Package 'compositions'

Description

"compositions" is a package for the analysis of compositional and multivariate positive data (generally called "amounts"), based on several alternative approaches.

Details

The DESCRIPTION file:

Index of help topics:

                        structure
Aar                     Composition of glaciar sediments from the Aar 
                        massif (Switzerland)
acomp                   Aitchison compositions
acompmargin             Marginal compositions in Aitchison Compositions
Activity10              Activity patterns of a statistician for 20 days
Activity31              Activity patterns of a statistician for 20 days
alr                     Additive log ratio transform
AnimalVegetation        Animal and vegetation measurement
+.aplus                 vectorial arithmetic for data sets with aplus
                        class
aplus                   Amounts analysed in log-scale
apt                     Additive planar transform
ArcticLake              Artic lake sediment samples of different water
                        depth
arrows3D                arrows in 3D, based on package rgl
as.data.frame.acomp     Convert "compositions" classes to data frames
axis3D                  Drawing a 3D coordiante system to a plot, based
                        on package rgl
balance                 Compute balances for a compositional dataset.
barplot.acomp           Bar charts of amounts
Bayesite                Permeabilities of bayesite
binary                  Treating binary and g-adic numbers
biplot3D                Three-dimensional biplots, based on package rgl
Blood23                 Blood samples
Boxite                  Compositions and depth of 25 specimens of
                        boxite
boxplot.acomp           Displaying compositions and amounts with
                        box-plots
cdt                     Centered default transform
ClamEast                Color-size compositions of 20 clam colonies
                        from East Bay
ClamWest                Color-size compositions of 20 clam colonies
                        from West Bay
clo                     Closure of a composition
clr                     Centered log ratio transform
clr2ilr                 Convert between clr and ilr, and between cpt
                        and ipt.
ClusterFinder1          Heuristics to find subpopulations of outliers
CoDaDendrogram          Dendrogram representation of acomp or rcomp
                        objects
coloredBiplot           A biplot providing somewhat easier access to
                        details of the plot.
colorsForOutliers1      Create a color/char palette or for groups of
                        outliers
CompLinModCoReg         Compositional Linear Model of Coregionalisation
compOKriging            Compositional Ordinary Kriging
compositions-package    library(compositions)
ConfRadius              Helper to compute confidence ellipsoids
cor.acomp               Correlations of amounts and compositions
Coxite                  Compositions, depths and porosities of 25
                        specimens of coxite
cpt                     Centered planar transform
DiagnosticProb          Diagnostic probabilities
dist                    Distances in variouse approaches
ellipses                Draw ellipses
endmemberCoordinates    Recast amounts as mixtures of end-members
Firework                Firework mixtures
geometricmean           The geometric mean
getDetectionlimit       Gets the detection limit stored in the data set
Glacial                 Compositions and total pebble counts of 92
                        glacial tills
groupparts              Group amounts of parts
Hongite                 Compositions of 25 specimens of hongite
HouseholdExp            Household Expenditures
Hydrochem               Hydrochemical composition data set of Llobregat
                        river basin water (NE Spain)
idt                     Isometric default transform
iit                     Isometric identity transform
ilr                     Isometric log ratio transform
ilrBase                 The canonical basis in the clr plane used for
                        ilr and ipt transforms.
ilt                     Isometric log transform
ipt                     Isometric planar transform
is.acomp                Check for compositional data type
IsMahalanobisOutlier    Checking for outliers
isoPortionLines         Isoportion- and Isoproportion-lines
juraset                 The jura dataset
kingTetrahedron         Ploting composition into rotable tetrahedron
Kongite                 Compositions of 25 specimens of kongite
lines.rmult             Draws connected lines from point to point.
logratioVariogram       Empirical variograms for compositions
MahalanobisDist         Compute Mahalanobis distances based von robust
                        Estimations
mean.acomp              Mean amounts and mean compositions
meanRow                 The arithmetic mean of rows or columns
Metabolites             Steroid metabolite patterns in adults and
                        children
missingProjector        Returns a projector the the observed space in
                        case of missings.
missingsInCompositions
                        The policy of treatment of missing values in
                        the "compositions" package
missingSummary          Classify and summarize missing values in a
                        dataset
mix.2aplus              Transformations from 'mixtures' to
                        'compositions' classes
mix.Read                Reads a data file in a mixR format
mvar                    Metric summary statistics of real, amount or
                        compositional data
names.acomp             The names of the parts
normalize               Normalize vectors to norm 1
norm.default            Vector space norm
oneOrDataset            Treating single compositions as one-row
                        datasets
OutlierClassifier1      Detect and classify compositional outliers.
outlierplot             Plot various graphics to analyse outliers.
outliersInCompositions
                        Analysing outliers in compositions.
pairwisePlot            Creates a paneled plot like pairs for two
                        different datasets.
parametricPosdefMat     Unique parametrisations for matrices.
perturbe                Perturbation of compositions
plot3D                  plot in 3D based on rgl
plot3D.acomp            3D-plot of compositional data
plot3D.aplus            3D-plot of positive data
plot3D.rmult            plot in 3D based on rgl
plot3D.rplus            plot in 3D based on rgl
plot.acomp              Ternary diagrams
plot.aplus              Displaying amounts in scatterplots
plot.logratioVariogram
                        Empirical variograms for compositions
plot.missingSummary     Plot a Missing Summary
pMaxMahalanobis         Compute distributions of empirical Mahalanobis
                        distances based on simulations
PogoJump                Honk Kong Pogo-Jumps Championship
power.acomp             Power transform in the simplex
powerofpsdmatrix        power transform of a matrix
princomp.acomp          Principal component analysis for Aitchison
                        compositions
princomp.aplus          Principal component analysis for amounts in log
                        geometry
princomp.rcomp          Principal component analysis for real
                        compositions
princomp.rmult          Principal component analysis for real data
princomp.rplus          Principal component analysis for real amounts
print.acomp             Printing compositional data.
qHotellingsTsq          Hotellings T square distribution
qqnorm.acomp            Normal quantile plots for compositions and
                        amounts
R2                      R square
rAitchison              Aitchison Distribution
+.rcomp                 Arithmetic operations for compositions in a
                        real geometry
rcomp                   Compositions as elements of the simplex
                        embedded in the D-dimensional real space
rcompmargin             Marginal compositions in real geometry
rDirichlet              Dirichlet distribution
read.geoeas             Reads a data file in a geoeas format
relativeLoadings        Loadings of relations of two amounts
replot                  Modify parameters of compositional plots.
rlnorm.rplus            The multivariate lognormal distribution

+.rmult                 vectorial arithmetic for datasets in a
                        classical vector scale
rmult                   Simple treatment of real vectors
rnorm.acomp             Normal distributions on special spaces
robustnessInCompositions
                        Handling robustness issues and outliers in
                        compositions.
+.rplus                 vectorial arithmetic for data sets with rplus
                        class
rplus                   Amounts i.e. positive numbers analysed as
                        objects of the real vector space
runif.acomp             The uniform distribution on the simplex
scalar                  Parallel scalar products
scale                   Normalizing datasets by centering and scaling
Sediments               Proportions of sand, silt and clay in sediments
                        specimens
segments.rmult          Draws straight lines from point to point.
SerumProtein            Serum Protein compositions of blood samples
ShiftOperators          Shifts of machine operators
simpleMissingSubplot    Ternary diagrams
SimulatedAmounts        Simulated amount datasets
simulateMissings        Artifical simulation of various kinds of
                        missings
Skulls                  Measurement of skulls
SkyeAFM                 AFM compositions of 23 aphyric Skye lavas
split.acomp             Splitting datasets in groups given by factors
straight                Draws straight lines.
summary.acomp           Summarizing a compositional dataset in terms of
                        ratios
summary.aplus           Summaries of amounts
summary.rcomp           Summary of compositions in real geometry
sumMissingProjector     Compute the global projector to the observed
                        subspace.
Supervisor              Proportions of supervisor's statements assigned
                        to different categories
ternaryAxis             Axis for ternary diagrams
totals                  Total sum of amounts
tryDebugger             Empirical variograms for compositions
ult                     Uncentered log transform
var.acomp               Variances and covariances of amounts and
                        compositions
variation               Variation matrices of amounts and compositions
var.lm                  Residual variance of a model
vcovAcomp               Variance covariance matrix of parameters in
                        compositional regression
vgmFit                  Compositional variogram model fitting
vgram2lrvgram           vgram2lrvgram
vgram.sph               Variogram functions
WhiteCells              White-cell composition of 30 blood samples by
                        two different methods
Yatquat                 Yatquat fruit evaluation
zeroreplace             Zero-replacement routine

Further information is available in the following vignettes:

To get detailed "getting started" introduction use help.start() or help.start(browser="myfavouritebrowser") Go to "Packages" then "compositions" and then "overview" and then launch the file "UsingCompositions.pdf" from there. Please also check the web-site: http://www.stat.boogaart.de/compositions/ for improved material and our new book expected to appear spring 2009.
The package is devoted to the analysis of multiple amounts. Amounts have typically non-negative values, and often sum up to 100% or one. These constraints lead to spurious effects on the covariance structure, as pointed out by Chayes (1960). The problem is treated rigorously in the monography by Aitchison (1986), who characterizes compositions as vectors having a relative scale, and identifies its sample space with the D-part simplex. However still (i.e. 2005) most statistical packages do not provided any support for this scale.
The grounding idea of the package exploits the class concept: the analyst gives the data a compositional or amount class, and then all further analysis are (should be) automatically done in a consistent way, e.g. x <- acomp(X); plot(x) should plot the data as a composition (in a ternary diagram) directly without any further interaction of the user.
The package provides four different approaches to analyse amounts. These approaches are associated to four R-classes, representing four different geometries of the sampling space of amounts. These geometries depend on two questions: whether the total sum of the amounts is a relevant information, and which is the meaningful measure of difference of the data.

rplus : (Real Plus) The total amount matters, and amounts should be compared on an absolute basis. i.e. the difference between 1g and 2g is the same as the difference between 1kg and 1001g, one gram.
aplus : (Aitchison Plus) The total amount matters, but amounts should be compared relatively, i.e. the difference between 1mg and 2mg is the same as that of 1g and 2g: the double.
acomp : (Aitchison composition) the total amount is constant (or an artifact of the sampling/measurement procedure), and the meaningful difference is a relative one. This class follows the original proposals of Aitchison.
rcomp : (Real composition) the sum is a constant, and the difference in amount from 0% to 1% and from 10% to 11% is regarded as equal. This class represents the raw/naive treatment of compositions as elements of the real simplex based on an absolute geometry. This treatment is implicitly used in most amalgamation problems. However the whole approach suffers from the drawbacks and problems discussed in Chayes (1960) and Aitchison (1986).
The aim of the package is to provide all the functionality to do a consistent analysis in all of these approaches and to make the results obtained with different geometries as easy to compare as possible.

Note

The package compositions has grown a lot in the last year: missings, robust estimations, outlier detection and classification, codadendrogram. This makes everything much more complex especially from the side of programm testing. Thus we would like to urge our users to report all errors and problems of the lastest version (please check first) to [email protected].

Author(s)

K. Gerald van den Boogaart <[email protected]>, Raimon Tolosana-Delgado, Matevz Bren

Maintainer: K. Gerald van den Boogaart <[email protected]>

References

Aitchison, J. (1986) The Statistical Analysis of Compositional Data Monographs on Statistics and Applied Probability. Chapman & Hall Ltd., London (UK). 416p.

Aitchison, J, C. Barcel'o-Vidal, J.J. Egozcue, V. Pawlowsky-Glahn (2002) A consise guide to the algebraic geometric structure of the simplex, the sample space for compositional data analysis, Terra Nostra, Schriften der Alfred Wegener-Stiftung, 03/2003

Billheimer, D., P. Guttorp, W.F. and Fagan (2001) Statistical interpretation of species composition, Journal of the American Statistical Association, 96 (456), 1205-1214

Chayes, F. (1960). On correlation between variables of constant sum. Journal of Geophysical Research 65~(12), 4185–4193.

Pawlowsky-Glahn, V. and J.J. Egozcue (2001) Geometric approach to statistical analysis on the simplex. SERRA 15(5), 384-398

Pawlowsky-Glahn, V. (2003) Statistical modelling on coordinates. In: Thi\'o -Henestrosa, S. and Mart\'in-Fern\'a ndez, J.A. (Eds.) Proceedings of the 1st International Workshop on Compositional Data Analysis, Universitat de Girona, ISBN 84-8458-111-X, https://ima.udg.edu/Activitats/CoDaWork03/

Mateu-Figueras, G. and Barcel\'o-Vidal, C. (Eds.) Proceedings of the 2nd International Workshop on Compositional Data Analysis, Universitat de Girona, ISBN 84-8458-222-1, https://ima.udg.edu/Activitats/CoDaWork05/

van den Boogaart, K.G. and R. Tolosana-Delgado (2008) "compositions": a unified R package to analyze Compositional Data, Computers & Geosciences, 34 (4), pages 320-338, doi:10.1016/j.cageo.2006.11.017.

See Also

compositions-package, missingsInCompositions, robustnessInCompositions, outliersInCompositions,

Examples

library(compositions)      # load library
data(SimulatedAmounts)     # load data sa.lognormals
x <- acomp(sa.lognormals)  # Declare the dataset to be compositional
                           # and use relative geometry
plot(x)                    # plot.acomp : ternary diagram
ellipses(mean(x),var(x),r=2,col="red")  # Simplex 2sigma predictive region
pr <- princomp(x)
straight(mean(x),pr$Loadings) 

x <- rcomp(sa.lognormals)  # Declare the dataset to be compositional
                           # and use absolute geometry
plot(x)                    # plot.acomp : ternary diagram
ellipses(mean(x),var(x),r=2,col="red")  # Real 2sigma predictive region
pr <- princomp(x)          
straight(mean(x),pr$Loadings)

Description

Geochemical composition of glaciar sediments from the Aar massif region (Switzerland), major oxides and trace elements.

Usage

data(Aar)

Details

Composition of recent sediments of several morraines and streams from glaciers around the Aar massif, including both major oxides and trace elements. The major oxides are expressed in weight percent (total sum reported in column SumOxides), from Silica (SiO2, column 3) to total Iron 3 Oxide (Fe2O3t, column12, incorporating FeO recasted to Fe2O3). The trace elements are reported in parts per million (ppm, mg/Kg) between columns 14 (Ba) and 29 (Nd). Partial sum of the trace elements (in ppm) and of all traces and major oxides (in %) are also reported.

Apart of the compositional information, two covariables are included: Sample and GS. The variable Sample reports the ID of the sample material. This material was sieved in 11 grain size fractions, and each fraction was analysed separately after drying. The grain size fraction of each subsample is reported in variable GS, representing the upper limit of the size fraction reported in $\phi$ scale, e.g. the binary log transformation of the average diameter $\bar{d}$

$\phi = -\log_2 (\bar{d})$

The Aar is a granitic-granodioritic-gneissic massif of the Alps, in Switzerland, comprised of several intrusions with different compositions within the range of granitoid lithologies. Details of the region, mineralogy, procedures and study questions behind the data can be found in von Eynatten at al (2012) and references thereon.

Note

Courtesy of H. von Eynatten

Source

von Eynatten H.; Tolosana-Delgado, R.; Karius, V (2012) Sediment generation in modern glacial settings: Grain-size and source-rock control on sediment composition. Sedimentary Geology 280 (1): 80-92 doi:10.1016/j.sedgeo.2012.03.008

References

von Eynatten H.; Tolosana-Delgado, R.; Karius, V (2012) Sediment generation in modern glacial settings: Grain-size and source-rock control on sediment composition. Sedimentary Geology 280 (1): 80-92 doi:10.1016/j.sedgeo.2012.03.008

Description

A class providing the means to analyse compositions in the philosophical framework of the Aitchison Simplex.

Usage

acomp(X,parts=1:NCOL(oneOrDataset(X)),total=1,warn.na=FALSE,
          detectionlimit=NULL,BDL=NULL,MAR=NULL,MNAR=NULL,SZ=NULL)

Arguments

Details

Many multivariate datasets essentially describe amounts of D different parts in a whole. This has some important implications justifying to regard them as a scale for its own, called a composition. This scale was in-depth analysed by Aitchison (1986) and the functions around the class "acomp" follow his approach.
Compositions have some important properties: Amounts are always positive. The amount of every part is limited to the whole. The absolute amount of the whole is noninformative since it is typically due to artifacts on the measurement procedure. Thus only relative changes are relevant. If the relative amount of one part increases, the amounts of other parts must decrease, introducing spurious anticorrelation (Chayes 1960), when analysed directly. Often parts (e.g H2O, Si) are missing in the dataset leaving the total amount unreported and longing for analysis procedures avoiding spurious effects when applied to such subcompositions. Furthermore, the result of an analysis should be indepent of the units (ppm, g/l, vol.%, mass.%, molar fraction) of the dataset.
From these properties Aitchison showed that the analysis should be based on ratios or log-ratios only. He introduced several transformations (e.g. clr,alr), operations (e.g. perturbe, power.acomp), and a distance (dist) which are compatible with these properties. Later it was found that the set of compostions equipped with perturbation as addition and power-transform as scalar multiplication and the dist as distance form a D-1 dimensional euclidean vector space (Billheimer, Fagan and Guttorp, 2001), which can be mapped isometrically to a usual real vector space by ilr (Pawlowsky-Glahn and Egozcue, 2001).
The general approach in analysing acomp objects is thus to perform classical multivariate analysis on clr/alr/ilr-transformed coordinates and to backtransform or display the results in such a way that they can be interpreted in terms of the original compositional parts.
A side effect of the procedure is to force the compositions to sum up to a total, which is done by the closure operation clo .

Value

a vector of class "acomp" representing one closed composition or a matrix of class "acomp" representing multiple closed compositions each in one row.

Missing Policy

The policy of treatment of zeroes, missing values and values below detecion limit is explained in depth in compositions.missing.

Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de, Raimon Tolosana-Delgado

References

Aitchison, J. (1986) The Statistical Analysis of Compositional Data Monographs on Statistics and Applied Probability. Chapman & Hall Ltd., London (UK). 416p.

Aitchison, J, C. Barcel'o-Vidal, J.J. Egozcue, V. Pawlowsky-Glahn (2002) A consise guide to the algebraic geometric structure of the simplex, the sample space for compositional data analysis, Terra Nostra, Schriften der Alfred Wegener-Stiftung, 03/2003

Billheimer, D., P. Guttorp, W.F. and Fagan (2001) Statistical interpretation of species composition, Journal of the American Statistical Association, 96 (456), 1205-1214

Chayes, F. (1960). On correlation between variables of constant sum. Journal of Geophysical Research 65~(12), 4185–4193.

Pawlowsky-Glahn, V. and J.J. Egozcue (2001) Geometric approach to statistical analysis on the simplex. SERRA 15(5), 384-398

Pawlowsky-Glahn, V. (2003) Statistical modelling on coordinates. In: Thi\'o-Henestrosa, S. and Mart\'in-Fern\'andez, J.A. (Eds.) Proceedings of the 1st International Workshop on Compositional Data Analysis, Universitat de Girona, ISBN 84-8458-111-X, https://ima.udg.edu/Activitats/CoDaWork03/

Mateu-Figueras, G. and Barcel\'o-Vidal, C. (Eds.) Proceedings of the 2nd International Workshop on Compositional Data Analysis, Universitat de Girona, ISBN 84-8458-222-1, https://ima.udg.edu/Activitats/CoDaWork05/

van den Boogaart, K.G. and R. Tolosana-Delgado (2008) "compositions": a unified R package to analyze Compositional Data, Computers & Geosciences, 34 (4), pages 320-338, doi:10.1016/j.cageo.2006.11.017.

See Also

clr,rcomp, aplus, princomp.acomp, plot.acomp, boxplot.acomp, barplot.acomp, mean.acomp, var.acomp, variation.acomp, cov.acomp, msd

Examples

data(SimulatedAmounts)
plot(acomp(sa.lognormals))

Description

The S4-version of the data container "acomp" for compositional data. More information in acomp

Objects from the Class

A virtual Class: No objects may be directly created from it. This is provided to ensure that acomp objects behave as data.frame or structure under certain circumstances. Use acomp to create these objects.

Slots

.Data:

Object of class "list" containing the data itself

names:

Object of class "character" with column names

row.names:

Object of class "data.frameRowLabels" with row names

.S3Class:

Object of class "character" with the class string

Extends

Class "data.frame", directly. Class "compositional", directly. Class "list", by class "data.frame", distance 2. Class "oldClass", by class "data.frame", distance 2. Class "vector", by class "data.frame", distance 3.

Methods

coerce

signature(from = "acomp", to = "data.frame"): to generate a data.frame

coerce

signature(from = "acomp", to = "structure"): to generate a structure (i.e. a vector, matrix or array)

coerce<-

signature(from = "acomp", to = "data.frame"): to overwrite a composition with a data.frame

Note

see acomp

Author(s)

Raimon Tolosana-Delgado

References

see acomp

See Also

see acomp

Examples

showClass("acomp")

Description

The Aitchison Simplex with its two operations perturbation as + and power transform as * is a vector space. This vector space is represented by these operations.

Usage

power.acomp(x,s)
## Methods for class "acomp"
## x*y
## x/y

Arguments

Details

The power transform is the basic multiplication operation of the Aitchison simplex seen as a vector space. It is defined as:

$(x*y)_i:= clo( (x_i^{y_i})_i )_i$

The division operation is just the multiplication with $1/y$.

Value

An "acomp" vector or matrix.

Note

For * the arguments x and y can be exchanged. Note that this definition generalizes the power by a scalar, since y or s may be given as a scalar, or as a vector with as many components as the composition in acomp x. The result is then a matrix where each row corresponds to the composition powered by one of the scalars in the vector.

Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

References

Aitchison, J. (1986) The Statistical Analysis of Compositional Data Monographs on Statistics and Applied Probability. Chapman & Hall Ltd., London (UK). 416p.

Aitchison, J, C. Barcel'o-Vidal, J.J. Egozcue, V. Pawlowsky-Glahn (2002) A consise guide to the algebraic geometric structure of the simplex, the sample space for compositional data analysis, Terra Nostra, Schriften der Alfred Wegener-Stiftung, 03/2003

Pawlowsky-Glahn, V. and J.J. Egozcue (2001) Geometric approach to statistical analysis on the simplex. SERRA 15(5), 384-398

https://ima.udg.edu/Activitats/CoDaWork03/

https://ima.udg.edu/Activitats/CoDaWork05/

See Also

ilr,clr, alr,

Examples

acomp(1:5)* -1 + acomp(1:5)
data(SimulatedAmounts)
cdata <- acomp(sa.lognormals)
plot( tmp <- (cdata-mean(cdata))/msd(cdata) )
class(tmp)
mean(tmp)
msd(tmp)
var(tmp)

Description

Compute marginal compositions of selected parts, by computing the rest as the geometric mean of the non-selected parts.

Usage

acompmargin(X,d=c(1,2),name="*",pos=length(d)+1,what="data")

Arguments

Details

The amalgamation column is simply computed by taking the geometric mean of the non-selected components. This is consistent with the acomp approach and gives clear ternary diagrams. However, this geometric mean is difficult to interpret.

Value

A closed compositions with class "acomp" containing the variables given by d and the the amalgamation column.

Missing Policy

MNAR has the highest priority, MAR afterwards, and WZERO (BDL,SZ) values are considered as 0 and finally reported as BDL.

Author(s)

Raimon Tolosana-Delgado, K.Gerald v.d. Boogaart http://www.stat.boogaart.de

References

Vera Pawlowsky-Glahn (2003) personal communication. Universitat de Girona.

van den Boogaart, K.G. and R. Tolosana-Delgado (2008) "compositions": a unified R package to analyze Compositional Data, Computers & Geosciences, 34 (4), pages 320-338, doi:10.1016/j.cageo.2006.11.017.

See Also

rcompmargin, acomp

Examples

data(SimulatedAmounts)
plot.acomp(sa.lognormals5,margin="acomp")
plot.acomp(acompmargin(sa.lognormals5,c("Pb","Zn")))
plot.acomp(acompmargin(sa.lognormals5,c(1,2)))

Description

acomp and aplus objects are considered as (sets of) vectors. The %*% is considered as the inner multiplication. An inner multiplication with another vector is the scalar product. An inner multiplication with a matrix is a matrix multiplication, where the vectors are either considered as row or as column vector.

Usage

## S3 method for class 'acomp'
x %*% y
## S3 method for class 'aplus'
x %*% y

Arguments

Details

The operators try to mimic the behavior of %*% on c()-vectors as inner product, applied in parallel to all row-vectors of the dataset. Thus the product of a vector with a vector of the same type results in the scalar product of both. For the multiplication with a matrix each vector is considered as a row or column, whatever is more appropriate. The matrix itself is considered as representing a linear mapping (endomorphism) of the vector space to a space of the same type. The mapping is represented in clr, ilr or ilt coordinates. Which of the aforementioned coordinate systems is used is judged from the type of x and from the dimensions of the A.

Value

Either a numeric vector containing the scalar products, or an object of type acomp or aplus containing the vectors transformed with the given matrix.

Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

See Also

%*%.rmult

Examples

x <- acomp(matrix( sqrt(1:12), ncol= 3 ))
x%*%x
A <- matrix( 1:9,nrow=3)
x %*% A %*% x
x %*% A
A %*% x
A <- matrix( 1:4,nrow=2)
x %*% A %*% x
x %*% A
A %*% x
x <- aplus(matrix( sqrt(1:12), ncol= 3 ))
x%*%x
A <- matrix( 1:9,nrow=3)
x %*% A %*% x
x %*% A
A %*% x

Description

Proportion of a day in activity teaching, consulting, administrating, research, other wakeful activities and sleep for 20 days are given.

Usage

data(Activity10)

Details

The activity of an academic statistician were divided into following six categories

Data show the proportions of the 24 hours devoted to each activity, recorded on each of 20 days, selected randomly from working days in alternate weeks, so as to avoid any possible carry-over effects, such as short-sleep day being compensated by make-up sleep on a succeeding day.

The six activity may be divided into two categories 'work' comprising activities 1,2,3,4: and 'leisure' comprising activities 5 and 6.

All rows sum to one.

Note

Courtesy of J. Aitchison

Source

Aitchison: CODA microcomputer statistical package, 1986, the file name STATDAY.DAT, here included under the GNU Public Library Licence Version 2 or newer.

References

Aitchison: The Statistical Analysis of Compositional Data, 1986, Data 10, pp15.

Description

Proportion of a day in activity teaching, consulting, administrating, research, other wakeful activities and sleep for 20 days are given.

Usage

data(Activity31)

Details

The activity of an academic statistician were divided into following six categories

Data shows the proportions of the 24 hours devoted to each activity, recorded on each of 20 days, selected randomly from working days in alternate weeks, so as to avoid any possible carry-over effects, such as short-sleep day being compensated by make-up sleep on a succeeding day.

The six activity may be divided into two categories 'work' comprising activities 1,2,3,4: and 'leisure' comprising activities 5 and 6.

Note

Courtesy of J. Aitchison

Source

Aitchison: CODA microcomputer statistical package, 1986, the file name ACTIVITY.DAT, here included under the GNU Public Library Licence Version 2 or newer.

References

Aitchison: The Statistical Analysis of Compositional Data, 1986, Data 31.

Description

Compute the additive log ratio transform of a (dataset of) composition(s), and its inverse.

Usage

alr( x ,ivar=ncol(x), ... )
          alrInv( z, ...,orig=gsi.orig(z))

Arguments

Details

The alr-transform maps a composition in the D-part Aitchison-simplex non-isometrically to a D-1 dimensonal euclidian vector, treating the last part as common denominator of the others. The data can then be analysed in this transformation by all classical multivariate analysis tools not relying on a distance. The interpretation of the results is relatively simple, since the relation to the original D-1 first parts is preserved. However distance is an extremely relevant concept in most types of analysis, where a clr or ilr transformation should be preferred.

The additive logratio transform is given by

$alr(x)_i := \ln\frac{x_i}{x_D}$

.

Value

alr gives the additive log ratio transform; accepts a compositional dataset alrInv gives a closed composition with the given alr-transform; accepts a dataset

Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

References

Aitchison, J. (1986) The Statistical Analysis of Compositional Data Monographs on Statistics and Applied Probability. Chapman & Hall Ltd., London (UK). 416p.

See Also

clr,ilr,apt, https://ima.udg.edu/Activitats/CoDaWork03/

Examples

(tmp <- alr(c(1,2,3)))
alrInv(tmp)
unclass(alrInv(tmp)) - clo(c(1,2,3)) # 0
data(Hydrochem)
cdata <- Hydrochem[,6:19]
pairs(alr(cdata),pch=".")

Description

Abstract class containing all amounts classes carrying total information: aplus, rplus and ccomp

Objects from the Class

A virtual Class: No objects may be created from it.

Methods

No methods defined with class "amounts" in the signature.

Author(s)

Raimon Tolosana-Delgado

See Also

compositional-class for classes with relative information

Examples

showClass("amounts")

Description

Areal compositions by abundance of vegetation and animals for 50 plots in each of regions A and B.

Usage

data(AnimalVegetation)

Details

In a regional ecology study, plots of land of equal area were inspected and the parts of each plot which were thick or thin in vegetation and dense or sparse in animals were identified. From this field work the areal proportions of each plot were calculated for the four mutually exclusive and exhaustive categories: thick-dense, thick-sparse, thin-dense, thin-sparse. These sets of proportions are recorded for 50 plots from each of two different regions A and B.

All rows sum to 1, except for some rounding errors.

Note

Courtesy of J. Aitchison

Source

Aitchison: CODA microcomputer statistical package, 1986, the file name ANIVEG.DAT, here included under the GNU Public Library Licence Version 2 or newer.

References

Aitchison: The Statistical Analysis of Compositional Data, 1986, Data 25, pp22.

Description

A class to analyse positive amounts in a logistic framework.

Usage

aplus(X,parts=1:NCOL(oneOrDataset(X)),total=NA,warn.na=FALSE,
          detectionlimit=NULL,BDL=NULL,MAR=NULL,MNAR=NULL,SZ=NULL)

Arguments

Details

Many multivariate datasets essentially describe amounts of D different parts in a whole. When the whole is large in relation to the considered parts, such that they do not exclude each other, or when the total amount of each componenten is indeed determined by the phenomenon under investigation and not by sampling artifacts (such as dilution or sample preparation), then the parts can be treated as amounts rather than as a composition (cf. acomp, rcomp).
Like compositions, amounts have some important properties. Amounts are always positive. An amount of exactly zero essentially means that we have a substance of another quality. Different amounts - spanning different orders of magnitude - are often given in different units (ppm, ppb, g/l, vol.%, mass %, molar fraction). Often, these amounts are also taken as indicators of other non-measured components (e.g. K as indicator for potassium feldspar), which might be proportional to the measured amount. However, in contrast to compositions, amounts themselves do matter. Amounts are typically heavily skewed and in many practical cases a log-transform makes their distribution roughly symmetric, even normal.
In full analogy to Aitchison's compositions, vector space operations are introduced for amounts: the perturbation perturbe.aplus as a vector space addition (corresponding to change of units), the power transformation power.aplus as scalar multiplication describing the law of mass action, and a distance dist which is independent of the chosen units. The induced vector space is mapped isometrically to a classical $R^D$ by a simple log-transformation called ilt, resembling classical log transform approaches.
The general approach in analysing aplus objects is thus to perform classical multivariate analysis on ilt-transformed coordinates (i.e., logs) and to backtransform or display the results in such a way that they can be interpreted in terms of the original amounts.
The class aplus is complemented by the rplus, allowing to analyse amounts directly as real numbers, and by the classes acomp and rcomp to analyse the same data as compositions disregarding the total amounts, focusing on relative weights only.
The classes rcomp, acomp, aplus, and rplus are designed as similar as possible in order to allow direct comparison between results achieved by the different approaches. Especially the acomp simplex transforms clr, alr, ilr are mirrored in the aplus class by the single bijective isometric transform ilt

Value

a vector of class "aplus" representing a vector of amounts or a matrix of class "aplus" representing multiple vectors of amounts, each vector in one row.

Missing Policy

The policy of treatment of zeroes, missing values and values below detecion limit is explained in depth in compositions.missing.

Author(s)

Raimon Tolosana-Delgado, K.Gerald v.d. Boogaart http://www.stat.boogaart.de

References

van den Boogaart, K.G. and R. Tolosana-Delgado (2008) "compositions": a unified R package to analyze Compositional Data, Computers & Geosciences, 34 (4), pages 320-338, doi:10.1016/j.cageo.2006.11.017.

See Also

ilt,acomp, rplus, princomp.aplus, plot.aplus, boxplot.aplus, barplot.aplus, mean.aplus, var.aplus, variation.aplus, cov.aplus, msd

Examples

data(SimulatedAmounts)
plot(aplus(sa.lognormals))

Description

The S4-version of the data container "aplus" for compositional data. More information in aplus

Objects from the Class

A virtual Class: No objects may be directly created from it. This is provided to ensure that aplus objects behave as data.frame or structure under certain circumstances. Use aplus to create these objects.

Slots

.Data:

Object of class "list" containing the data itself

names:

Object of class "character" with column names

row.names:

Object of class "data.frameRowLabels" with row names

.S3Class:

Object of class "character" with the class string

Extends

Class "data.frame", directly. Class "compositional", directly. Class "list", by class "data.frame", distance 2. Class "oldClass", by class "data.frame", distance 2. Class "vector", by class "data.frame", distance 3.

Methods

coerce

signature(from = "aplus", to = "data.frame"): to generate a data.frame

coerce

signature(from = "aplus", to = "structure"): to generate a structure (i.e. a vector, matrix or array)

coerce<-

signature(from = "aplus", to = "data.frame"): to overwrite a composition with a data.frame

Note

see aplus

Author(s)

Raimon Tolosana-Delgado

References

see aplus

See Also

see aplus

Examples

showClass("aplus")

Description

The positive vectors equipped with the perturbation (defined as the element-wise product) as Abelian sum, and powertransform (defined as the element-wise powering with a scalar) as scalar multiplication forms a real vector space. These vector space operations are defined here in a similar way to +.rmult.

Usage

perturbe.aplus(x,y)
## S3 method for class 'aplus'
x + y
## S3 method for class 'aplus'
x - y
## S3 method for class 'aplus'
x * y
## S3 method for class 'aplus'
x / y
##  Methods for aplus
##   x+y
##   x-y
##   -x
##   x*r
##   r*x
##   x/r
power.aplus(x,r)

Arguments

Details

The operators try to mimic the parallel operation of R for vectors of real numbers to vectors of amounts, represented as matrices containing the vectors as rows and works like the operators for {rmult}

Value

an object of class "aplus" containing the result of the corresponding operation on the vectors.

Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

See Also

rmult, %*%.rmult

Examples

x <- aplus(matrix( sqrt(1:12), ncol= 3 ))
x
x+x
x + aplus(1:3)
x * 1:4
1:4 * x
x / 1:4
x / 10
power.aplus(x,1:4)

Description

Compute the additive planar transform of a (dataset of) compositions or its inverse.

Usage

apt( x ,...)
          aptInv( z ,..., orig=gsi.orig(z))

Arguments

Details

The apt-transform maps a composition in the D-part real-simplex linearly to a D-1 dimensional euclidian vector. Although the transformation does not reach the whole $R^{D-1}$, resulting covariance matrices are typically of full rank.

The data can then be analysed in this transformation by all classical multivariate analysis tools not relying on distances. See cpt and ipt for alternatives. The interpretation of the results is easy since the relation to the first D-1 original variables is preserved.

The additive planar transform is given by

$apt(x)_i := clo(x)_i, i=1,\ldots,D-1$

Value

apt gives the centered planar transform, aptInv gives closed compositions with the given apt-transforms

Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

References

van den Boogaart, K.G. and R. Tolosana-Delgado (2008) "compositions": a unified R package to analyze Compositional Data, Computers & Geosciences, 34 (4), pages 320-338, doi:10.1016/j.cageo.2006.11.017.

See Also

alr,cpt,ipt

Examples

(tmp <- apt(c(1,2,3)))
aptInv(tmp)
aptInv(tmp) - clo(c(1,2,3)) # 0
data(Hydrochem)
cdata <- Hydrochem[,6:19]
pairs(apt(cdata),pch=".")

Description

Sand, silt and clay compositions of 39 sediment samples of different water depth in an Arctic lake.

Usage

data(ArcticLake)

Details

Sand, silt and clay compositions of 39 sediment samples at different water depth (in meters) in an Arctic lake. The additional feature is a concomitant variable or covariate, water depth, which may account for some of the variation in the compositions. In statistical terminology we have a multivariate regression problem with sediment composition as regressand and water depth as regressor.

All row percentage sums to 100, except for rounding errors.

Note

Courtesy of J. Aitchison

Source

Aitchison: CODA microcomputer statistical package, 1986, the file name ARCTIC.DAT, here included under the GNU Public Library Licence Version 2 or newer.

References

Aitchison: The Statistical Analysis of Compositional Data, 1986, Data 5, pp5.

Description

adds 3-dimensional arrows to an rgl plot.

Usage

arrows3D(...)
## Default S3 method:
arrows3D(x0,x1,...,length=0.25,
                     angle=30,code=2,col="black",
                     lty=NULL,lwd=2,orth=c(1,0.0001,0.0000001),
                     labs=NULL,size=lwd)

Arguments

Details

The function is called to plot arrows into an rgl plot. The size of the arrow head is given in a absolute way. Therefore it is important to give the right scale for the length, to see the arrow head and that it does not fill the whole window.

Value

the 3D plotting coordinates of the tips of the arrows displayed, returned invisibly

Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

See Also

plot3D, rgl::points3d, graphics::plot

Examples

x <- cbind(rnorm(10),rnorm(10),rnorm(10))
if(requireNamespace("rgl", quietly = TRUE)) {
  plot3D(x)
  x0 <- x*0
  arrows3D(x0,x)
} ## this function requires package 'rgl'

Description

Convert a compositional object to a dataframe

Usage

## S3 method for class 'acomp'
as.data.frame(x,...)
## S3 method for class 'rcomp'
as.data.frame(x,...)
## S3 method for class 'aplus'
as.data.frame(x,...)
## S3 method for class 'rplus'
as.data.frame(x,...)
## S3 method for class 'rmult'
as.data.frame(x,...)
## S3 method for class 'ccomp'
as.data.frame(x,...)
## S3 method for class 'rmult'
as.matrix(x,...)

Arguments

Value

a data frame containing the given data, or (for rmult only) as matrix.

Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

Examples

data(SimulatedAmounts)
as.data.frame(acomp(sa.groups))
# The central perpose of providing this command is that the following
# works properly:
data.frame(acomp(sa.groups),groups=sa.groups.area)

Description

Adds a coordinate system to a 3D rgl graphic. In future releases, functionality to add tickmarks will be (hopefully) provided. Now, it is just a system of arrows giving the directions of the three axes.

Usage

axis3D(axis.origin=c(0,0,0),axis.scale=1,axis.col="gray",vlabs=c("x","y","z"),
       vlabs.col=axis.col,bbox=FALSE,axis.lwd=2,axis.len=mean(axis.scale)/10,
       axis.angle=30,orth=c(1,0.0001,0.000001),axes=TRUE,...)

Arguments

Details

The function is called to plot a coordiante system consisting of arrows into an rgl plot.

Value

Nothing

Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

See Also

rgl::points3d, graphics::plot, plot3D,arrows3D

Examples

x <- cbind(rnorm(10),rnorm(10),rnorm(10))
if(requireNamespace("rgl", quietly = TRUE)) {
  plot3D(x)
  x0 <- x*0
  axis3D()
} ## this function requires package 'rgl'

Description

Functions to automatically determine and compute the relevant back-transformation for a rmult object.

Usage

backtransform(x, as=x)
          backtransform.rmult(x, as=x)
          gsi.orig(x,y=NULL)
          gsi.getV(x,y=NULL)

Arguments

Details

The general idea of this package is to analyse the same data with different geometric concepts, in a fashion as similar as possible. For each of the four concepts there exists a family of transforms expressing the geometry in aan appropriate manner. Transformed data can be further analysed, and certain results may be back-transformed to the original scale. These functions take care of tracking, constructing and computing the inverse transformation, whichever was the original geometry and forward transformation used.

Value

For functions backtransform or backtransform.rmult, a corresponding matrix or vector containing the backtransformation of x. Efforts are taken to keep any extra attributes (beyond, "dim", "dimnames" and "class") the argument "x" may have \ For function gsi.orig, the original data with a compositional class, if it exists (or NULL otherwise). \ For function gsi.getV, the transposed, inverse matrix of log-contrasts originally used to forward transform the original composition orig to its coefficients/coordinates. If it does not exists, the output is NULL.

Author(s)

R. Tolosana-Delgado, K.Gerald v.d. Boogaart http://www.stat.boogaart.de

References

van den Boogaart, K.G. and R. Tolosana-Delgado (2008) "compositions": a unified R package to analyze Compositional Data, Computers & Geosciences, 34 (4), pages 320-338, doi:10.1016/j.cageo.2006.11.017.

See Also

cdt, idt, clr, cpt, ilt, iit, ilr, ipt, alr, apt

Examples

x <- acomp(1:5)
x
backtransform(ilr(x))
backtransform(clr(x))
backtransform(idt(x))
backtransform(cdt(x))
backtransform(alr(x))

Description

Compute balances in a compositional dataset.

Usage

balance(X,...)
## S3 method for class 'acomp'
balance(X,expr,...)
## S3 method for class 'rcomp'
balance(X,expr,...)
## S3 method for class 'aplus'
balance(X,expr,...)
## S3 method for class 'rplus'
balance(X,expr,...)
balance01(X,...)
## S3 method for class 'acomp'
balance01(X,expr,...)
## S3 method for class 'rcomp'
balance01(X,expr,...)
balanceBase(X,...)
## S3 method for class 'acomp'
balanceBase(X,expr,...)
## S3 method for class 'rcomp'
balanceBase(X,expr,...)
## S3 method for class 'acomp'
balanceBase(X,expr,...)
## S3 method for class 'rcomp'
balanceBase(X,expr,...)

Arguments

Details

For acomp-compositions balances are defined as orthogonal projections representing the log ratio of the geometric means of subsets of elements. Based on a recursive subdivision (provided by the expr=) this projections provide a (complete or incomplete) basis of the clr-plane. The basis is given by the balanceBase functions. The transform is given by the balance functions. The balance01 functions are a backtransform of the balances to the amount of the first portion if this was the only balance in a 2 element composition, providing an "interpretation" for the values of the balances.

The package tries to give similar concepts for the other scales. For rcomp objects the concept is mainly unchanges but augmented by a virtual component 1, which always has portion 1.

For rcomp objects, we choose not a "orthogonal" transformation since such a concept anyway does not really exist in the given space, but merily use the difference of one subset to the other. The balance01 is than not really a transform of the balance but simply the portion of the first group of parts in all contrasted parts.

For rplus objects we just used an analog to generalisation from the rcomp defintion as aplus is generalized from acomp. However at this time we have no idea wether this has any usefull interpretation.

Value

References

https://ima.udg.edu/Activitats/CoDaWork08/ Papers of Boogaart and Tolosana https://ima.udg.edu/Activitats/CoDaWork05/ Paper of Egozcue

See Also

clr,ilr,ipt, ilrBase

Examples

X <- rnorm(100)
Y <- rnorm.acomp(100,acomp(c(A=1,B=1,C=1)),0.1*diag(3))+acomp(t(outer(c(0.2,0.3,0.4),X,"^")))
colnames(Y) <- c("A","B","C")

subComps <- function(X,...,all=list(...)) {
  X <- oneOrDataset(X)
  nams <- sapply(all,function(x) paste(x[[2]],x[[3]],sep=","))
  val  <- sapply(all,function(x){
              a = X[,match(as.character(x[[2]]),colnames(X)) ]
              b = X[,match(as.character(x[[2]]),colnames(X)) ]
              c = X[,match(as.character(x[[3]]),colnames(X)) ] 
              return(a/(b+c))
             }) 
  colnames(val)<-nams
  val
}
pairs(cbind(ilr(Y),X),panel=function(x,y,...) {points(x,y,...);abline(lm(y~x))})
pairs(cbind(balance(Y,~A/B/C),X),panel=function(x,y,...) {points(x,y,...);abline(lm(y~x))})

pairwisePlot(balance(Y,~A/B/C),X)
pairwisePlot(X,balance(Y,~A/B/C),panel=function(x,y,...) {plot(x,y,...);abline(lm(y~x))})
pairwisePlot(X,balance01(Y,~A/B/C))
pairwisePlot(X,subComps(Y,A~B,A~C,B~C))



balance(rcomp(Y),~A/B/C)
balance(aplus(Y),~A/B/C)
balance(rplus(Y),~A/B/C)

Description

Compositions and amounts dispalyed as bar plots.

Usage

## S3 method for class 'acomp'
barplot(height,...,legend.text=TRUE,beside=FALSE,total=1,
plotMissings=TRUE,missingColor="red",missingPortion=0.01)
## S3 method for class 'rcomp'
barplot(height,...,legend.text=TRUE,beside=FALSE,total=1,
plotMissings=TRUE,missingColor="red",missingPortion=0.01)
## S3 method for class 'aplus'
barplot(height,...,legend.text=TRUE,beside=TRUE,total=NULL,
plotMissings=TRUE,missingColor="red",missingPortion=0.01)
## S3 method for class 'rplus'
barplot(height,...,legend.text=TRUE,beside=TRUE,total=NULL,
plotMissings=TRUE,missingColor="red",missingPortion=0.01)
## S3 method for class 'ccomp'
barplot(height,...,legend.text=TRUE,beside=FALSE,total=1,
plotMissings=TRUE,missingColor="red",missingPortion=0.01)

Arguments

Details

These functions are essentially light-weighted wrappers for barplot, just adding an adequate default behavior for each of the scales. The missingplot functionality will work well with the default settings.

If plotMissings is true, there will be an additional portion introduced, which is not counted in the total. This might make the plots looking less nice, however they make clear to the viewer that it is by no means clear how the rest of the plot should be interpreted and that the missing value really casts some unsureness on the rest of the data.

Value

A numeric vector (or matrix, when beside = TRUE) giving the coordinates of all the bar midpoints drawn, as in barplot

Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

See Also

acomp, rcomp, rplus aplus, plot.acomp, boxplot.acomp

Examples

data(SimulatedAmounts)
barplot(mean(acomp(sa.lognormals[1:10,])))
barplot(mean(rcomp(sa.lognormals[1:10,])))
barplot(mean(aplus(sa.lognormals[1:10,])))
barplot(mean(rplus(sa.lognormals[1:10,])))

barplot(acomp(sa.lognormals[1:10,]))
barplot(rcomp(sa.lognormals[1:10,]))
barplot(aplus(sa.lognormals[1:10,]))
barplot(rplus(sa.lognormals[1:10,]))

barplot(acomp(sa.tnormals))

Description

Relation of mechanical properties of a new fibreboard with its composition

Usage

data(Bayesite)

Details

In the development of bayesite, a new fibreboard, experiments were conducted to obtain some insight into the nature of the relationship of its permeability to the mix of its four ingredients

and the pressure of which these are bonded. The results of 21 such experiments are reported. It is required to investigate the dependence of permeability of mixture and bonding pressure.

All 4-part compositions sum to one.

Note

Courtesy of J. Aitchison

Source

Aitchison: CODA microcomputer statistical package, 1986, the file name BAYESITE.DAT, here included under the GNU Public Library Licence Version 2 or newer.

References

Aitchison: The Statistical Analysis of Compositional Data, 1986, Data 21, pp21.

Description

Allows the access to individual digits in binary (and general g-adic) numbers.

Usage

binary(x,mb=max(maxBit(x,g)),g=2)
unbinary(x,g=2)
bit(x,b,g=2)                       
## S3 method for class 'numeric'
bit(x,b=0:maxBit(x,g),g=2)
## S3 method for class 'character'
bit(x,b=0:maxBit(x,g),g=2)
bit(x,b,g=2) <- value                      
## S3 replacement method for class 'numeric'
bit(x,b=0:maxBit(x,g),g=2) <- value
## S3 replacement method for class 'character'
bit(x,b=0:maxBit(x,g),g=2) <- value
maxBit(x,g=2)
## S3 method for class 'numeric'
maxBit(x,g=2)
## S3 method for class 'character'
maxBit(x,g=2)
bitCount(x,mb=max(maxBit(x,g)),g=2)
gsi.orSum(...,g=2)
whichBits(x,mb=max(maxBit(x,g)),g=2,values=c(TRUE))
binary2logical(x,mb=max(maxBit(x,g)),g=2,values=c(TRUE))

Arguments

Details

These routines are primerily intended to manipulate g-adic numbers for user interface purposes and condensed representation of information. They are not intended for a long number arithmetic.

Value

Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

See Also

outlierplot

Examples

(x<-unbinary("10101010"))
(y<-binary(x))
bit(x,1:3)
bit(y,0:3)
maxBit(x)
maxBit(y)
whichBits(x)
whichBits(y)
binary2logical(y)
bit(x) 
bit(y) 
gsi.orSum(y,1)
bitCount(x)
bitCount(y)
bit(x,2)<-1
x
bit(y,2)<-1
y

Description

Plots variables and cases in the same plot, based on a principal component analysis.

Usage

biplot3D(x,...)
## Default S3 method:
biplot3D(x,y,var.axes=TRUE,col=c("green","red"),cex=c(2,2),
            xlabs = NULL, ylabs = NULL, expand = 1,arrow.len = 0.1,
            ...,add=FALSE)
 ## S3 method for class 'princomp'
biplot3D(x,choices=1:3,scale=1,...,
            comp.col=1,comp.labs=paste("Comp.",1:3),
            scale.scores=lambda[choices]^(1-scale),
            scale.var=scale.comp, scale.comp=sqrt(lambda[choices]), 
            scale.disp=1/scale.comp)

Arguments

Details

This "biplot" is a triplot, relating data, variables and principal components. The relative scaling of the components is still experimental, meant to mimic the behavior of classical biplots.

Value

the 3D plotting coordinates of the tips of the arrows of the variables displayed, returned invisibly

Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

See Also

gsi

Examples

data(SimulatedAmounts)
pc <- princomp(acomp(sa.lognormals5))
pc
summary(pc)
plot(pc)      #plot(pc,type="screeplot")
biplot(pc)
if(requireNamespace("rgl", quietly = TRUE)) {
  biplot3D(pc)
} ## this function requires package 'rgl'

Description

Percentage of different leukocytes in blood samples of ten patients, determined by four different methods.

Usage

data(Blood23)

Details

In a comparative study of four different methods of assessing leukocytes composition of a blood sample, aliquots of blood samples from ten patients were assessed by the four methods. Data show the percentage in the 40 analyses of:

All rows sum to 100.

Note

Courtesy of J. Aitchison

Source

Aitchison: CODA microcomputer statistical package, 1986, the file name BLOOD.DAT, here included under the GNU Public Library Licence Version 2 or newer.

References

Aitchison: The Statistical Analysis of Compositional Data, 1986, Data 23, pp22.

Description

A mineral compositions of 25 rock specimens of boxite type. Each composition consists of the percentage by weight of five minerals, albite, blandite, cornite, daubite, endite, as well as the depth of location.

Usage

data(Boxite)

Details

A mineral compositions of 25 rock specimens of boxite type are given. Each composition consists of the percentage by weight of five minerals, albite, blandite, cornite, daubite, endite, and the recorded depth of location of each specimen. We abbreviate the minerals names to A, B, C, D, E.

All row percentage sums to 100, except the 6-th 102.3 and the 10-th 99.9.

Note

Courtesy of J. Aitchison

Source

Aitchison: CODA microcomputer statistical package, 1986, the file name BOXITE.DAT, here included under the GNU Public Library Licence Version 2 or newer.

References

Aitchison: The Statistical Analysis of Compositional Data, 1986, Data 3, pp4.

Description

For the different interpretations of amounts or compositional data, a different type of boxplot is feasible. Thus different boxplots are drawn.

Usage

## S3 method for class 'acomp'
boxplot(x,fak=NULL,...,
                         xlim=NULL,ylim=NULL,log=TRUE,
                         panel=vp.logboxplot,dots=!boxes,boxes=TRUE,
                          notch=FALSE,
                          plotMissings=TRUE,
                          mp=~simpleMissingSubplot(missingPlotRect,
                                                missingInfo,c("NM","TM",cn))
                          )
## S3 method for class 'rcomp'
boxplot(x,fak=NULL,...,
                         xlim=NULL,ylim=NULL,log=FALSE,
                         panel=vp.boxplot,dots=!boxes,boxes=TRUE,
                          notch=FALSE,
                          plotMissings=TRUE,
                          mp=~simpleMissingSubplot(missingPlotRect,
                                                missingInfo,c("NM","TM",cn)))
## S3 method for class 'aplus'
boxplot(x,fak=NULL,...,log=TRUE,
                          plotMissings=TRUE,
                          mp=~simpleMissingSubplot(missingPlotRect,
                                                   missingInfo,
                                                   names(missingInfo)))
## S3 method for class 'rplus'
boxplot(x,fak=NULL,...,ylim=NULL,log=FALSE,
                          plotMissings=TRUE,
                          mp=~simpleMissingSubplot(missingPlotRect,
                                                   missingInfo,
                                                   names(missingInfo)))
vp.boxplot(x,y,...,dots=FALSE,boxes=TRUE,xlim=NULL,ylim=NULL,log=FALSE,
                          notch=FALSE,plotMissings=TRUE,
                          mp=~simpleMissingSubplot(missingPlotRect,
                                                   missingInfo,c("NM","TM",cn)),
                          missingness=attr(y,"missingness") ) 
vp.logboxplot(x,y,...,dots=FALSE,boxes=TRUE,xlim,ylim,log=TRUE,notch=FALSE,
                          plotMissings=TRUE, 
                          mp=~simpleMissingSubplot(missingPlotRect,
                                                   missingInfo,c("NM","TM",cn)),
                          missingness=attr(y,"missingness"))

Arguments

Details

boxplot.aplus and boxplot.rplus are wrappers of bxp, which just take into account the possible logarithmic scale of the data.

boxplot.acomp and boxplot.rcomp generate a matrix of box-plots, where each cell represents the difference between the row and column variables. Such difference is respectively computed as a log-ratio and a rest.

vp.boxplot and vp.logboxplot are only used as panel functions. They should not be directly called.

Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

See Also

plot.acomp, qqnorm.acomp

Examples

data(SimulatedAmounts)
boxplot(acomp(sa.lognormals))
boxplot(rcomp(sa.lognormals))
boxplot(aplus(sa.lognormals))
boxplot(rplus(sa.lognormals))
# And now with missing!!!
boxplot(acomp(sa.tnormals))

Description

A class providing the means to analyse count compositions understood as Poisson or multinomial realisation, where the portions are given by an unkown Aitchison compositions.

Usage

ccomp(X,parts=1:NCOL(oneOrDataset(X)),total=NA,warn.na=FALSE,
            detectionlimit=NULL,BDL=NULL,MAR=NULL,MNAR=NULL,SZ=NULL)

Arguments

Details

A count composition contains an indirect observation of an Aitchison composition by a Poisson or multinomial variable. A count composition can only contain integer counts. It is assumed that the total sum is a an artefact and does not contain information on the actual composition. But it does contain information on the precision of the relative observation.

Value

a vector of class "ccomp" representing count composition or a matrix of class "ccomp" representing multiple count compositions each in one row.

Missing Policy

The policy of treatment of zeroes, missing values and values below detecion limit is explained in depth in compositions.missing.

Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

See Also

barplot.ccomp ccompMultinomialGOF.test ccompPoissonGOF.test cdt.ccomp cdtInv.ccomp fitSameMeanDifferentVarianceModel groupparts.ccomp idt.ccomp idtInv.ccomp is.ccomp mean.ccomp names<-.ccomp names.ccomp plot.ccomp PoissonGOF.test rmultinom.ccomp rnorm.ccomp rpois.ccomp split.ccomp totals.ccomp

Examples

data(SimulatedAmounts)
plot(acomp(sa.lognormals))

Description

The S4-version of the data container "ccomp" for compositional data. More information in ccomp

Objects from the Class

A virtual Class: No objects may be directly created from it. This is provided to ensure that ccomp objects behave as data.frame or structure under certain circumstances. Use ccomp to create these objects.

Slots

.Data:

Object of class "list" containing the data itself

names:

Object of class "character" with column names

row.names:

Object of class "data.frameRowLabels" with row names

.S3Class:

Object of class "character" with the class string

Extends

Class "data.frame", directly. Class "compositional", directly. Class "list", by class "data.frame", distance 2. Class "oldClass", by class "data.frame", distance 2. Class "vector", by class "data.frame", distance 3.

Methods

coerce

signature(from = "ccomp", to = "data.frame"): to generate a data.frame

coerce

signature(from = "ccomp", to = "structure"): to generate a structure (i.e. a vector, matrix or array)

coerce<-

signature(from = "ccomp", to = "data.frame"): to overwrite a composition with a data.frame

Note

see ccomp

Author(s)

Raimon Tolosana-Delgado

References

see ccomp

See Also

see ccomp

Examples

showClass("ccomp")

Description

Goodness of fit tests for count compositional data.

Usage

PoissonGOF.test(x,lambda=mean(x),R=999,estimated=missing(lambda))
ccompPoissonGOF.test(x,simulate.p.value=TRUE,R=1999)
ccompMultinomialGOF.test(x,simulate.p.value=TRUE,R=1999)

Arguments

Details

The compositional goodness of fit testing problem is essentially a multivariate goodness of fit test. However there is a lack of standardized multivariate goodness of fit tests in R. Some can be found in the energy-package.

In principle there is only one test behind the Goodness of fit tests provided here, a two sample test with test statistic.

$\frac{\sum_{ij} k(x_i,y_i)}{\sqrt{\sum_{ij} k(x_i,x_i)\sum_{ij} k(y_i,y_i)}}$

The idea behind that statistic is to measure the cos of an angle between the distributions in a scalar product given by

$(X,Y)=E[k(X,Y)]=E[\int K(x-X)K(x-Y) dx]$

where k and K are Gaussian kernels with different spread. The bandwith is actually the standarddeviation of k.
The other goodness of fit tests against a specific distribution are based on estimating the parameters of the distribution, simulating a large dataset of that distribution and apply the two sample goodness of fit test.

Value

A classical "htest" object

Missing Policy

Up to now the tests can not handle missings.

Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

References

Aitchison, J. (1986) The Statistical Analysis of Compositional Data Monographs on Statistics and Applied Probability. Chapman & Hall Ltd., London (UK). 416p.

See Also

fitDirichlet,rDirichlet, runif.acomp, rnorm.acomp,

Examples

## Not run: 
x <- runif.acomp(100,4)
y <- runif.acomp(100,4)

erg <- acompGOF.test(x,y)
#continue
erg
unclass(erg)
erg <- acompGOF.test(x,y)


x <- runif.acomp(100,4)
y <- runif.acomp(100,4)
dd <- replicate(1000,acompGOF.test(runif.acomp(100,4),runif.acomp(100,4))$p.value)
hist(dd)

dd <- replicate(1000,acompGOF.test(runif.acomp(20,4),runif.acomp(100,4))$p.value)
hist(dd)
dd <- replicate(1000,acompGOF.test(runif.acomp(10,4),runif.acomp(100,4))$p.value)

hist(dd)
dd <- replicate(1000,acompGOF.test(runif.acomp(10,4),runif.acomp(400,4))$p.value)
hist(dd)
dd <- replicate(1000,acompGOF.test(runif.acomp(400,4),runif.acomp(10,4),bandwidth=4)$p.value)
hist(dd)


dd <- replicate(1000,acompGOF.test(runif.acomp(20,4),runif.acomp(100,4)+acomp(c(1,2,3,1)))$p.value)

hist(dd)


x <- runif.acomp(100,4)
acompUniformityGOF.test(x)

dd <- replicate(1000,acompUniformityGOF.test(runif.acomp(10,4))$p.value)

hist(dd)


## End(Not run)

Description

Compute the centered default transform of a (data set of) compositions or amounts (or its inverse).

Usage

cdt(x,...)
          ## Default S3 method:
cdt( x ,...)
          ## S3 method for class 'acomp'
cdt( x ,...)
          ## S3 method for class 'rcomp'
cdt( x ,...)
          ## S3 method for class 'aplus'
cdt( x ,...)
          ## S3 method for class 'rplus'
cdt( x ,...)
          ## S3 method for class 'rmult'
cdt( x ,...)
          ## S3 method for class 'ccomp'
cdt( x ,...)
          ## S3 method for class 'factor'
cdt( x ,...)
          ## S3 method for class 'data.frame'
cdt( x ,...)
          cdtInv(x,orig=gsi.orig(x),...)
          ## Default S3 method:
cdtInv( x ,orig=gsi.orig(x),...)
          ## S3 method for class 'acomp'
cdtInv( x ,orig=gsi.orig(x),...)
          ## S3 method for class 'rcomp'
cdtInv( x ,orig=gsi.orig(x),...)
          ## S3 method for class 'aplus'
cdtInv( x ,orig=gsi.orig(x),...)
          ## S3 method for class 'rplus'
cdtInv( x ,orig=gsi.orig(x),...)
          ## S3 method for class 'rmult'
cdtInv( x ,orig=gsi.orig(x),...)
          ## S3 method for class 'ccomp'
cdtInv( x ,orig=gsi.orig(x),...)
          ## S3 method for class 'factor'
cdtInv( x ,orig=gsi.orig(x),...)
          ## S3 method for class 'data.frame'
cdtInv( x ,orig=gsi.orig(x),...)

Arguments

Details

The general idea of this package is to analyse the same data with different geometric concepts, in a fashion as similar as possible. For each of the four concepts there exists a unique transform expressing the geometry in a linear subspace, keeping the relation to the variables. This unique transformation is computed by cdt. For acomp the transform is clr, for rcomp it is cpt, for aplus it is ilt, and for rplus it is iit. Each component of the result is identified with a unit vector in the direction of the corresponding component of the original composition or amount. Keep in mind that the transform is not necessarily surjective and thus variances in the image space might be singular.

Value

A corresponding matrix or vector containing the transforms. (Exception: cdt.data.frame can return a data.frame if the input has no "origClass"-attribute)

Author(s)

R. Tolosana-Delgado, K.Gerald v.d. Boogaart http://www.stat.boogaart.de

References

van den Boogaart, K.G. and R. Tolosana-Delgado (2008) "compositions": a unified R package to analyze Compositional Data, Computers & Geosciences, 34 (4), pages 320-338, doi:10.1016/j.cageo.2006.11.017.

See Also

backtransform, idt, clr, cpt, ilt, iit

Examples

## Not run: 
# the cdt is defined by
cdt         <- function(x) UseMethod("cdt",x)
cdt.default <- function(x) x
cdt.acomp   <- clr 
cdt.rcomp   <- cpt 
cdt.aplus   <- ilt 
cdt.rplus   <- iit 

## End(Not run)
x <- acomp(1:5)
(ds <- cdt(x))
cdtInv(ds,x)
(ds <- cdt(rcomp(1:5)))
cdtInv(ds,rcomp(x))
  data(Hydrochem)
  x = Hydrochem[,c("Na","K","Mg","Ca")]
  y = acomp(x)
  z = cdt(y)
  y2 = cdtInv(z,y)
  par(mfrow=c(2,2))
  for(i in 1:4){plot(y[,i],y2[,i])}

Description

From East Bay, 20 clam colonies were randomly selected and from each a sample of clams were taken. Each sample was sieved into three size ranges, large, medium, and small. Then each size range was sorted by the shale colour, dark or light.

Usage

data(ClamEast)

Details

The data consist of 20 cases and $2\times 3$ variables denoted:

All 6-part compositions sum to one, except for rounding errors.

Note

Courtesy of J. Aitchison

Source

Aitchison: CODA microcomputer statistical package, 1986, the file name CLAMEAST.DAT, here included under the GNU Public Library Licence Version 2 or newer.

References

Aitchison: The Statistical Analysis of Compositional Data, 1986, Data 14, pp18.

Description

From West Bay, 20 clam colonies were randomly selected, and from each a sample of clams were taken. Each sample was sieved into three size ranges, large, medium, and small. Then each size range was sorted by the shale colour, dark or light.

Usage

data(ClamWest)

Details

The data consist of 20 cases and $2\times 3$ variables denoted:

All 6-part compositions sum up to one.

Note

Courtesy of J. Aitchison

Source

Aitchison: CODA microcomputer statistical package, 1986, the file name CLAMWEST.DAT, here included under the GNU Public Library Licence Version 2 or newer.

References

Aitchison: The Statistical Analysis of Compositional Data, 1986, Data 15, pp17.

Description

Closes compositions to sum up to one (or an optional total), by dividing each part by the sum.

Usage

clo( X, parts=1:NCOL(oneOrDataset(X)),total=1,
               detectionlimit=attr(X,"detectionlimit"),
               BDL=NULL,MAR=NULL,MNAR=NULL,SZ=NULL,
               storelimit=!is.null(attr(X,"detectionlimit"))
               )

Arguments

Details

The closure operation is given by

$clo(x) := \left(x_i / \sum_{j=1}^D x_j\right)$

clo generates a composition without assigning one of the compositional classes acomp or rcomp. Note that after computing the closed-to-one version, obtaining a version closed to any other value is done by simple multiplication.

Value

a composition or a data matrix of compositions, maybe without compositional class. The individual compositions are forced to sum to 1 (or to the optionally-specified total). The result should have the same shape as the input (vector, row, matrix).

Missing Policy

How missing values are coded in the output always follows the general rules described in compositions.missing. The BDL values are accordingly scaled during the scaling operations but not taken into acount for the calculation of the total sum.

Note

clo can be used to unclass compositions.

Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de, Raimon Tolosana-Delgado

References

Aitchison, J. (1986) The Statistical Analysis of Compositional Data Monographs on Statistics and Applied Probability. Chapman & Hall Ltd., London (UK). 416p.

See Also

clr,acomp,rcomp

Examples

(tmp <- clo(c(1,2,3)))
clo(tmp,total=100)
data(Hydrochem)
plot( clo(Hydrochem,8:9) ) # Giving points on a line

Description

Compute the centered log ratio transform of a (dataset of) composition(s) and its inverse.

Usage

clr( x,... )
          clrInv( z,..., orig=gsi.orig(z) )

Arguments

Details

The clr-transform maps a composition in the D-part Aitchison-simplex isometrically to a D-dimensonal euclidian vector subspace: consequently, the transformation is not injective. Thus resulting covariance matrices are always singular.
The data can then be analysed in this transformation by all classical multivariate analysis tools not relying on a full rank of the covariance. See ilr and alr for alternatives. The interpretation of the results is relatively easy since the relation between each original part and a transformed variable is preserved.
The centered logratio transform is given by

$clr(x) := \left(\ln x_i - \frac1D \sum_{j=1}^D \ln x_j\right)_i$

The image of the clr is a vector with entries summing to 0. This hyperplane is also called the clr-plane.

Value

clr gives the centered log ratio transform, clrInv gives closed compositions with the given clr-transform

Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

References

Aitchison, J. (1986) The Statistical Analysis of Compositional Data, Monographs on Statistics and Applied Probability. Chapman & Hall Ltd., London (UK). 416p.

See Also

ilr,alr,apt

Examples

(tmp <- clr(c(1,2,3)))
clrInv(tmp)
clrInv(tmp) - clo(c(1,2,3)) # 0
data(Hydrochem)
cdata <- Hydrochem[,6:19]
pairs(clr(cdata),pch=".")

Description

Compute the centered log ratio transform of a (dataset of) from isometric log-ratio transform(s) and its inverse. Equivalently, compute centered and isometric planar transforms from each other. Acts in vectors and in bilinear forms. For bilinear forms, transform between variation-form from clr-form.

Usage

clr2ilr( x , V=ilrBase(x=x) )
ilr2clr( z , V=ilrBase(z=z), x=gsi.orig(z) )
clrvar2ilr( varx , V=ilrBase(D=ncol(varx)) )
ilrvar2clr( varz , V=ilrBase(D=ncol(varz)+1) ,x=NULL)
clrvar2variation(Sigma)
variation2clrvar(TT)
is.clrvar(M, tol=1e-10)
is.ilrvar(M, tol=1e-10)

Arguments

Details

These functions perform a matrix multiplication with V in an appropriate way.

Value

clr2ilr gives the ilr/ipt transform of the same composition(s),
ilr2clr gives the clr/cpt transform of the same composition(s),
clrvar2ilr gives the variance-/covariance-matrix of the ilr/ipt transform of the same compositional data set,
ilrvar2clr and clrvar2variation give the variance-/covariance-matrix of the clr/cpt transform of the same compositional data set.
variation2clrvar gives the variation matrix from the clr-covariance matrix
is.*var check if the given matrix satisfies the conditions to be an ilr-variance resp. a clr-variance

Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

References

Egozcue J.J., V. Pawlowsky-Glahn, G. Mateu-Figueras and C. Barcel'o-Vidal (2003) Isometric logratio transformations for compositional data analysis. Mathematical Geology, 35(3) 279-300
Aitchison, J, C. Barcel'o-Vidal, J.J. Egozcue, V. Pawlowsky-Glahn (2002) A consise guide to the algebraic geometric structure of the simplex, the sample space for compositional data analysis, Terra Nostra, Schriften der Alfred Wegener-Stiftung, 03/2003

See Also

variation, ilr, ipt, clr, cpt

Examples

data(SimulatedAmounts)
ilrInv(clr2ilr(clr(sa.lognormals)))-clo(sa.lognormals)
clrInv(ilr2clr(ilr(sa.lognormals)))-clo(sa.lognormals)
ilrvar2clr(var(ilr(sa.lognormals)))-var(clr(sa.lognormals))
clrvar2ilr(var(cpt(sa.lognormals)))-var(ipt(sa.lognormals))
variation(acomp(sa.lognormals))
clrvar2variation(var(acomp(sa.lognormals)))

Description

The ClusterFinder is a heuristic to find subpopulations of outliers essentially by looking for secondary modes in a density estimate.

Usage

ClusterFinder1(X,...)
## S3 method for class 'acomp'
ClusterFinder1(X,...,sigma=0.3,radius=1,asig=1,minGrp=3,
                                 robust=TRUE)

Arguments

Details

See outliersInCompositions for a comprehensive introduction into the outlier treatment in compositions.
The ClusterFinder is labeled with a number to make clear that this is just an implementation of some heuristic and not based on some eternal truth. Other might give better Clusterfinders.
Unlike other Clustering Algorithms the basic model of this algorithm assumes that there is one dominating subpopulation and an unkown number of smaller subpopulations with a similar covariance structure but a different mean. The algorithm thus first estimates the covariance structure of the main population by a robust location scale estimator. Then it uses a simplified (Gaussian) kernel density estimator to find nonrandom secondary modes. The it tries to a assign the different observations according to discrimination analysis model to the different modes. Groups under a given size are considered as single outliers forming a seperate group. In this way the number of clusters is kept low even if there are many erratic measurements in the dataset.
The main use of the clusters is descriptive plotting. The advantage of these cluster against other cluster techniques like k-mean or hclust is that it does not tear appart the central mass of the data, as these methods do to make the clusters as compact as possible.

Value

A list

Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

See Also

hclust, kmeans

Examples

data(SimulatedAmounts)
  cl <- ClusterFinder1(sa.outliers5,sigma=0.4,radius=1) 
  plot(sa.outliers5,col=as.numeric(cl$types),pch=as.numeric(cl$types))
  legend(1,1,legend=levels(cl$types),xjust=1,col=1:length(levels(cl$types)),
                     pch=1:length(levels(cl$types)))

Description

Function for plotting CoDa-dendrograms of acomp or rcomp objects.

Usage

CoDaDendrogram(X, V = NULL, expr=NULL, mergetree = NULL, signary = NULL, 
    range = c(-4,4), ..., xlim = NULL, ylim = NULL, yaxt = NULL, box.pos = 0,
    box.space = 0.25, col.tree = "black", lty.tree = 1, lwd.tree = 1,
    col.leaf = "black", lty.leaf = 1, lwd.leaf = 1, add = FALSE,border=NULL,
    type = "boxplot")

Arguments

Details

The object and an isometric basis are represented in a CoDa-dendrogram, as defined by Egozcue and Pawlowsky-Glahn (2005). This is a representation of the following elements:

a

a hierarchical partition (which can be specified either through an ilrBase matrix (see ilrBase), a merging tree structure (see hclust) or a signary matrix (see gsi.merge2signary))

b

the sample mean of each coordinate of the ilr basis associated to that partition

c

the sample variance of each coordinate of the ilr basis associated to that partition

d

optionally (potentially!), any graphical representation of each coordinate, as long as this representation is suitable for a univariate data set (box-plot, histogram, dispersion and kernel density are programmed or intended to, but any other may be added with little work).

Each coordinate is represented in a horizontal axis, which limits correspond to the values given in the parameter range. The vertical bar going up from each one of these coordinate axes represent the variance of that specific coordinate, and the contact point the coordinate mean. Note that to be able to represent an initial dendrogram, the first call to this function must be given a full data set, as means and variances must be computed. This information is afterwards stored in a global list, to add any sort of new material to all coordinates.
The default option is type="boxplot", which produces a box-plot for each coordinate, customizable using box.pos and box.space, as well as typical par parameters (col, border, lty, lwd, etc.). To obtain only the first three aspects, the function must be called with type="lines". As extensions, one might represent a single datum/few data (e.g., a mean or a random subsample of the data set) calling the function with add=TRUE and type="points". Other options (calling functions histogram or density, and admitting their parameters) will be also soon available.
Note that the original coda-dendrogram as defined by Egozcue and Pawlowsky-Glahn (2005) works with acomp objects and ilr bases. Functionality is extended to rcomp objects using calls to idt.

Author(s)

Raimon Tolosana-Delgado, K.Gerald v.d. Boogaart http://www.stat.boogaart.de

References

Egozcue J.J., V. Pawlowsky-Glahn, G. Mateu-Figueras and C. Barcel'o-Vidal (2003) Isometric logratio transformations for compositional data analysis. Mathematical Geology, 35(3) 279-300

Egozcue, J.J. and V. Pawlowsky-Glahn (2005). CoDa-Dendrogram: a new exploratory tool. In: Mateu-Figueras, G. and Barcel\'o-Vidal, C. (Eds.) Proceedings of the 2nd International Workshop on Compositional Data Analysis, Universitat de Girona, ISBN 84-8458-222-1, https://ima.udg.edu/Activitats/CoDaWork05/

See Also

ilrBase,balanceBase, rcomp, acomp,

Examples

# first example: take the data set from the example, select only
# compositional parts
data(Hydrochem)
x = acomp(Hydrochem[,-c(1:5)])
gr = Hydrochem[,4] # river groups (useful afterwards)
# use an ilr basis coming from a clustering of parts
dd = dist(t(clr(x)))
hc1 = hclust(dd,method="ward.D")
plot(hc1)
mergetree=hc1$merge
CoDaDendrogram(X=acomp(x),mergetree=mergetree,col="red",range=c(-8,8),box.space=1)
# add the mean of each river
color=c("green3","red","blue","darkviolet")
aux = sapply(split(x,gr),mean)
aux
CoDaDendrogram(X=acomp(t(aux)),add=TRUE,col=color,type="points",pch=4)

# second example: box-plots by rivers (filled)
CoDaDendrogram(X=acomp(x),mergetree=mergetree,col="black",range=c(-8,8),type="l")
xsplit = split(x,gr)
for(i in 1:4){
 CoDaDendrogram(X=xsplit[[i]],col=color[i],type="box",box.pos=i-2.5,box.space=0.5,add=TRUE)
}

# third example: fewer parts, partition defined by a signary, and empty box-plots
x = acomp(Hydrochem[,c("Na","K","Mg","Ca","Sr","Ba","NH4")])
signary = t(matrix(  c(1,   1,   1,  1,   1,   1,  -1,
                       1,   1,  -1, -1,  -1,  -1,   0,
                       1,  -1,   0,  0,   0,   0,   0,
                       0,   0,  -1,  1,  -1,  -1,   0,
                       0,   0,   1,  0,  -1,   1,   0,
                       0,   0,   1,  0,   0,  -1,   0),ncol=7,nrow=6,byrow=TRUE))

CoDaDendrogram(X=acomp(x),signary=signary,col="black",range=c(-8,8),type="l")
xsplit = split(x,gr)
for(i in 1:4){
  CoDaDendrogram(X=acomp(xsplit[[i]]),border=color[i],
       type="box",box.pos=i-2.5,box.space=1.5,add=TRUE)
  CoDaDendrogram(X=acomp(xsplit[[i]]),col=color[i],
       type="line",add=TRUE)
}

Description

This function generates a simple biplot out of various sources and allows to give color and symbol to the x-objects individually.

Usage

## Default S3 method:
coloredBiplot(x, y, var.axes = TRUE, col, 
         cex = rep(par("cex"), 2), xlabs = NULL, ylabs = NULL, expand=1, 
         xlim = NULL, ylim = NULL, arrow.len = 0.1, main = NULL, sub = NULL, 
         xlab = NULL, ylab = NULL, xlabs.col = NULL, xlabs.bg = NULL, 
         xlabs.pc=NULL, ...)
## S3 method for class 'princomp'
coloredBiplot(x, choices = 1:2, scale = 1, 
         pc.biplot=FALSE, ...)
## S3 method for class 'prcomp'
coloredBiplot(x, choices = 1:2, scale = 1, 
         pc.biplot=FALSE, ...)

Arguments

Details

The functions is provided for convenience.

Value

The function is called only for the side effect of plotting. It is a modification of the standard R routine 'biplot'.

Author(s)

Raimon Tolosana-Delgado, K.Gerald v.d. Boogaart http://www.stat.boogaart.de

See Also

biplot, plot.acomp

Examples

data(SimulatedAmounts)
coloredBiplot(x=princomp(acomp(sa.outliers5)),pc.biplot=FALSE,
          xlabs.pc=c(1,2,3), xlabs.col=2:4, col="black")

Description

Conveniance Functions to generate meaningfull color palettes for factors representing different types of outliers.

Usage

colorsForOutliers1(outfac, family=rainbow,
                          extreme="cyan",outlier="red",ok="gray40",unknown="blue")
colorsForOutliers2(outfac,use=whichBits(gsi.orSum(levels(outfac))),
                        codes=c(2^outer(c(24,16,8),1:7,"-")),ok="yellow")
pchForOutliers1(outfac,ok='.',outlier='\004',extreme='\003',unknown='\004',...,
  other=c('\001','\002','\026','\027','\010','\011','\012','\013','\014','\015',
    '\016',strsplit("abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ","")[[1]])
    )

Arguments

Details

This functions are provided for coveniance to quickly generate a palette of reasonable colors or plotting chars for groups of outliers classified by OutlierClassifier1.

Value

a character vector of colors or a numeric vector of plot chars.

Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

See Also

OutlierClassifier1

Examples

## Not run: 
data(SimulatedAmounts)
data5 <- acomp(sa.outliers5)
olc <- OutlierClassifier1(data5)
plot(data5,col=colorsForOutliers1(olc)[olc])
olc <- OutlierClassifier1(data5,type="all")
plot(data5,col=colorsForOutliers2(olc)[olc])

## End(Not run)

Description

Creates a Variogram model according to the linear model of spatial corregionalisation for a compositional geostatistical analysis.

Usage

CompLinModCoReg(formula,comp,D=ncol(comp),envir=environment(formula))

Arguments

Details

The linear model of coregionalisation uses the fact that sums of valid variogram models are valid variograms, and that scalar variograms multiplied with a positive definite matrix are valid variograms for vector-valued random functions.

This command computes such a variogram function from a formal description, via a formula without left-hand side. The right-hand side of the formula is a sum. Each summand is either a product of a matrix description and a scalar variogram description or only a scalar variogram description. Scalar variogram descriptions are either formal function calls to

sph(range)

for spherical variogram with range range

exp(range)

for an exponential variogram with effective range range

gauss(range)

for a Gaussian variogram with effective range range

gauss(range)

for a cardinal sine variogram with range parameter range

pow(range)

for an power variogram with range parameter range

lin(unit)

linear variogram 1 at unit.

nugget()

for adding a nuggeteffect.

Alternatively it can be any expression, which will be evaluated in envir and should depende on a dataset of distantce vectrs h. An effective range is that distance at which one reaches the sill (for spherical) of 95% of its values (for all other models). Parametric ranges are given for those models that do not have an effective range formula.
The matrix description always comes first. It can be R1 for a rank 1 matrix; PSD for a Positive Semidefinite matrix; \(S\) for a scalar Sill factor to be multiplied with the identity matrix; or any other construct evaluating to a matrix, like e.g. a function of some parameters with default values, that if called is evaluated to a positive semidefinite matrix. R1 and PSD can also be written as calls providing a vector or respectively a matrix providing the parameter.
The variogram is created with default parameter values. The parameters can later be modified by modifiying the default parameter with assignments like formals(vg)$sPSD1 = parameterPosdefMat(4*diag(5)). We would anyway expect you to fit the model to the data by a command like fit.lmc(logratioVariogram(...),CompLinModCoReg(...))

Value

A variogram function, with the extra class "CompLinModCoReg".

Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

References

What to cite??

See Also

vgram2lrvgram, vgmFit2lrv

Examples

## Not run: 
data(juraset)
X <- with(juraset,cbind(X,Y))
comp <- acomp(juraset,c("Cd","Cu","Pb","Co","Cr"))
CompLinModCoReg(~nugget()+sph(0.5)+R1*exp(0.7),comp)
CompLinModCoReg(~nugget()+R1*sph(0.5)+R1*exp(0.7)+(0.3*diag(5))*gauss(0.3),comp)
CompLinModCoReg(~nugget()+R1*sph(0.5)+R1(c(1,2,3,4,5))*exp(0.7),comp)

## End(Not run)

Description

Geostatistical prediction for compositional data with missing values.

Usage

compOKriging(comp,X,Xnew,vg,err=FALSE)

Arguments

Details

The function performes multivariate ordinary kriging of compositions based on transformes addapted to the missings in every case. The variogram is assumed to be a clr variogram.

Value

A list of class "logratioVariogram"

Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

References

Pawlowsky-Glahn, Vera and Olea, Ricardo A. (2004) Geostatistical Analysis of Compositional Data, Oxford University Press, Studies in Mathematical Geology

Tolosana (2008) ...

Tolosana, van den Boogaart, Pawlowsky-Glahn (2009) Estimating and modeling variograms of compositional data with occasional missing variables in R, StatGis09

See Also

vgram2lrvgram, CompLinModCoReg, vgmFit

Examples

## Not run: 
# Load data
data(juraset)
X <- with(juraset,cbind(X,Y))
comp <- acomp(juraset,c("Cd","Cu","Pb","Co","Cr"))
lrv <- logratioVariogram(comp,X,maxdist=1,nbins=10)
plot(lrv)

# Fit a variogram model
vgModel <- CompLinModCoReg(~nugget()+sph(0.5)+R1*exp(0.7),comp)
fit <- vgmFit2lrv(lrv,vgModel)
fit
plot(lrv,lrvg=vgram2lrvgram(fit$vg))

# Define A grid
x <- (0:10/10)*6
y <- (0:10/10)*6
Xnew <- cbind(rep(x,length(y)),rep(y,each=length(x)))

# Kriging
erg <- compOKriging(comp,X,Xnew,fit$vg,err=FALSE)
par(mar=c(0,0,1,0))
pairwisePlot(erg$Z,panel=function(a,b,xlab,ylab) {image(x,y,
                     structure(log(a/b),dim=c(length(x),length(y))),
                     main=paste("log(",xlab,"/",ylab,")",sep=""));points(X,pch=".")})


# Check interpolation properties 
ergR <- compOKriging(comp,X,X,fit$vg,err=FALSE)
pairwisePlot(ilr(comp),ilr(ergR$Z))
ergR <- compOKriging(comp,X,X+1E-7,fit$vg,err=FALSE)
pairwisePlot(ilr(comp),ilr(ergR$Z))
ergR <- compOKriging(comp,X,X[rev(1:31),],fit$vg,err=FALSE)
pairwisePlot(ilr(comp)[rev(1:31),],ilr(ergR$Z))

## End(Not run)