <- superpose(g21, g22) 
  
  g3 <- triangle.label(w, plab.cex = 0.75, label = row.names(w), adjust = FALSE, plot = FALSE)
  g4 <- triangle.label(w, plab.cex = 0.75, label = row.names(w), adjust = TRUE, plot = FALSE)
  
  G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))
  
} else {
  s.arrow(dudi1$c1, sub = "Classical", possub = "bottomright", csub = 2.5)
  s.label(suprow(dudi1, w), add.plot = TRUE, clab = 0.75)
  
  s.arrow(dudi1$c1, sub = "Without centring", possub = "bottomright", csub = 2.5)
  s.label(suprow(dudi1, w), clab = 0.75, add.plot = TRUE)
  
  triangle.plot(w, clab = 0.75, label = row.names(w), scal = FALSE)
  triangle.plot(w, clab = 0.75, label = row.names(w), scal = TRUE)
}

data(rpjdl)
rpjdl.coa <- dudi.coa(rpjdl$fau, scann = FALSE, nf = 4)
rpjdl.coa$li[1:3, ]
suprow(rpjdl.coa,rpjdl$fau[1:3, ])$lisup  #the same

data(deug)
deug.dudi <- dudi.pca(df = deug$tab, center = deug$cent, scale = FALSE, scannf = FALSE)
suprow(deug.dudi, deug$tab[1:3, ])$lisup  #the supplementary individuals are centered
deug.dudi$li[1:3, ]  # the same

Projections of Supplementary Rows for a Partial Triadic Analysis of K-tables

Description

This function performs a projection of supplementary rows (i.e. supplementary individuals) for a Partial Triadic Analysis (pta) of K-tables. Computations are valid ONLY if the pta has been done on a K-Tables obtained by the withinpca function, followed by calls to the ktab.within and t functions.

Usage

## S3 method for class 'pta'
suprow(x, Xsup, facSup, ...)

Arguments

x

an object of class pta
Xsup

a table with the supplementary rows
facSup

a factor partitioning the rows of Xsup
...

further arguments passed to or from other methods

Details

This function computes the coordinates of the supplementary rows for a K-tables. The table of supplementary rows is standardized according to the 'Bouroche' standardization used in the Within Analysis of the original pta. In a first step, the table of supplementary rows is standardized (centred and normed) with the mean and variance of the original table of active individuals (i.e. the K-tables used in pta). Then, according to the withinpca procedure, a second transformation is applied.

For "partial", supplementary rows are standardized in each sub-table (corresponding to each level of the factor) by the mean and variance of each corresponding sub-sample in the table of active individuals. Hence, supplementary rows have null mean and unit variance in each sub-table.

For "total", supplementary rows are centred in each sub-table with the mean of each coresponding sub-sample in the table of active individuals and then normed with the global variance ot the table of active individuals. Hence, supplementary rows have a null mean in each sub-table and a global variance equal to one.

Value

Returns a list with the transformed table Xsup in tabsup and the coordinates of the supplementary rows in lisup.

Author(s)

Benjamin Alric [email protected]
Jean Thioulouse [email protected]

References

Bouroche, J. M. (1975) Analyse des données ternaires: la double analyse en composantes principales. Thèse de 3ème cycle, Université de Paris VI.

Examples

data(meau)
# Active rows
actenv <- meau$env[meau$design$site != "S6", -c(5)]
actfac <- meau$design$season[meau$design$site != "S6"]
# Suplementary rows
supenv <- meau$env[meau$design$site == "S6", -c(5)]
supfac <- meau$design$season[meau$design$site == "S6"]
# Total = active + suplementary rows
totenv <- meau$env[, -c(5)]
totfac <- meau$design$season
# PTA with 6 sampling sites
wittot <- withinpca(df = totenv, fac = totfac, scannf = FALSE, scaling = "partial")
kta1tot <- ktab.within(wittot, colnames = rep(c("S1", "S2", "S3", "S4", "S5", "S6"), 4))
kta2tot <- t(kta1tot)
pta1tot <- pta(kta2tot, scann = FALSE)
# PTA with 5 sampling sites and site 6 added as supplementary element
wit1 <- withinpca(df = actenv, fac = actfac, scannf = FALSE, scaling = "partial")
kta1 <- ktab.within(wit1, colnames = rep(c("S1", "S2", "S3", "S4", "S5"), 4))
kta2 <- t(kta1)
pta1 <- pta(kta2, scann = FALSE)
supenv.pta <- suprow(x = pta1, Xsup = supenv, facSup = supfac)
if (adegraphicsLoaded()) {
# g1t = active + suplementary rows
	g1t <- s.label(pta1tot$Tli, labels = rownames(totenv), 
	  plabels = list(box = list(draw = FALSE), optim = TRUE), xlim = c(-6, 5), ylim = c(-5, 5), 
	  psub = list(text="Total", position="topleft"), plot = FALSE)
# g1 = Active rows
	g1 <- s.label(pta1$Tli, labels = rownames(actenv), 
	  plabels = list(box = list(draw = FALSE), optim =TRUE), xlim = c(-6, 5), ylim = c(-5, 5), 
	  psub = list(text="Active", position="topleft"), pgrid = list(text=list(cex = 0)), 
	  plot = FALSE)
# g2 = Supplementary rows
	g2 <- s.label(supenv.pta$lisup, plabels = list(box = list(draw = FALSE), optim = TRUE), 
	  ppoints = list(col = "red"), psub = list(text="Supplementary", position="topright"), 
	  pgrid = list(text=list(cex = 0)), plot = FALSE)
# g3 = superposition of active and suplementary rows
	g3 <- g1 + g2
# Comparison of the total analysis and the analysis with supplementary rows
	ADEgS(list(g1t,g3))
} else {
	par(mfrow=c(2,2))
# g1t = active + suplementary rows
	g1t <- s.label(pta1tot$Tli, label = rownames(totenv), xlim = c(-6, 5), ylim = c(-5, 5), 
	  sub="Total")
# g1 = Active rows
	g1 <- s.label(pta1$Tli, label = rownames(actenv), clabel = 1, xlim = c(-6, 5),
	  ylim = c(-5, 5), sub="Active+Supplementary")
# g2 = Supplementary rows
	g2 <- s.label(supenv.pta$lisup, clabel = 1.5, xlim = c(-6, 5), ylim = c(-5, 5), 
	  add.plot = TRUE)  
}

Representation of a quantitative variable in front of a phylogenetic tree

Description

symbols.phylog draws the phylogenetic tree and represents the values of the variable by symbols (squares or circles) which size is proportional to value. White symbols correspond to values which are below the mean, and black symbols correspond to values which are over.

Usage

symbols.phylog(phylog, circles, squares, csize = 1, clegend = 1,
 sub = "", csub = 1, possub = "topleft")

Arguments

phylog

an object of class phylog
circles

a vector giving the radii of the circles
squares

a vector giving the length of the sides of the squares
csize

a size coefficient for symbols
clegend

a character size for the legend used by par("cex")*clegend
sub

a string of characters to be inserted as legend
csub

a character size for the legend, used with par("cex")*csub
possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")

Author(s)

Daniel Chessel
Sébastien Ollier [email protected]

See Also

table.phylog and dotchart.phylog for many variables

Examples

data(mjrochet)
mjrochet.phy <- newick2phylog(mjrochet$tre)
tab0 <- data.frame(scalewt(log(mjrochet$tab)))
par(mfrow=c(3,2))
for (j in 1:6) {
    w <- tab0[,j]
    symbols.phylog(phylog = mjrochet.phy, w, csi = 1.5, cleg = 1.5,
     sub = names(tab0)[j], csub = 3)
}
par(mfrow=c(1,1))

Two Questions asked on a Sample of 1000 Respondents

Description

This data set is extracted from an opinion poll (period 1970-1980) on 1000 respondents.

Usage

data(syndicats)

Format

The syndicats data frame has 5 rows and 4 columns.
"Which politic family are you agreeing about?" has 5 response items : extgauche (extreme left) left center right and extdroite (extreme right)
"What do you think of the trade importance?" has 4 response items : trop (too important) adequate insufficient nesaispas (no opinion)

Source

unknown

Examples

data(syndicats)
par(mfrow = c(1,2))
dudi1 <- dudi.coa(syndicats, scan = FALSE)
score (dudi1, 1, TRUE)
score (dudi1, 1, FALSE)

Average temperatures of 30 French cities

Description

This data set gives the average temperatures of 30 French cities during 12 months.

Usage

data(t3012)

Format

t3012 is a list with the following components:

xy

a data frame with 30 rows (cities) and 2 coordinates (x, y)

temp

a data frame with 30 rows (cities) and 12 columns (months). Each column contains the average temperature in tenth of degree Celsius.

contour

a data frame with 4 columns (x1, y1, x2, y2) for the contour display of France

Spatial

an object of the class SpatialPolygons of sp, containing the map

Source

Besse, P. (1979) Etude descriptive d'un processus; approximation, interpolation. Thèse de troisième cycle, Université Paul Sabatier, Toulouse.

Examples

data(t3012)
data(elec88)

if(adegraphicsLoaded()) {
  if(requireNamespace("sp", quietly = TRUE)) {
    s.arrow(t3012$xy, pori.ori = as.numeric(t3012$xy["Paris", ]), Sp = t3012$Spatial, 
      pSp.col = "white", pgrid.draw = FALSE)
  }
} else {
  area.plot(elec88$area)
  s.arrow(t3012$xy, ori = as.numeric(t3012$xy["Paris", ]), add.p = TRUE)
}

Plot of Contingency Tables

Description

presents a graph for viewing contingency tables.

Usage

table.cont(df, x = 1:ncol(df), y = 1:nrow(df),
    row.labels = row.names(df), col.labels = names(df),
    clabel.row = 1, clabel.col = 1, abmean.x = FALSE, abline.x = FALSE,
    abmean.y = FALSE, abline.y = FALSE, csize = 1, clegend = 0, grid = TRUE)

Arguments

df

a data frame with only positive or null values
x

a vector of values to position the columns
y

a vector of values to position the rows
row.labels

a character vector for the row labels
col.labels

a character vetor for the column labels
clabel.row

a character size for the row labels
clabel.col

a character size for the column labels
abmean.x

a logical value indicating whether the column conditional means should be drawn
abline.x

a logical value indicating whether the regression line of y onto x should be plotted
abmean.y

a logical value indicating whether the row conditional means should be drawn
abline.y

a logical value indicating whether the regression line of x onto y should be plotted
csize

a coefficient for the square size of the values
clegend

if not NULL, a character size for the legend used with par("cex")*clegend
grid

a logical value indicating whether a grid in the background of the plot should be drawn

Author(s)

Daniel Chessel

Examples

data(chats)
chatsw <- data.frame(t(chats))
chatscoa <- dudi.coa(chatsw, scann = FALSE)
par(mfrow = c(2,2))
table.cont(chatsw, abmean.x = TRUE, csi = 2, abline.x = TRUE, 
    clabel.r = 1.5, clabel.c = 1.5)
table.cont(chatsw, abmean.y = TRUE, csi = 2, abline.y = TRUE, 
    clabel.r = 1.5, clabel.c = 1.5)
table.cont(chatsw, x = chatscoa$c1[,1], y = chatscoa$l1[,1],
    abmean.x = TRUE, csi = 2, abline.x = TRUE, clabel.r = 1.5, clabel.c = 1.5)
table.cont(chatsw, x = chatscoa$c1[,1], y = chatscoa$l1[,1],
    abmean.y = TRUE, csi = 2, abline.y = TRUE, clabel.r = 1.5, clabel.c = 1.5)
par(mfrow = c(1,1))

## Not run: 
data(rpjdl)
w <- data.frame(t(rpjdl$fau))
wcoa <- dudi.coa(w, scann = FALSE)
table.cont(w, abmean.y = TRUE, x = wcoa$c1[,1], y = rank(wcoa$l1[,1]),
    csi = 0.2, clabel.c = 0, row.labels = rpjdl$lalab, clabel.r = 0.75)

## End(Not run)

Graph Display for Distance Matrices

Description

presents a graph for viewing distance matrices.

Usage

table.dist(d, x = 1:(attr(d, "Size")), labels = as.character(x), 
    clabel = 1, csize = 1, grid = TRUE)

Arguments

d

an object of class dist
x

a vector of the row and column positions
labels

a vector of strings of characters for the labels
clabel

a character size for the labels
csize

a coefficient for the circle size
grid

a logical value indicating whether a grid in the background of the plot should be drawn

Author(s)

Daniel Chessel

Examples

data(eurodist)
table.dist(eurodist, labels = attr(eurodist, "Labels"))

Plot of the arrays by grey levels

Description

presents a graph for viewing the numbers of a table by grey levels.

Usage

table.paint(df, x = 1:ncol(df), y = nrow(df):1, 
    row.labels = row.names(df), col.labels = names(df), 
    clabel.row = 1, clabel.col = 1, csize = 1, clegend = 1)

Arguments

df

a data frame
x

a vector of values to position the columns, used only for the ordered values
y

a vector of values to position the rows, used only for the ordered values
row.labels

a character vector for the row labels
col.labels

a character vector for the column labels
clabel.row

a character size for the row labels
clabel.col

a character size for the column labels
csize

if 'clegend' not NULL, a coefficient for the legend size
clegend

a character size for the legend, otherwise no legend

Author(s)

Daniel Chessel

Examples

data(rpjdl)
X <- data.frame(t(rpjdl$fau))
Y <- data.frame(t(rpjdl$mil))
layout(matrix(c(1,2,2,2,1,2,2,2,1,2,2,2,1,2,2,2), 4, 4))
coa1 <- dudi.coa(X, scan = FALSE)
x <- rank(coa1$co[,1])
y <- rank(coa1$li[,1])
table.paint(Y, x = x, y = 1:8, clabel.c = 0, cleg = 0)
abline(v = 114.9, lwd = 3, col = "red")
abline(v = 66.4, lwd = 3, col = "red")
table.paint(X, x = x, y = y, clabel.c = 0, cleg = 0,
    row.lab = paste("  ", row.names(X), sep = ""))
abline(v = 114.9, lwd = 3, col = "red")
abline(v = 66.4, lwd = 3, col = "red")
par(mfrow = c(1, 1))

Plot arrays in front of a phylogenetic tree

Description

This function gives a graphical display for viewing the numbers of a table by square sizes in front of the corresponding phylogenetic tree.

Usage

table.phylog(df, phylog, x = 1:ncol(df), f.phylog = 0.5,
 labels.row = gsub("[_]", " ", row.names(df)), clabel.row = 1,
 labels.col = names(df), clabel.col = 1,
 labels.nod = names(phylog$nodes), clabel.nod = 0, cleaves = 1,
 cnodes = 1, csize = 1, grid = TRUE, clegend = 0.75)

Arguments

df

: a data frame or a matrix
phylog

: an object of class 'phylog'
x

: a vector of values to position the columns
f.phylog

: a size coefficient for tree size (a parameter to draw the tree in proportion to leaves labels)
labels.row

: a vector of strings of characters for row labels
clabel.row

: a character size for the leaves labels, used with par("cex")*clabel.row. If zero, no row labels are drawn
labels.col

: a vector of strings of characters for columns labels
clabel.col

: a character size for the leaves labels, used with par("cex")*clabel.col. If zero, no column labels are drawn
labels.nod

: a vector of strings of characters for the nodes labels
clabel.nod

: a character size for the nodes labels, used with par("cex")*clabel.nodes. If zero, no nodes labels are drawn
cleaves

: a character size for plotting the points that represent the leaves, used with par("cex")*cleaves. If zero, no points are drawn
cnodes

: a character size for plotting the points that represent the nodes, used with par("cex")*cnodes. If zero, no points are drawn
csize

: a size coefficient for symbols
grid

: a logical value indicating whether the grid should be plotted
clegend

: a character size for the legend (if 0, no legend)

Details

The function verifies that sort(row.names(df))==sort(names(phylog$leaves)). If df is a matrix the function uses as.data.frame(df).

Author(s)

Daniel Chessel
Sébastien Ollier [email protected]

See Also

symbols.phylog for one variable

Examples

## Not run: 
data(newick.eg)
w.phy <- newick2phylog(newick.eg[[9]])
w.tab <- data.frame(matrix(rnorm(620), 31, 20))
row.names(w.tab) <- sort(names(w.phy$leaves))
table.phylog(w.tab, w.phy, csi = 1.5, f = 0.5,
 clabel.n = 0.75, clabel.c = 0.5)

## End(Not run)

Plot of the Arrays

Description

presents a graph for viewing the numbers of a table by square sizes.

Usage

table.value(df, x = 1:ncol(df), y = nrow(df):1, 
    row.labels = row.names(df), col.labels = names(df), clabel.row = 1, 
    clabel.col = 1, csize = 1, clegend = 1, grid = TRUE)

Arguments

df

a data frame
x

a vector of values to position the columns
y

a vector of values to position the rows
row.labels

a character vector for the row labels
col.labels

a character vector for the column labels
clabel.row

a character size for the row labels
clabel.col

a character size for the column labels
csize

a coefficient for the square size of the values
clegend

a character size for the legend (if 0, no legend)
grid

a logical value indicating whether the grid should be plotted

Author(s)

Daniel Chessel

Examples

if(!adegraphicsLoaded()) {
  data(olympic)
  w <- olympic$tab
  w <- data.frame(scale(w))
  wpca <- dudi.pca(w, scann = FALSE)
  par(mfrow = c(1, 3))
  table.value(w, csi = 2, clabel.r = 2, clabel.c = 2)
  table.value(w, y = rank(wpca$li[, 1]), x = rank(wpca$co[, 1]), csi = 2,
    clabel.r = 2, clabel.c = 2)
  table.value(w, y = wpca$li[, 1], x = wpca$co[, 1], csi = 2, 
    clabel.r = 2, clabel.c = 2)
  par(mfrow = c(1, 1))
}

Mountain Avifauna

Description

This data set gives informations between sites, species, environmental and biolgoical variables.

Usage

data(tarentaise)

Format

tarentaise is a list of 5 components.

ecol

is a data frame with 376 sites and 98 bird species.

frnames

is a vector of the 98 French names of the species.

alti

is a vector giving the altitude of the 376 sites in m.

envir

is a data frame with 14 environmental variables.

traits

is a data frame with 29 biological variables of the 98 species.

Details

The attribute col.blocks of the data frame tarentaise$traits indicates it is composed of 6 units of variables.

Source

Original data from Hubert Tournier, University of Savoie and Philippe Lebreton, University of Lyon 1.

References

Lebreton, P., Tournier H. and Lebreton J. D. (1976) Etude de l'avifaune du Parc National de la Vanoise VI Recherches d'ordre quantitatif sur les Oiseaux forestiers de Vanoise. Travaux Scientifiques du parc National de la vanoise, 7, 163–243.

Lebreton, Ph. and Martinot, J.P. (1998) Oiseaux de Vanoise. Guide de l'ornithologue en montagne. Libris, Grenoble. 1–240.

Lebreton, Ph., Lebrun, Ph., Martinot, J.P., Miquet, A. and Tournier, H. (1999) Approche écologique de l'avifaune de la Vanoise. Travaux scientifiques du Parc national de la Vanoise, 21, 7–304.

See a data description at http://pbil.univ-lyon1.fr/R/pdf/pps038.pdf (in French).

Examples

data(tarentaise)
coa1 <- dudi.coa(tarentaise$ecol, sca = FALSE, nf = 2)
s.class(coa1$li, tarentaise$envir$alti, wt = coa1$lw)
## Not run: 
acm1 <- dudi.acm(tarentaise$envir, sca = FALSE, nf = 2)
s.class(acm1$li, tarentaise$envir$alti)

## End(Not run)

Examples of taxonomy

Description

This data sets contains two taxonomies.

Usage

data(taxo.eg)

Format

taxo.eg is a list containing the 2 following objects:

taxo.eg[[1]]

is a data frame with 15 species and 3 columns.

taxo.eg[[2]]

is a data frame with 40 species and 2 columns.

Details

Variables of the first data frame are : genre (a factor genre with 8 levels), famille (a factor familiy with 5 levels) and ordre (a factor order with 2 levels).

Variables of the second data frame are : gen(a factor genre with 29 levels), fam (a factor family with 19 levels).

Examples

data(taxo.eg)
taxo.eg[[1]]
as.taxo(taxo.eg[[1]])
class(taxo.eg[[1]])
class(as.taxo(taxo.eg[[1]]))

tax.phy <- taxo2phylog(as.taxo(taxo.eg[[1]]),  add.tools = TRUE)
plot(tax.phy,clabel.l=1)

par(mfrow = c(1,2))
table.phylog(tax.phy$Bindica,tax.phy)
table.phylog(tax.phy$Bscores,tax.phy)
par(mfrow = c(1,1))

radial.phylog(taxo2phylog(as.taxo(taxo.eg[[2]])))

Function to perform a test of dimensionality

Description

This functions allow to test for the number of axes in multivariate analysis. The procedure testdim.pca implements a method for principal component analysis on correlation matrix. The procedure is based on the computation of the RV coefficient.

Usage

testdim(object, ...)
## S3 method for class 'pca'
testdim(object, nrepet = 99, nbax = object$rank, alpha = 0.05, ...)

Arguments

object

an object corresponding to an analysis (e.g. duality diagram, an object of class dudi)
nrepet

the number of repetitions for the permutation procedure
nbax

the number of axes to be tested, by default all axes
alpha

the significance level
...

other arguments

Value

An object of the class krandtest. It contains also:

nb

The estimated number of axes to keep
nb.cor

The number of axes to keep estimated using a sequential Bonferroni procedure

Author(s)

Stéphane Dray [email protected]

References

Dray, S. (2008) On the number of principal components: A test of dimensionality based on measurements of similarity between matrices. Computational Statistics and Data Analysis, Volume 52, 2228–2237. doi:10.1016/j.csda.2007.07.015

See Also

dudi.pca, RV.rtest,testdim.multiblock

Examples

tab <- data.frame(matrix(rnorm(200),20,10))
pca1 <- dudi.pca(tab,scannf=FALSE)
test1 <- testdim(pca1)
test1
test1$nb
test1$nb.cor
data(doubs)
pca2 <- dudi.pca(doubs$env,scannf=FALSE)
test2 <- testdim(pca2)
test2
test2$nb
test2$nb.cor

Selection of the number of dimension by two-fold cross-validation for multiblock methods

Description

Function to perform a two-fold cross-validation to select the optimal number of dimensions of multiblock methods, i.e., multiblock principal component analysis with instrumental Variables or multiblock partial least squares

Usage

## S3 method for class 'multiblock'
testdim(object, nrepet = 100, quantiles = c(0.25, 0.75), ...)

Arguments

object

an object of class multiblock created by mbpls or mbpcaiv
nrepet

integer indicating the number of repetitions
quantiles

a vector indicating the lower and upper quantiles to compute
...

other arguments to be passed to methods

Value

An object of class krandxval

Author(s)

Stéphanie Bougeard ([email protected]) and Stéphane Dray ([email protected])

References

Stone M. (1974) Cross-validatory choice and assessment of statistical predictions. Journal of the Royal Statistical Society, 36, 111-147.

Bougeard, S. and Dray S. (2018) Supervised Multiblock Analysis in R with the ade4 Package. Journal of Statistical Software, 86 (1), 1-17. doi:10.18637/jss.v086.i01

See Also

mbpcaiv, mbpls, randboot.multiblock, as.krandxval

Examples

data(chickenk)
Mortality <- chickenk[[1]]
dudiY.chick <- dudi.pca(Mortality, center = TRUE, scale = TRUE, scannf =
FALSE)
ktabX.chick <- ktab.list.df(chickenk[2:5])
resmbpcaiv.chick <- mbpcaiv(dudiY.chick, ktabX.chick, scale = TRUE,
option = "uniform", scannf = FALSE)
## nrepet should be higher for a real analysis
test <- testdim(resmbpcaiv.chick, nrepet = 10)
test
if(adegraphicsLoaded())
plot(test)

Tinto and Odiel estuary geochemistry

Description

This data set contains informations about geochemical characteristics of heavy metal pollution in surface sediments of the Tinto and Odiel river estuary (south-western Spain).

Usage

data(tintoodiel)

Format

tintoodiel is a list with the following components:

xy

a data frame that contains spatial coordinates of the 52 sites

tab

a data frame with 12 columns (concentration of heavy metals) and 52 rows (sites)

neig

an object of class neig

nb

the neighbourhood graph of the 52 sites (an object of class nb)

Source

Borrego, J., Morales, J.A., de la Torre, M.L. and Grande, J.A. (2002) Geochemical characteristics of heavy metal pollution in surface sediments of the Tinto and Odiel river estuary (south-western Spain). Environmental Geology, 41, 785–796.

Examples

data(tintoodiel)
if(!adegraphicsLoaded()) {
  ## Not run: 
  if(requireNamespace("pixmap", quietly = TRUE)) {
    estuary.pnm <- pixmap::read.pnm(system.file("pictures/tintoodiel.pnm", package = "ade4"))
    s.label(tintoodiel$xy, pixmap = estuary.pnm, neig = tintoodiel$neig,
      clab = 0, cpoi = 2, cneig = 3, addax = FALSE, cgrid = 0, grid = FALSE)
  }
## End(Not run)
  
  estuary.pca <- dudi.pca(tintoodiel$tab, scan = FALSE, nf = 4)
  
  if(requireNamespace("spdep", quietly = TRUE)) {
    estuary.listw <- spdep::nb2listw(neig2nb(tintoodiel$neig))
    estuary.pca.ms <- multispati(estuary.pca, estuary.listw, scan = FALSE, nfposi = 3, nfnega = 2)
    summary(estuary.pca.ms)
    par(mfrow = c(1, 2))
    barplot(estuary.pca$eig)
    barplot(estuary.pca.ms$eig)
    par(mfrow = c(1, 1))
}}

Phylogeny and quantitative traits of flowers

Description

This data set describes the phylogeny of 11 flowers as reported by Morales (2000). It also gives morphologic and demographic traits corresponding to these 11 species.

Usage

data(tithonia)

Format

tithonia is a list containing the 2 following objects :

tre

is a character string giving the phylogenetic tree in Newick format.

tab

is a data frame with 11 species and 14 traits (6 morphologic traits and 8 demographic).

Details

Variables of tithonia$tab are the following ones :
morho1: is a numeric vector that describes the seed size (mm)
morho2: is a numeric vector that describes the flower size (mm)
morho3: is a numeric vector that describes the female leaf size (cm)
morho4: is a numeric vector that describes the head size (mm)
morho5: is a integer vector that describes the number of flowers per head
morho6: is a integer vector that describes the number of seeds per head
demo7: is a numeric vector that describes the seedling height (cm)
demo8: is a numeric vector that describes the growth rate (cm/day)
demo9: is a numeric vector that describes the germination time
demo10: is a numeric vector that describes the establishment (per cent)
demo11: is a numeric vector that describes the viability (per cent)
demo12: is a numeric vector that describes the germination (per cent)
demo13: is a integer vector that describes the resource allocation
demo14: is a numeric vector that describes the adult height (m)

Source

Data were obtained from Morales, E. (2000) Estimating phylogenetic inertia in Tithonia (Asteraceae) : a comparative approach. Evolution, 54, 2, 475–484.

Examples

data(tithonia)
phy <- newick2phylog(tithonia$tre)
tab <- log(tithonia$tab + 1)
table.phylog(scalewt(tab), phy)
gearymoran(phy$Wmat, tab)
gearymoran(phy$Amat, tab)

Morphological Study of the Painted Turtle

Description

This data set gives a morphological description (4 characters) of 48 turtles.

Usage

data(tortues)

Format

a data frame with 48 rows and 4 columns (length (mm), maximum width(mm), height (mm), gender).

Source

Jolicoeur, P. and Mosimann, J. E. (1960) Size and shape variation in the painted turtle. A principal component analysis. Growth, 24, 339–354.

Examples

data(tortues)
xyz <- as.matrix(tortues[, 1:3])
ref <- -svd(xyz)$u[, 1]
pch0 <- c(1, 20)[as.numeric(tortues$sexe)]
plot(ref, xyz[, 1], ylim = c(40, 180), pch = pch0)
abline(lm(xyz[, 1] ~ -1 + ref))
points(ref,xyz[, 2], pch = pch0)
abline(lm(xyz[, 2] ~ -1 + ref))
points(ref,xyz[, 3], pch = pch0)
abline(lm(xyz[, 3] ~ -1 + ref))

Homogeneous Table

Description

This data set gives the toxicity of 7 molecules on 17 targets expressed in -log(mol/liter)

Usage

data(toxicity)

Format

toxicity is a list of 3 components.

tab

is a data frame with 7 columns and 17 rows

species

is a vector of the names of the species in the 17 targets

chemicals

is a vector of the names of the 7 molecules

Source

Devillers, J., Thioulouse, J. and Karcher W. (1993) Chemometrical Evaluation of Multispecies-Multichemical Data by Means of Graphical Techniques Combined with Multivariate Analyses. Ecotoxicology and Environnemental Safety, 26, 333–345.

Examples

data(toxicity)
if(adegraphicsLoaded()) {
  table.image(toxicity$tab, labelsy = toxicity$species, labelsx = toxicity$chemicals, nclass = 7, 
    ptable.margin = list(b = 5, l = 25, t = 25, r = 5), ptable.y.pos = "left", pgrid.draw = TRUE)
  table.value(toxicity$tab, labelsy = toxicity$species, labelsx = toxicity$chemicals, 
    ptable.margin = list(b = 5, l = 5, t = 25, r = 26))
} else {
  table.paint(toxicity$tab, row.lab = toxicity$species, col.lab = toxicity$chemicals)
  table.value(toxicity$tab, row.lab = toxicity$species, col.lab = toxicity$chemicals)
}

Triangular Representation and Groups of points

Description

Function to plot triangular data (i.e. dataframe with 3 columns of positive or null values) and a partition

Usage

triangle.class(ta, fac, col = rep(1, length(levels(fac))), 
    wt = rep(1, length(fac)), cstar = 1, cellipse = 0, axesell = TRUE, 
    label = levels(fac), clabel = 1, cpoint = 1, pch = 20, draw.line = TRUE, 
    addaxes = FALSE, addmean = FALSE, labeltriangle = TRUE, sub = "", csub = 1, 
    possub = "bottomright", show.position = TRUE, scale = TRUE, min3 = NULL, 
    max3 = NULL)

Arguments

ta

a data frame with 3 columns of null or positive numbers

fac

a factor of length the row number of ta

col

a vector of color for showing the groups

wt

a vector of row weighting for the computation of the gravity centers by class

cstar

a character size for plotting the stars between 0 (no stars) and 1 (complete star) for a line linking a point to the gravity center of its belonging class.

cellipse

a positive coefficient for the inertia ellipse size

axesell

a logical value indicating whether the ellipse axes should be drawn

label

a vector of strings of characters for the labels of gravity centers

clabel

if not NULL, a character size for the labels, used with par("cex")*clabel

cpoint

a character size for plotting the points, used with par("cex")*cpoint. If zero, no points are drawn

pch

if cpoint > 0, an integer specifying the symbol or the single character to be used in plotting points

draw.line

a logical value indicating whether the triangular lines should be drawn

addaxes

a logical value indicating whether the axes should be plotted

addmean

a logical value indicating whether the mean point should be plotted

labeltriangle

a logical value indicating whether the varliable labels of ta should be drawn on the triangular sides

sub

a string of characters for the graph title

csub

a character size for plotting the graph title

possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")

show.position

a logical value indicating whether the sub-triangle containing the data should be put back in the total triangle

scale

a logical value for the graph representation : the total triangle (FALSE) or the sub-triangle (TRUE)

min3

if not NULL, a vector with 3 numbers between 0 and 1

max3

if not NULL, a vector with 3 numbers between 0 and 1. Let notice that min3+max3 must equal c(1,1,1)

Author(s)

Daniel Chessel

Examples

if(!adegraphicsLoaded()) {
  data(euro123)
  par(mfrow = c(2, 2))
  x <- rbind.data.frame(euro123$in78, euro123$in86, euro123$in97)
  triangle.plot(x)
  triangle.class(x, as.factor(rep("G", 36)), csta = 0.5, cell = 1)
  triangle.class(x, euro123$plan$an)
  triangle.class(x, euro123$plan$pays)
  triangle.class(x, euro123$plan$an, cell = 1, axesell = TRUE)
  triangle.class(x, euro123$plan$an, cell = 0, csta = 0, 
    col = c("red", "green", "blue"), axesell = TRUE, clab = 2, cpoi = 2)
  triangle.class(x, euro123$plan$an, cell = 2, csta = 0.5, 
    axesell = TRUE, clab = 1.5)
  triangle.class(x, euro123$plan$an, cell = 0, csta = 1, scale = FALSE, 
    draw.line = FALSE, show.posi = FALSE)
  par(mfrow = c(2, 2))
}

Triangular Plotting

Description

Graphs for a dataframe with 3 columns of positive or null values
triangle.plot is a scatterplot
triangle.biplot is a paired scatterplots
triangle.posipoint, triangle.param, add.position.triangle are utilitaries functions.

Usage

triangle.plot(ta, label = as.character(1:nrow(ta)), clabel = 0, 
    cpoint = 1, draw.line = TRUE, addaxes = FALSE, addmean = FALSE, 
    labeltriangle = TRUE, sub = "", csub = 0, possub = "topright", 
    show.position = TRUE, scale = TRUE, min3 = NULL, max3 = NULL, 
    box = FALSE)
triangle.biplot (ta1, ta2, label = as.character(1:nrow(ta1)), 
    draw.line = TRUE, show.position = TRUE, scale = TRUE)

Arguments

ta, ta1, ta2

data frame with three columns, will be transformed in percentages by rows
label

a vector of strings of characters for the point labels
clabel

if not NULL, a character size for the labels, used with par("cex")*clabel
cpoint

a character size for plotting the points, used with par("cex")*cpoint. If zero, no points are drawn
draw.line

a logical value indicating whether the lines into the triangle should be drawn
addaxes

a logical value indicating whether the principal axes should be drawn
addmean

a logical value indicating whether the mean should be plotted
labeltriangle

a logical value indicating whether the variable names should be wrote
sub

a string of characters to be inserted as legend
csub

a character size for the legend, used with par("cex")*csub
possub

a string of characters indicating the sub-title position ("topleft", "topright", "bottomleft", "bottomright")
show.position

a logical value indicating whether the used triangle should be shown in the complete one
scale

a logical value indicating whether the smaller equilateral triangle containing the plot should be used
min3

If scale is FALSE, a vector of three values for the minima e.g. c(0.1,0.1,0.1) can be used
max3

If scale is FALSE a vector of three values for the maxima e.g. c(0.9,0.9,0.9) can be used
box

a logical value indicating whether a box around the current plot should be drawn

Value

triangle.plot returns an invisible matrix containing the coordinates used for the plot. The graph can be supplemented in various ways.

Author(s)

Daniel Chessel

Examples

data(euro123)
tot <- rbind.data.frame(euro123$in78, euro123$in86, euro123$in97)
row.names(tot) <- paste(row.names(euro123$in78), rep(c(1, 2, 3), rep(12, 3)), sep = "")
triangle.plot(tot, label = row.names(tot), clab = 1)

par(mfrow = c(2, 2))
triangle.plot(euro123$in78, clab = 0, cpoi = 2, addmean = TRUE, show = FALSE)
triangle.plot(euro123$in86, label = row.names(euro123$in78), clab = 0.8)
triangle.biplot(euro123$in78, euro123$in86)
triangle.plot(rbind.data.frame(euro123$in78, euro123$in86), clab = 1, 
  addaxes = TRUE, sub = "Principal axis", csub = 2, possub = "topright")

triangle.plot(euro123[[1]], min3 = c(0, 0.2, 0.3), max3 = c(0.5, 0.7, 0.8),
  clab = 1, label = row.names(euro123[[1]]), addax = TRUE)
triangle.plot(euro123[[2]], min3 = c(0, 0.2, 0.3), max3 = c(0.5, 0.7, 0.8), 
  clab = 1, label = row.names(euro123[[1]]), addax = TRUE)
triangle.plot(euro123[[3]], min3 = c(0, 0.2, 0.3), max3 = c(0.5, 0.7, 0.8), 
  clab = 1, label = row.names(euro123[[1]]), addax = TRUE)
triangle.plot(rbind.data.frame(euro123[[1]], euro123[[2]], euro123[[3]]))

par(mfrow = c(1, 1))
wtriangleplot <- cbind.data.frame(a = runif(100), b = runif(100), c = runif(100, 4, 5))
wtriangleplot <- triangle.plot(wtriangleplot)
points(wtriangleplot, col = "blue", cex = 2)
wtriangleplot <- colMeans(wtriangleplot)
points(wtriangleplot[1], wtriangleplot[2], pch = 20, cex = 3, col = "red")
rm(wtriangleplot)

Pair of Ecological Data

Description

This data set gives for trappong nights informations about species and meteorological variables.

Usage

data(trichometeo)

Format

trichometeo is a list of 3 components.

fau

is a data frame with 49 rows (trapping nights) and 17 species.

meteo

is a data frame with 49 rows and 11 meteorological variables.

cla

is a factor of 12 levels for the definition of the consecutive night groups

Source

Data from P. Usseglio-Polatera

References

Usseglio-Polatera, P. and Auda, Y. (1987) Influence des facteurs météorologiques sur les résultats de piégeage lumineux. Annales de Limnologie, 23, 65–79. (code des espèces p. 76)

See a data description at http://pbil.univ-lyon1.fr/R/pdf/pps034.pdf (in French).

Examples

data(trichometeo)
faulog <- log(trichometeo$fau + 1)
pca1 <- dudi.pca(trichometeo$meteo, scan = FALSE)
niche1 <- niche(pca1, faulog, scan = FALSE)

if(adegraphicsLoaded()) {
  g1 <- s.distri(niche1$ls, faulog, plab.cex = 0.6, ellipseSize = 0, starSize = 0.3, plot = FALSE)
  g2 <- s.arrow(7 * niche1$c1, plab.cex = 1, plot = FALSE)
  G <- superpose(g1, g2, plot = TRUE)
  
} else {
  s.label(niche1$ls, clab = 0)
  s.distri(niche1$ls, faulog, clab = 0.6, add.p = TRUE, cell = 0, csta = 0.3)
  s.arrow(7 * niche1$c1, clab = 1, add.p = TRUE)
}

Phylogeny and quantitative traits of ungulates.

Description

This data set describes the phylogeny of 18 ungulates as reported by Pélabon et al. (1995). It also gives 4 traits corresponding to these 18 species.

Usage

data(ungulates)

Format

fission is a list containing the 2 following objects :

tre

is a character string giving the phylogenetic tree in Newick format.

tab

is a data frame with 18 species and 4 traits

Details

Variables of ungulates$tab are the following ones :
afbw: is a numeric vector that describes the adult female body weight (g)
mnw: is a numeric vector that describes the male neonatal weight (g)
fnw: is a numeric vector that describes the female neonatal weight (g)
ls: is a numeric vector that describes the litter size

Source

Data were obtained from Pélabon, C., Gaillard, J.M., Loison, A. and Portier, A. (1995) Is sex-biased maternal care limited by total maternal expenditure in polygynous ungulates? Behavioral Ecology and Sociobiology, 37, 311–319.

Examples

data(ungulates)
ung.phy <- newick2phylog(ungulates$tre)
plot(ung.phy,clabel.l=1.25,clabel.n=0.75)
ung.x <- log(ungulates$tab[,1])
ung.y <- log((ungulates$tab[,2]+ungulates$tab[,3])/2)
names(ung.x) <- names(ung.phy$leaves)
names(ung.y) <- names(ung.x)
plot(ung.x,ung.y)
abline(lm(ung.y~ung.x))
symbols.phylog(ung.phy,ung.x-mean(ung.x))
dotchart.phylog(ung.phy,ung.x,cle=1.5,cno=1.5,cdot=1)
if (requireNamespace("adephylo", quietly = TRUE) & requireNamespace("ape", quietly = TRUE)) {
  tre <- ape::read.tree(text = ungulates$tre)
  adephylo::orthogram(ung.x, tre)
  ung.z <- residuals(lm(ung.y~ung.x))
  names(ung.z) <- names(ung.phy$leaves)
  dotchart.phylog(ung.phy,ung.z,cle=1.5,cno=1.5,cdot=1,ceti=0.75)
  adephylo::orthogram(ung.z, tre)
}

Elimination of Duplicated Rows in a Array

Description

An utility function to eliminate the duplicated rows in a array.

Usage

uniquewt.df(x)

Arguments

x

a data frame which contains duplicated rows

Value

The function returns a y which contains once each duplicated row of x.
y is an attribut 'factor' which gives the number of the row of y in which each row of x is found
y is an attribut 'length.class' which gives the number of duplicates in x with an attribut of each row of y with an attribut

Author(s)

Daniel Chessel

Examples

data(ecomor)
forsub.r <- uniquewt.df(ecomor$forsub)
attr(forsub.r, "factor")
forsub.r[1,]
ecomor$forsub[126,] #idem

dudi.pca(ecomor$forsub, scale = FALSE, scann = FALSE)$eig
# [1] 0.36845 0.24340 0.15855 0.09052 0.07970 0.04490
w1 <- attr(forsub.r, "len.class") / sum(attr(forsub.r,"len.class"))
dudi.pca(forsub.r, row.w = w1, scale = FALSE, scann = FALSE)$eig
# [1] 0.36845 0.24340 0.15855 0.09052 0.07970 0.04490

The phylogenetic ANOVA

Description

This function performs the variance analysis of a trait on eigenvectors associated to a phylogenetic tree.

Usage

variance.phylog(phylog, z, bynames = TRUE,
 na.action = c("fail", "mean"))

Arguments

phylog

: an object of class phylog
z

: a numeric vector of the values corresponding to the variable
bynames

: if TRUE checks if z labels are the same as phylog leaves label, possibly in a different order. If FALSE the check is not made and z labels must be in the same order than phylog leaves label
na.action

: if 'fail' stops the execution of the current expression when z contains any missing value. If 'mean' replaces any missing values by mean(z)

Details

phylog$Amat defines a set of orthonormal vectors associated the each nodes of the phylogenetic tree.
phylog$Adim defines the dimension of the subspace A defined by the first phylog$Adim vectors of phylog$Amat that corresponds to phylogenetic inertia.
variance.phylog performs the linear regression of z on A.

Value

Returns a list containing

lm

: an object of class lm that corresponds to the linear regression of z on A.
anova

: an object of class anova that corresponds to the anova of the precedent model.
smry

: an object of class anova that is a summary of the precedent object.

Author(s)

Sébastien Ollier [email protected]
Daniel Chessel

References

Grafen, A. (1989) The phylogenetic regression. Philosophical Transactions of the Royal Society London B, 326, 119–156.

Diniz-Filho, J. A. F., Sant'Ana, C.E.R. and Bini, L.M. (1998) An eigenvector method for estimating phylogenetic inertia. Evolution, 52, 1247–1262.

See Also

phylog, lm

Examples

data(njplot)
njplot.phy <- newick2phylog(njplot$tre)
variance.phylog(njplot.phy,njplot$tauxcg)
par(mfrow = c(1,2))
table.phylog(njplot.phy$Ascores, njplot.phy, clabel.row = 0,
  clabel.col = 0.1, clabel.nod = 0.6, csize = 1)
dotchart.phylog(njplot.phy, njplot$tauxcg, clabel.nodes = 0.6)
if (requireNamespace("adephylo", quietly = TRUE) & requireNamespace("ape", quietly = TRUE)) {
  tre <- ape::read.tree(text = njplot$tre)
  adephylo::orthogram(njplot$tauxcg, tre = tre)
}

Partition of the variation of a response multivariate table by 2 explanatory tables

Description

The function partitions the variation of a response table (usually community data) with respect to two explanatory tables. The function performs the variation partitioning based on redundancy analysis (RDA, if dudiY is obtained by dudi.pca) or canonical correspondance analysis (CCA, if dudiY is obtained by dudi.coa) and computes unadjusted and adjusted R-squared. The significance of R-squared are evaluated by a randomization procedure where the rows of the explanatory tables are permuted.

Usage

varipart(Y, X, W = NULL, nrepet = 999, type = c("simulated", "parametric"),
scale = FALSE, ...)
## S3 method for class 'varipart'
print(x, ...)

Arguments

Y

a vector, matrix or data frame or an object of class dudi. If not a dudi object, the data are trated by a principal component analysis (dudi.pca).
X, W

dataframes or matrices of explanatory (co)variables (numeric and/or factor variables). By default, no covariables are considered (W is NULL) and this case corresponds to simple caonical ordination.
nrepet

an integer indicating the number of permutations .
type

a character specifying the algorithm which should be used to adjust R-squared (either "simulated" or \ code"parametric").
scale

If Y is not a dudi, a logical indicating if variables should be scaled
...

further arguments passed to as.krandtest or as.randtest (if no covariables are considered) for function varipart.
x

an object of class varipart

Details

Two types of algorithm are provided to adjust R-squared. The "simulated" procedure estimates the unadjusted R-squared expected under the null hypothesis H0 and uses it to adjust the observed R-squared as follows: R2.adj = 1 - (1 - R2) / (1 - E(R2|H0)) with R2.adj the adjusted R-squared and R2 the unadjusted R-squared. The "parametric" procedure performs the Ezequiel's adjustement on the unadjusted R-squared as: R2.adj = 1 - (1 - R2) / (1 - p / (n - 1)) where n is the number of sites, and p the number of predictors.

Value

It returns an object of class varipart. It is a list with:

test

the significance test of fractions [ab], [bc], and [abc] based on randomization procedure. An object of class krandtest

R2

unadjusted estimations of fractions [a], [b], [c], and [d]

R2.adj

adjusted estimations of fractions [a], [b], [c], and [d]

call

the matched call

Author(s)

Stephane Dray [email protected] and Sylvie Clappe [email protected]

References

Borcard, D., P. Legendre, and P. Drapeau. 1992. Partialling out the spatial component of ecological variation. Ecology 73:1045.

Peres-Neto, P. R., P. Legendre, S. Dray, and D. Borcard. 2006. Variation partitioning of species data matrices: estimation and comparison of fractions. Ecology 87:2614-2625.

See Also

pcaiv

Examples

data(mafragh)

# PCA on response table Y
Y <- mafragh$flo
dudiY <- dudi.pca(Y, scannf = FALSE, scale = FALSE)

# Variation partitioning based on RDA
# without covariables
vprda <- varipart(dudiY,  mafragh$env)
vprda
# Variation partitioning based on RDA
# with covariables and parametric estimation
vprda <- varipart(dudiY,  mafragh$env, mafragh$xy, type = "parametric")
vprda
names(vprda)

Vegetation in Trois-Fontaines

Description

This data set contains abundance values (Braun-Blanquet scale) of 80 plant species for 337 sites. Data have been collected by Sonia Said and Francois Debias.

Usage

data(vegtf)

Format

vegtf is a list with the following components:

veg

a data.frame with the abundance values of 80 species (columns) in 337 sites (rows)

xy

a data.frame with the spatial coordinates of the sites

area

a data.frame (area) which define the boundaries of the study site

sp.names

a vector containing the species latin names

nb

a neighborhood object (class nb defined in package spdep)

Spatial

an object of the class SpatialPolygons of sp, containing the map

Source

Dray, S., Said, S. and Debias, F. (2008) Spatial ordination of vegetation data using a generalization of Wartenberg's multivariate spatial correlation. Journal of vegetation science, 19, 45–56.

Examples

if(requireNamespace("spdep", quietly = TRUE)) {
  data(vegtf)
  coa1 <- dudi.coa(vegtf$veg, scannf = FALSE)
  ms.coa1 <- multispati(coa1, listw = spdep::nb2listw(vegtf$nb), nfposi = 2, 
    nfnega = 0, scannf = FALSE)
  summary(ms.coa1)
  plot(ms.coa1)
  
  if(adegraphicsLoaded()) {
    g1 <- s.value(vegtf$xy, coa1$li[, 1], Sp = vegtf$Spatial, pSp.col = "white", plot = FALSE)
    g2 <- s.value(vegtf$xy, ms.coa1$li[, 1], Sp = vegtf$Spatial, pSp.col = "white", plot = FALSE)
    g3 <- s.label(coa1$c1, plot = FALSE)
    g4 <- s.label(ms.coa1$c1, plot = FALSE)
    G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))
  } else {
    par(mfrow = c(2, 2))
    s.value(vegtf$xy, coa1$li[, 1], area = vegtf$area, include.origin = FALSE)
    s.value(vegtf$xy, ms.coa1$li[, 1], area = vegtf$area, include.origin = FALSE)
    s.label(coa1$c1)
    s.label(ms.coa1$c1)
  }
}

Example for Centring in PCA

Description

The data come from the INSEE (National Institute of Statistics and Economical Studies). It is an array of widower percentages in relation with the age and the socioprofessional category.

Usage

data(veuvage)

Format

veuvage is a list of 2 components.

tab

is a data frame with 37 rows (widowers) 6 columns (socio-professional categories)

age

is a vector of the ages of the 37 widowers.

Details

The columns contain the socioprofessional categories:
1- Farmers, 2- Craftsmen, 3- Executives and higher intellectual professions,
4- Intermediate Professions, 5- Others white-collar workers and 6- Manual workers.

Source

unknown

Examples

data(veuvage)
par(mfrow = c(3,2))
for (j in 1:6) plot(veuvage$age, veuvage$tab[,j],
    xlab = "age", ylab = "pourcentage de veufs",
    type = "b", main = names(veuvage$tab)[j])

Within-Class Analysis

Description

Performs a particular case of an Orthogonal Principal Component Analysis with respect to Instrumental Variables (orthopcaiv), in which there is only a single factor as covariable.

Usage

## S3 method for class 'dudi'
wca(x, fac, scannf = TRUE, nf = 2, ...)

Arguments

x

a duality diagram, object of class dudi from one of the functions dudi.coa, dudi.pca,...
fac

a factor partitioning the rows of dudi$tab in classes
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes
...

further arguments passed to or from other methods

Value

Returns a list of the sub-class within in the class dudi

tab

a data frame containing the transformed data (substraction of the class mean)
call

the matching call
nf

number of kept axes
rank

the rank of the analysis
ratio

percentage of within-class inertia
eig

a numeric vector containing the eigenvalues
lw

a numeric vector of row weigths
cw

a numeric vector of column weigths
tabw

a numeric vector of class weigths
fac

the factor defining the classes
li

data frame row coordinates
l1

data frame row normed scores
co

data frame column coordinates
c1

data frame column normed scores
ls

data frame supplementary row coordinates
as

data frame inertia axis onto within axis

Note

To avoid conflict names with the base:::within function, the function within is now deprecated and removed. It is replaced by the method wca.dudi of the new generic wca function.

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

References

Benzécri, J. P. (1983) Analyse de l'inertie intra-classe par l'analyse d'un tableau de correspondances. Les Cahiers de l'Analyse des données, 8, 351–358.

Dolédec, S. and Chessel, D. (1987) Rythmes saisonniers et composantes stationnelles en milieu aquatique I- Description d'un plan d'observations complet par projection de variables. Acta Oecologica, Oecologia Generalis, 8, 3, 403–426.

Examples

data(meaudret)
pca1 <- dudi.pca(meaudret$env, scan = FALSE, nf = 4)
wit1 <- wca(pca1, meaudret$design$site, scan = FALSE, nf = 2)

if(adegraphicsLoaded()) {
  g1 <- s.traject(pca1$li, meaudret$design$site, psub.text = "Principal Component Analysis", 
    plines.lty = 1:nlevels(meaudret$design$site), psub.cex = 1.5, plot = FALSE)
  g2 <- s.traject(wit1$li, meaudret$design$site, 
    psub.text = "Within site Principal Component Analysis", 
    plines.lty = 1:nlevels(meaudret$design$site), psub.cex = 1.5, plot = FALSE)
  g3 <- s.corcircle (wit1$as, plot = FALSE)
  G <- ADEgS(list(g1, g2, g3), layout = c(2, 2))
  
} else {
  par(mfrow = c(2, 2))
  s.traject(pca1$li, meaudret$design$site, sub = "Principal Component Analysis", csub = 1.5)
  s.traject(wit1$li, meaudret$design$site, sub = "Within site Principal Component Analysis", 
    csub = 1.5)
  s.corcircle (wit1$as)
  par(mfrow = c(1,1))
}
plot(wit1)

Within-class coinertia analysis

Description

Performs a within-class analysis after a coinertia analysis

Usage

## S3 method for class 'coinertia'
wca(x, fac, scannf = TRUE, nf = 2, ...)

Arguments

x

a coinertia analysis (object of class coinertia) obtained by the function coinertia
fac

a factor partitioning the rows in classes
scannf

a logical value indicating whether the eigenvalues barplot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes
...

further arguments passed to or from other methods

Details

This analysis is equivalent to do a within-class analysis on each initial dudi, and a coinertia analysis on the two within analyses. This function returns additional outputs for the interpretation.

Value

An object of the class witcoi. Outputs are described by the print function

Note

To avoid conflict names with the base:::within function, the function within is now deprecated and removed. To be consistent, the withincoinertia function is also deprecated and is replaced by the method wca.coinertia of the generic wca function.

Author(s)

Stéphane Dray [email protected] and Jean Thioulouse [email protected]

References

Franquet E., Doledec S., and Chessel D. (1995) Using multivariate analyses for separating spatial and temporal effects within species-environment relationships. Hydrobiologia, 300, 425–431.

See Also

coinertia, wca

Examples

data(meaudret)
pca1 <- dudi.pca(meaudret$env, scan = FALSE, nf = 4)
pca2 <- dudi.pca(meaudret$spe, scal = FALSE, scan = FALSE, nf = 4)
   
wit1 <- wca(pca1, meaudret$design$site, scan = FALSE, nf = 2)
wit2 <- wca(pca2, meaudret$design$site, scan = FALSE, nf = 2)
coiw <- coinertia(wit1, wit2, scannf = FALSE)

coi <- coinertia(pca1, pca2, scannf = FALSE, nf = 3)
coi.w <- wca(coi, meaudret$design$site, scannf = FALSE)
## coiw and coi.w are equivalent

plot(coi.w)

Within-Class RLQ analysis

Description

Performs a particular RLQ analysis where a partition of sites (rows of R) is taken into account. The within-class RLQ analysis search for linear combinations of traits and environmental variables of maximal covariance.

Usage

## S3 method for class 'rlq'
wca(x, fac, scannf = TRUE, nf = 2, ...)
## S3 method for class 'witrlq'
plot(x, xax = 1, yax = 2, ...)
## S3 method for class 'witrlq'
print(x, ...)

Arguments

x

an object of class rlq (created by the rlq function) for the wca.rlq function. An object of class witrlq for the print and plot functions
fac

a factor partitioning the rows of R
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes
xax

the column number for the x-axis
yax

the column number for the y-axis
...

further arguments passed to or from other methods

Value

The wca.rlq function returns an object of class 'betrlq' (sub-class of 'dudi'). See the outputs of the print function for more details.

Author(s)

Stéphane Dray [email protected]

References

Wesuls, D., Oldeland, J. and Dray, S. (2012) Disentangling plant trait responses to livestock grazing from spatio-temporal variation: the partial RLQ approach. Journal of Vegetation Science, 23, 98–113.

See Also

rlq, wca, wca.rlq

Examples

data(piosphere)
afcL <- dudi.coa(log(piosphere$veg + 1), scannf = FALSE)
acpR <- dudi.pca(piosphere$env, scannf = FALSE, row.w = afcL$lw)
acpQ <- dudi.hillsmith(piosphere$traits, scannf = FALSE, row.w = afcL$cw)
rlq1 <- rlq(acpR, afcL, acpQ, scannf = FALSE)

wrlq1 <- wca(rlq1, fac = piosphere$habitat, scannf = FALSE)
wrlq1
plot(wrlq1)

Freshwater fish zoogeography in west Africa

Description

This data set contains informations about faunal similarities between river basins in West africa.

Usage

data(westafrica)

Format

westafrica is a list containing the following objects :

tab

: a data frame with absence/presence of 268 species (rows) at 33 embouchures (columns)

spe.names

: a vector of string of characters with the name of species

spe.binames

: a data frame with the genus and species (columns) of the 256 species (rows)

riv.names

: a vector of string of characters with the name of rivers

atlantic

: a data frame with the coordinates of a polygon that represents the limits of atlantic (see example)

riv.xy

: a data frame with the coordinates of embouchures

lines

: a data frame with the coordinates of lines to complete the representation (see example)

cadre

: a data frame with the coordinates of points used to make the representation (see example)

Source

Data provided by B. Hugueny [email protected].

Paugy, D., Traoré, K. and Diouf, P.F. (1994) Faune ichtyologique des eaux douces d'Afrique de l'Ouest. In Diversité biologique des poissons des eaux douces et saumâtres d'Afrique. Synthèses géographiques, Teugels, G.G., Guégan, J.F. and Albaret, J.J. (Editors). Annales du Musée Royal de l'Afrique Centrale, Zoologie, 275, Tervuren, Belgique, 35–66.

Hugueny, B. (1989) Biogéographie et structure des peuplements de Poissons d'eau douce de l'Afrique de l'ouest : approches quantitatives. Thèse de doctorat, Université Paris 7.

References

Hugueny, B., and Lévêque, C. (1994) Freshwater fish zoogeography in west Africa: faunal similarities between river basins. Environmental Biology of Fishes, 39, 365–380.

Examples

data(westafrica)

if(!adegraphicsLoaded()) {
  s.label(westafrica$cadre, xlim = c(30, 500), ylim = c(50, 290),
    cpoi = 0, clab = 0, grid = FALSE, addax = 0)
  old.par <- par(no.readonly = TRUE)
  par(mar = c(0.1, 0.1, 0.1, 0.1))
  rect(30, 0, 500, 290)
  polygon(westafrica$atlantic, col = "lightblue")
  points(westafrica$riv.xy, pch = 20, cex = 1.5)
  apply(westafrica$lines, 1, function(x) segments(x[1], x[2], x[3], x[4], lwd = 1))
  apply(westafrica$riv.xy,1, function(x) segments(x[1], x[2], x[3], x[4], lwd = 1))
  text(c(175, 260, 460, 420), c(275, 200, 250, 100), c("Senegal", "Niger", "Niger", "Volta"))
  par(srt = 270)
  text(westafrica$riv.xy$x2, westafrica$riv.xy$y2-10, westafrica$riv.names, adj = 0, cex = 0.75)
  par(old.par)
  rm(old.par)
}

# multivariate analysis
afri.w <- data.frame(t(westafrica$tab))
afri.dist <- dist.binary(afri.w,1)
afri.pco <- dudi.pco(afri.dist, scannf = FALSE, nf = 3)
if(adegraphicsLoaded()) {
  G1 <- s1d.barchart(afri.pco$li[, 1:3], p1d.horizontal = FALSE, plabels.cex = 0)
} else {
  par(mfrow = c(3, 1))
  barplot(afri.pco$li[, 1])
  barplot(afri.pco$li[, 2])
  barplot(afri.pco$li[, 3])
}

if(requireNamespace("spdep", quietly = TRUE)) {
  # multivariate spatial analysis
  afri.neig <- neig(n.line = 33)
  afri.nb <- neig2nb(afri.neig)
  afri.listw <- spdep::nb2listw(afri.nb)
  afri.ms <- multispati(afri.pco, afri.listw, scannf = FALSE, nfposi = 6, nfnega = 0)
  
  if(adegraphicsLoaded()) {
    G2 <- s1d.barchart(afri.ms$li[, 1:3], p1d.horizontal = FALSE, plabels.cex = 0)
    
    g31 <- s.label(afri.ms$li, plabels.cex = 0.75, ppoints.cex = 0, nb = afri.nb, plot = FALSE)
    g32 <- s.value(afri.ms$li, afri.ms$li[, 3], plot = FALSE)
    g33 <- s.value(afri.ms$li, afri.ms$li[, 4], plot = FALSE)
    g34 <- s.value(afri.ms$li, afri.ms$li[, 5], plot = FALSE)
    G3 <- ADEgS(list(g31, g32, g33, g34), layout = c(2, 2))
    
  } else {
    par(mfrow = c(3, 1))
    barplot(afri.ms$li[, 1])
    barplot(afri.ms$li[, 2])
    barplot(afri.ms$li[, 3])
    
    par(mfrow = c(2, 2))
    s.label(afri.ms$li, clab = 0.75, cpoi = 0, neig = afri.neig, cneig = 1.5)
    s.value(afri.ms$li, afri.ms$li[, 3])
    s.value(afri.ms$li, afri.ms$li[, 4])
    s.value(afri.ms$li, afri.ms$li[, 5])
  }
  summary(afri.ms)
}

par(mfrow = c(1, 1))
plot(hclust(afri.dist, "ward.D"), h = -0.2)

Within-Class Analysis

Description

Outputs and graphical representations of the results of a within-class analysis.

Usage

## S3 method for class 'within'
plot(x, xax = 1, yax = 2, ...) 
## S3 method for class 'within'
print(x, ...)
## S3 method for class 'witcoi'
plot(x, xax = 1, yax = 2, ...)
## S3 method for class 'witcoi'
print(x, ...)
## S3 method for class 'within'
summary(object, ...)

Arguments

x, object

an object of class within or witcoi
xax

the column index for the x-axis
yax

the column index for the y-axis
...

further arguments passed to or from other methods

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]
Stéphane Dray [email protected]

References

Benzécri, J. P. (1983) Analyse de l'inertie intra-classe par l'analyse d'un tableau de correspondances. Les Cahiers de l'Analyse des données, 8, 351–358.

Dolédec, S. and Chessel, D. (1987) Rythmes saisonniers et composantes stationnelles en milieu aquatique I- Description d'un plan d'observations complet par projection de variables. Acta Oecologica, Oecologia Generalis, 8, 3, 403–426.

See Also

wca.dudi, wca.coinertia

Examples

data(meaudret)
pca1 <- dudi.pca(meaudret$env, scan = FALSE, nf = 4)
wit1 <- wca(pca1, meaudret$design$site, scan = FALSE, nf = 2)

if(adegraphicsLoaded()) {
  g1 <- s.traject(pca1$li, meaudret$design$site, psub.text = "Principal Component Analysis", 
    plines.lty = 1:length(levels(meaudret$design$site)), plot = FALSE)
  g2 <- s.traject(wit1$li, meaudret$design$site, psub.text = 
    "Within site Principal Component Analysis", 
    plines.lty = 1:length(levels(meaudret$design$site)), plot = FALSE)
  g3 <- s.corcircle (wit1$as, plot = FALSE)
  G <- ADEgS(list(g1, g2, g3), layout = c(2, 2))
  
} else {
  par(mfrow = c(2, 2))
  s.traject(pca1$li, meaudret$design$site, sub = "Principal Component Analysis", csub = 1.5)
  s.traject(wit1$li, meaudret$design$site, sub = "Within site Principal Component Analysis", 
    csub = 1.5)
  s.corcircle (wit1$as)
  par(mfrow = c(1, 1))
}

plot(wit1)

Normed within principal component analysis

Description

Performs a normed within Principal Component Analysis.

Usage

withinpca(df, fac, scaling = c("partial", "total"), 
    scannf = TRUE, nf = 2)

Arguments

df

a data frame with quantitative variables
fac

a factor partitioning the rows of df in classes
scaling

a string of characters as a scaling option :
if "partial", the sub-table corresponding to each class is centred and normed.
If "total", the sub-table corresponding to each class is centred and the total table is then normed.
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes

Details

This functions implements the 'Bouroche' standardization. In a first step, the original variables are standardized (centred and normed). Then, a second transformation is applied according to the value of the scaling argument. For "partial", variables are standardized in each sub-table (corresponding to each level of the factor). Hence, variables have null mean and unit variance in each sub-table. For "total", variables are centred in each sub-table and then normed globally. Hence, variables have a null mean in each sub-table and a global variance equal to one.

Value

returns a list of the sub-class within of class dudi. See wca

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [email protected]

References

Bouroche, J. M. (1975) Analyse des données ternaires: la double analyse en composantes principales. Thèse de 3ème cycle, Université de Paris VI.

Examples

data(meaudret)
wit1 <- withinpca(meaudret$env, meaudret$design$season, scannf = FALSE, scaling = "partial")
kta1 <- ktab.within(wit1, colnames = rep(c("S1", "S2", "S3", "S4", "S5"), 4))
unclass(kta1)

# See pta
plot(wit1)

Internal Correspondence Analysis

Description

witwit.coa performs an Internal Correspondence Analysis. witwitsepan gives the computation and the barplot of the eigenvalues for each separated analysis in an Internal Correspondence Analysis.

Usage

witwit.coa(dudi, row.blocks, col.blocks, scannf = TRUE, nf = 2)
## S3 method for class 'witwit'
summary(object, ...)
witwitsepan(ww, mfrow = NULL, csub = 2, plot = TRUE)

Arguments

dudi

an object of class coa

row.blocks

a numeric vector indicating the row numbers for each block of rows
col.blocks

a numeric vector indicating the column numbers for each block of columns
scannf

a logical value indicating whether the eigenvalues bar plot should be displayed
nf

if scannf FALSE, an integer indicating the number of kept axes


object

an object of class witwit
...

further arguments passed to or from other methods


ww

an object of class witwit
mfrow

a vector of the form "c(nr,nc)", otherwise computed by a special own function 'n2mfrow'
csub

a character size for the sub-titles, used with par("cex")*csub
plot

if FALSE, numeric results are returned

Value

returns a list of class witwit, coa and dudi (see as.dudi) containing

rbvar

a data frame with the within variances of the rows of the factorial coordinates
lbw

a data frame with the marginal weighting of the row classes
cvar

a data frame with the within variances of the columns of the factorial coordinates
cbw

a data frame with the marginal weighting of the column classes

Author(s)

Daniel Chessel Anne-Béatrice Dufour [email protected] Correction by Campo Elías PARDO [email protected]

References

Cazes, P., Chessel, D. and Dolédec, S. (1988) L'analyse des correspondances internes d'un tableau partitionné : son usage en hydrobiologie. Revue de Statistique Appliquée, 36, 39–54.

Examples

data(ardeche)
coa1 <- dudi.coa(ardeche$tab, scann = FALSE, nf = 4)
ww <- witwit.coa(coa1, ardeche$row.blocks, ardeche$col.blocks, scann = FALSE)
ww
summary(ww)

if(adegraphicsLoaded()) {
  g1 <- s.class(ww$co, ardeche$sta.fac, plab.cex = 1.5, ellipseSi = 0, paxes.draw = FALSE, 
    plot = FALSE)
  g2 <- s.label(ww$co, plab.cex = 0.75, plot = FALSE)
  G <- superpose(g1, g2, plot = TRUE)
  
} else {
  s.class(ww$co, ardeche$sta.fac, clab = 1.5, cell = 0, axesell = FALSE)
  s.label(ww$co, add.p = TRUE, clab = 0.75)
}

witwitsepan(ww, c(4, 6))

Plant assemblages in woodlands of the conurbation of Angers (France)

Description

This data set gives the presence of plant species in relevés of woodlands in the conurbation of Angers; and their biological traits.

Usage

data(woangers)

Format

woangers is a list of 2 components.

  1. flo: is a data frame that contains the presence/absence of species in each sample site. In the codes for the sample sites (first column of the data frame), the first three letters provide the code of the woodland and the numbers represent the 5 quadrats sampled in each site. Codes for the woodlands are based on either their local name when they have one or on the name of the nearest locality.

  2. traits: is a data frame that contains the values of the 13 functional traits considered in the paper. One trait can be encoded by several columns. The codes are as follows:

    • Column 1: Species names;

    • Column 2: li, nominal variable that indicates the presence (y) or absence (n) of ligneous structures;

    • Column 3: pr, nominal variable that indicates the presence (y) or absence (n) of prickly structures;

    • Column 4: fo, circular variable that indicates the month when the flowering period starts (from 1 January to 9 September);

    • Column 5: he, ordinal variable that indicates the maximum height of the leaf canopy;

    • Column 6: ae, ordinal variable that indicates the degree of aerial vegetative multiplication;

    • Column 7: un, ordinal variable that indicates the degree of underground vegetative multiplication;

    • Column 8: lp, nominal variable that represents the leaf position by 3 levels (ros = rosette, semiros = semi-rosette and leafy = leafy stem);

    • Column 9: le, nominal variable that represents the mode of leaf persistence by 5 levels (seasaes = seasonal aestival, seashib = seasonal hibernal, seasver = seasonal vernal, everalw = always evergreen, everparti = partially evergreen);

    • Columns 10, 11 and 12: fuzzy variable that describes the modes of pollination with 3 levels (auto = autopollination, insects = pollination by insects, wind = pollination by wind); this fuzzy variable is expressed as proportions, i.e. for each row, the sum of the three columns equals 1;

    • Columns 13, 14 and 15: fuzzy variable that describes the life cycle with 3 levels (annual, monocarpic and polycarpic); this fuzzy variable is expressed as proportions, i.e. for each row, the sum of the three column equals 1;

    • Columns 16 to 20: fuzzy variable that describes the modes of dispersion with 5 levels (elaio = dispersion by ants, endozoo = injection by animals, epizoo = external transport by animals, wind = transport by wind, unsp = unspecialized transport); this fuzzy variable is expressed as proportions, i.e. for each row, the sum of the three columns equals 1;

    • Column 21: lo, quantitative variable that provides the seed bank longevity index;

    • Column 22: lf, quantitative variable that provides the length of the flowering period.

Source

Pavoine, S., Vallet, J., Dufour, A.-B., Gachet, S. and Daniel, H. (2009) On the challenge of treating various types of variables: Application for improving the measurement of functional diversity. Oikos, 118, 391–402.

Examples

# Loading the data
data(woangers)

# Preparating of the traits
traits <- woangers$traits
# Nominal variables 'li', 'pr', 'lp' and 'le'
# (see table 1 in the main text for the codes of the variables)
tabN <- traits[, c(1:2, 7, 8)]
# Circular variable 'fo'
tabC <- traits[3]
tabCp <- prep.circular(tabC, 1, 12)
# The levels of the variable lie between 1 (January) and 12 (December).
# Ordinal variables 'he', 'ae' and 'un'
tabO <- traits[, 4:6]
# Fuzzy variables 'mp', 'pe' and 'di'
tabF <- traits[, 9:19]
tabFp <- prep.fuzzy(tabF, c(3, 3, 5), labels = c("mp", "pe", "di"))
# 'mp' has 3 levels, 'pe' has 3 levels and 'di' has 5 levels.
# Quantitative variables 'lo' and 'lf'
tabQ <- traits[, 20:21]

# Combining the traits
ktab1 <- ktab.list.df(list(tabN, tabCp, tabO, tabFp, tabQ))
## Not run: 
# Calculating the distances for all traits combined
distrait <- dist.ktab(ktab1, c("N", "C", "O", "F", "Q"))
is.euclid(distrait)

# Calculating the contribution of each trait in the combined distances
contrib <- kdist.cor(ktab1, type = c("N", "C", "O", "F", "Q"))
contrib
dotchart(sort(contrib$glocor), labels = rownames(contrib$glocor)[order(contrib$glocor[, 1])])

## End(Not run)

French Worker Survey (1970)

Description

The worksurv data frame gives 319 response items and 4 questions providing from a French Worker Survey.

Usage

data(worksurv)

Format

This data frame contains the following columns:

  1. pro: Professional elections. In professional elections in your firm, would you rather vote for a list supported by?

    • CGT

    • CFDT

    • FO

    • CFTC

    • Auton Autonomous

    • Abst

    • Nonaffi Not affiliated

    • NR No response

  2. una: Union affiliation. At the present time, are you affiliated to a Union, and in the affirmative, which one?

    • CGT

    • CFDT

    • FO

    • CFTC

    • Auton Autonomous

    • CGC

    • Notaffi Not affiliated

    • NR No response

  3. pre: Presidential election. On the last presidential election (1969), can you tell me the candidate for whom you havevoted?

    • Duclos

    • Deferre

    • Krivine

    • Rocard

    • Poher

    • Ducatel

    • Pompidou

    • NRAbs No response, abstention

  4. pol: political sympathy. Which political party do you feel closest to, as a rule?

    • Communist (PCF)

    • Socialist (SFIO+PSU+FGDS)

    • Left (Party of workers,...)

    • Center MRP+RAD.

    • RI

    • Right INDEP.+CNI

    • Gaullist UNR

    • NR No response

Details

The data frame worksurv has the attribute 'counts' giving the number of responses for each item.

Source

Rouanet, H. and Le Roux, B. (1993) Analyse des données multidimensionnelles. Dunod, Paris.

References

Le Roux, B. and Rouanet, H. (1997) Interpreting axes in multiple correspondence analysis: method of the contributions of points and deviation. Pages 197-220 in B. J. and M. Greenacre, editors. Visualization of categorical data, Acamedic Press, London.

Examples

data(worksurv)
acm1 <- dudi.acm(worksurv, row.w = attr(worksurv, "counts"), scan = FALSE)

if(adegraphicsLoaded()) {
  s.class(acm1$li, worksurv)
} else {
  par(mfrow = c(2, 2))
  apply(worksurv, 2, function(x) s.class(acm1$li, factor(x), attr(worksurv, 'counts')))
  par(mfrow = c(1, 1))
}

Distance Matrices

Description

This data set gives 3 matrices about geographical, genetic and anthropometric distances.

Usage

data(yanomama)

Format

yanomama is a list of 3 components:

geo

is a matrix of 19-19 geographical distances

gen

is a matrix of 19-19 SFA (genetic) distances

ant

is a matrix of 19-19 anthropometric distances

Source

Spielman, R.S. (1973) Differences among Yanomama Indian villages: do the patterns of allele frequencies, anthropometrics and map locations correspond? American Journal of Physical Anthropology, 39, 461–480.

References

Table 7.2 Distance matrices for 19 villages of Yanomama Indians. All distances are as given by Spielman (1973), multiplied by 100 for convenience in: Manly, B.F.J. (1991) Randomization and Monte Carlo methods in biology Chapman and Hall, London, 1–281.

Examples

data(yanomama)
    gen <- quasieuclid(as.dist(yanomama$gen)) # depends of mva
    ant <- quasieuclid(as.dist(yanomama$ant)) # depends of mva
    par(mfrow = c(2,2))
    plot(gen, ant)
    t1 <- mantel.randtest(gen, ant, 99);
    plot(t1, main = "gen-ant-mantel") ; print(t1)
    t1 <- procuste.rtest(pcoscaled(gen), pcoscaled(ant), 99)
    plot(t1, main = "gen-ant-procuste") ; print(t1)
    t1 <- RV.rtest(pcoscaled(gen), pcoscaled(ant), 99)
    plot(t1, main = "gen-ant-RV") ; print(t1)

Road distances in New-Zealand

Description

This data set gives the road distances between 13 towns in New-Zealand.

Usage

data(zealand)

Format

zealand is a list with the following components:

road

a data frame with 13 rows (New Zealand towns) and 13 columns (New Zealand towns) containing the road distances between these towns

xy

a data frame containing the coordinates of the 13 towns

neig

an object of class neig, a neighbour graph to visualize the map shape

nb

a neighborhood object (class nb defined in package spdep)

Source

Manly, B.F. (1994). Multivariate Statistical Methods. A primer., Second edition, Chapman and Hall, London, 1–215, page 172.

Examples

data(zealand)
d0 <- as.dist(as.matrix(zealand$road))
d1 <- cailliez (d0)
d2 <- lingoes(d0)

if(adegraphicsLoaded()) {
  G1 <- s.label(zealand$xy, lab = as.character(1:13), nb = zealand$nb)
  
  g1 <- s.label(cmdscale(dist(zealand$xy)), lab = as.character(1:13), nb = zealand$nb, 
    psub.text = "Distance canonique", plot = FALSE)
  g2 <- s.label(cmdscale(d0), lab = as.character(1:13), nb = zealand$nb, 
    psub.text = "Distance routiere", plot = FALSE)
  g3 <- s.label(cmdscale(d1), lab = as.character(1:13), nb = zealand$nb, 
    psub.text = "Distance routiere / Cailliez", plot = FALSE)
  g4 <- s.label(cmdscale(d2), lab = as.character(1:13), nb = zealand$nb, 
    psub.text = "Distance routiere / Lingoes", plot = FALSE)
  G2 <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))

} else {
  s.label(zealand$xy, lab = as.character(1:13), neig = zealand$neig)
  par(mfrow = c(2, 2))
  s.label(cmdscale(dist(zealand$xy)), lab = as.character(1:13), 
    neig = zealand$neig, sub = "Distance canonique", csub = 2)
  s.label(cmdscale(d0), lab = as.character(1:13), neig = zealand$neig, 
    sub = "Distance routiere", csub = 2)
  s.label(cmdscale(d1), lab = as.character(1:13), neig = zealand$neig, 
    sub = "Distance routiere / Cailliez", csub = 2)
  s.label(cmdscale(d2), lab = as.character(1:13), neig = zealand$neig, 
    sub = "Distance routiere / Lingoes", csub = 2)
}