Package 'ca' reference manual

Title:	Simple, Multiple and Joint Correspondence Analysis
Description:	Computation and visualization of simple, multiple and joint correspondence analysis.
Authors:	Michael Greenacre [aut], Oleg Nenadic [aut, cre], Michael Friendly [ctb]
Maintainer:	Oleg Nenadic <[email protected]>
License:	GPL
Version:	0.71.1
Built:	2024-10-31 22:26:11 UTC
Source:	CRAN

Author dataset

Description

This data matrix contains the counts of the 26 letters of the alphabet (columns of matrix) for 12 different novels (rows of matrix). Each row contains letter counts in a sample of text from each work, excluding proper nouns.

Usage

data("author")data("author")

Format

Data frame containing the 12 x 26 matrix.

Source

Larsen, W.A. and McGill, R., unpublished data collected in 1973.

Simple correspondence analysis

Description

Computation of simple correspondence analysis.

Usage

ca(obj, ...)

## S3 method for class 'matrix'
ca(obj, nd = NA, suprow = NA, supcol = NA, 
   subsetrow = NA, subsetcol = NA, ...)

## S3 method for class 'data.frame'
ca(obj, ...)

## S3 method for class 'table'
ca(obj, ...)

## S3 method for class 'xtabs'
ca(obj, ...)

## S3 method for class 'formula'
ca(formula, data, ...)

ca(obj, ...)

## S3 method for class 'matrix'
ca(obj, nd = NA, suprow = NA, supcol = NA, 
   subsetrow = NA, subsetcol = NA, ...)

## S3 method for class 'data.frame'
ca(obj, ...)

## S3 method for class 'table'
ca(obj, ...)

## S3 method for class 'xtabs'
ca(obj, ...)

## S3 method for class 'formula'
ca(formula, data, ...)

Arguments

`obj`, `formula`	The function is generic, accepting various forms of the principal argument for specifying a two-way frequency table. Currently accepted forms are matrices, data frames (coerced to frequency tables), objects of class `"xtabs"` or `"table"` and one-sided formulae of the form `~ F1 + F2`, where `F1` and `F2` are factors.
`nd`	Number of dimensions to be included in the output; if NA the maximum possible dimensions are included.
`suprow`	Indices of supplementary rows.
`supcol`	Indices of supplementary columns.
`subsetrow`	Row indices of subset.
`subsetcol`	Column indices of subset.
`data`	A data frame against which to preferentially resolve variables in the `formula`
`...`	Other arguments passed to the `ca.matrix` method

Details

The function ca computes a simple correspondence analysis based on the singular value decomposition.
The options suprow and supcol allow supplementary (passive) rows and columns to be specified. Using the options subsetrow and/or subsetcol result in a subset CA being performed.

Value

`sv`	Singular values
`nd`	Dimenson of the solution
`rownames`	Row names
`rowmass`	Row masses
`rowdist`	Row chi-square distances to centroid
`rowinertia`	Row inertias
`rowcoord`	Row standard coordinates
`rowsup`	Indices of row supplementary points
`colnames`	Column names
`colmass`	Column masses
`coldist`	Column chi-square distances to centroid
`colinertia`	Column inertias
`colcoord`	Column standard coordinates
`colsup`	Indices of column supplementary points
`N`	The frequency table

References

Nenadic, O. and Greenacre, M. (2007). Correspondence analysis in R, with two- and three-dimensional graphics: The ca package. Journal of Statistical Software, 20 (3), http://www.jstatsoft.org/v20/i03/

Greenacre, M. (2007). Correspondence Analysis in Practice. Second Edition. London: Chapman & Hall / CRC. Blasius, J. and Greenacre, M. J. (1994), Computation of correspondence analysis, in Correspondence Analysis in the Social Sciences, pp. 53-75, London: Academic Press.

Greenacre, M.J. and Pardo, R. (2006), Subset correspondence analysis: visualizing relationships among a selected set of response categories from a questionnaire survey. Sociological Methods and Research, 35, pp. 193-218.

Examples

 
data("author")
ca(author)
plot(ca(author))

# table method
haireye <- margin.table(HairEyeColor, 1:2)
haireye.ca <- ca(haireye)
haireye.ca
plot(haireye.ca)
# some plot options
plot(haireye.ca, lines=TRUE)
plot(haireye.ca, arrows=c(TRUE, FALSE))

 data("author")
ca(author)
plot(ca(author))

# table method
haireye <- margin.table(HairEyeColor, 1:2)
haireye.ca <- ca(haireye)
haireye.ca
plot(haireye.ca)
# some plot options
plot(haireye.ca, lines=TRUE)
plot(haireye.ca, arrows=c(TRUE, FALSE))

Converting data types in CA and MCA

Description

Conversion from and to a number of different data types commonly used in CA and MCA (frequency tables, response pattern matrices, indicator matrices and Burt matrices).

Usage

caconv(x, from = c("freq", "rpm", "ind", "Burt"), to = c("rpm", "ind", "Burt", "freq"), 
              nlev = NA, vars = c(1,2), ...)caconv(x, from = c("freq", "rpm", "ind", "Burt"), to = c("rpm", "ind", "Burt", "freq"), 
              nlev = NA, vars = c(1,2), ...)

Arguments

`x`	A matrix (two-way frequency table, indicator matrix, or Burt matrix) or data frame (response pattern matrix).
`from`	The type of input data in `x`: a frequency table (`"freq"`), or a response pattern matrix (`"rpm"`), or an indicator matrix (`"ind"`), or a Burt matrix (`"Burt"`).
`to`	The data type into which `x` should be converted.
`nlev`	A vector containing the number of levels for each categorical variable (for `from="ind"` or `from="Burt"`). If `NA`, `nlev` is computed from the data.
`vars`	A vector of length 2 specifying the index of the variables to use for converting to `"freq"` (i.e. to a regular two-way frequency table).
`...`	Further arguments (ignored).

Details

The function caconv converts between data types in CA and MCA. Note that a conversion from from="Burt" to to="ind" or to="rpm" is not supported.

Value

A matrix or data frame containing the converted data (with the type specified in to).

Extracting coordinates from ca and mjca objects.

Description

Extracting standard and principal coordinates as well as various row and column scaling configurations for visual display from ca and mjca objects.

Usage

cacoord(obj, 
               type = c("standard", "principal", 
                        "symmetric", "rowprincipal", "colprincipal", "symbiplot", 
                        "rowgab", "colgab", "rowgreen", "colgreen"), 
               dim  = NA,
               rows = NA,
               cols = NA,
               ...)cacoord(obj, 
               type = c("standard", "principal", 
                        "symmetric", "rowprincipal", "colprincipal", "symbiplot", 
                        "rowgab", "colgab", "rowgreen", "colgreen"), 
               dim  = NA,
               rows = NA,
               cols = NA,
               ...)

Arguments

`obj`	A `ca` or `mjca` object returned by `ca` or `mjca`.
`type`	The type of coordinates to extract (`"standard"` or `"principal"`). The remaining options (`"symmetric"`, ..., `"colgreen"`) return the corresponding row/column coordinate configuration for the map scaling options described in `plot.ca` where the corresponding argument is `map`.
`dim`	The dimensions to return. If `NA`, all available dimensions are returned.
`rows`	Logical indicating whether to return the row coordinates (see below for details).
`cols`	Logical indicating whether to return the column coordinates (see below for details).
`...`	Further arguments (ignored).

Details

The function cacoord returns the standard or principal coordinates of a CA or MCA solution. Additionally, row and column scaling configurations for plotting methods can be computed (see plot.ca for details).
Note that by default row and column coordinates are computed (i.e. for (rows=NA&cols=NA)|(rows=TRUE&cols=TRUE)). Using rows=TRUE (and cols=NA or cols=FALSE) returns a matrix with the row coordinates, and for cols=TRUE (and cols=NA or cols=FALSE) a matrix with the column coordinates is returned.

Value

A list with the slots rows (row coordinates) and columns (column coordinates). When computing only row or only column coordinates, a matrix (with the corresponding row or column coordinates) is returned.

Updating a Burt matrix in Joint Correspondence Analysis

Description

Updating a Burt matrix in Joint Correspondence Analysis based on iteratively weighted least squares.

Usage

iterate.mjca(B, lev.n, nd = 2, maxit = 50, epsilon = 0.0001)iterate.mjca(B, lev.n, nd = 2, maxit = 50, epsilon = 0.0001)

Arguments

`B`	A Burt matrix.
`lev.n`	The number of levels for each factor from the original response pattern matrix.
`nd`	The required dimensionality of the solution.
`maxit`	The maximum number of iterations.
`epsilon`	A convergence criterion for the maximum absolute difference of updated values compared to the previous values. The iteration is completed when all differences are smaller than `epsilon`.

Details

The function iterate.mjca computes the updated Burt matrix. This function is called from the function mjca when the option lambda="JCA", i.e. when a Joint Correspondence Analysis is performed.

Value

`B.star`	The updated Burt matrix
`crit`	Vector of length 2 containing the number of iterations and epsilon

Multiple and joint correspondence analysis

Description

Computation of multiple and joint correspondence analysis.

Usage


mjca(obj, ...)

## S3 method for class 'data.frame'
mjca(obj, ...)
## S3 method for class 'table'
mjca(obj, ...)
## S3 method for class 'array'
mjca(obj, ...)

## Default S3 method:
mjca(obj, nd = 2, lambda = c("adjusted", "indicator", "Burt", "JCA"), 
     supcol = NA, subsetcat = NA, 
     ps = ":", maxit = 50, epsilon = 0.0001, reti = FALSE, ...)

mjca(obj, ...)

## S3 method for class 'data.frame'
mjca(obj, ...)
## S3 method for class 'table'
mjca(obj, ...)
## S3 method for class 'array'
mjca(obj, ...)

## Default S3 method:
mjca(obj, nd = 2, lambda = c("adjusted", "indicator", "Burt", "JCA"), 
     supcol = NA, subsetcat = NA, 
     ps = ":", maxit = 50, epsilon = 0.0001, reti = FALSE, ...)

Arguments

`obj`	A response pattern matrix (data frame containing factors), or a frequency table (a “table” object) or an integer array.
`nd`	Number of dimensions to be included in the output; if NA the maximum possible dimensions are included.
`lambda`	Gives the scaling method. Possible values include `"indicator"`, `"Burt"`, `"adjusted"` and `"JCA"`. Using `lambda = "JCA"` results in a joint correspondence analysis using iterative adjusment of the Burt matrix in the solution space. See Details for descriptions of these options.
`supcol`	Indices of supplementary columns.
`subsetcat`	Indices of subset categories (previously `subsetcol`).
`ps`	Separator used for combining variable and category names.
`maxit`	The maximum number of iterations (Joint Correspondence Analysis).
`epsilon`	A convergence criterion (Joint Correspondence Analysis).
`reti`	Logical indicating whether the indicator matrix should be included in the output.
`...`	Arguments passed to `mjca.default`

Details

The function mjca computes a multiple or joint correspondence analysis based on the eigenvalue decomposition of the Burt matrix. The lambda option selects the scaling variant desired for reporting inertias.

lambda="indicator" gives multiple correspondence analysis based on the correspondence analysis of the indicator matrix, with corresponding inertias (eigenvalues).
lambda="Burt" gives the version of multiple correspondence analysis based on the correspondence analysis of the Burt matrix, the inertias of which are the squares of those for the indicator option.
lambda="adjusted" is the default option, giving improved percentages of inertia based on fitting the off-diagonal submatrices of the Burt matrix by rescaling the multiple correspondence analysis solution. All these first three options give the same standard coordinates of the categories.
lambda="JCA" gives a joint correspondence analysis, which uses an iterative algorithm that optimally fits the off-diagonal submatrices of the Burt matrix. The JCA solution does not have strictly nested dimensions, so the percentage of inertia explained is given for the whole solution of chosen dimensionality, not for each dimension, but this percentage is optimal.

Value

`sv`	Eigenvalues (`lambda = "indicator"`) or singular values (`lambda = "Burt"`, `"adjusted"` or `"JCA"`)
`lambda`	Scaling method
`inertia.e`	Percentages of explained inertia
`inertia.t`	Total inertia
`inertia.et`	Total percentage of explained inertia with the `nd`-dimensional solution
`levelnames`	Names of the factor/level combinations, joined using `ps`
`factors`	A matrix containing the names of the factors and the names of the factor levels
`levels.n`	Number of levels in each factor
`nd`	User-specified dimensionality of the solution
`nd.max`	Maximum possible dimensionality of the solution
`rownames`	Row names
`rowmass`	Row masses
`rowdist`	Row chi-square distances to centroid
`rowinertia`	Row inertias
`rowcoord`	Row standard coordinates
`rowpcoord`	Row principal coordinates
`rowctr`	Row contributions
`rowcor`	Row squared correlations
`colnames`	Column names
`colmass`	Column masses
`coldist`	Column chi-square distances to centroid
`colinertia`	Column inertias
`colcoord`	Column standard coordinates
`colpcoord`	Column principal coordinates
`colctr`	column contributions
`colcor`	Column squared correlations
`colsup`	Indices of column supplementary points (of the Burt and Indicator matrix)
`subsetcol`	Indices of subset columns (`subsetcat`)
`Burt`	Burt matrix
`Burt.upd`	The updated Burt matrix (JCA only)
`subinertia`	Inertias of sub-matrices
`JCA.iter`	Vector of length two containing the number of iterations and the epsilon (JCA only)
`indmat`	Indicator matrix if `reti` was set to `TRUE`
`call`	Return of `match.call`

References

Nenadic, O. and Greenacre, M. (2007), Correspondence analysis in R, with two- and three-dimensional graphics: The ca package. Journal of Statistical Software, 20 (3), http://www.jstatsoft.org/v20/i03/
Nenadic, O. and Greenacre, M. (2007), Computation of Multiple Correspondence Analysis, with Code in R, in Multiple Correspondence Analysis and Related Methods (eds. M. Greenacre and J. Blasius), Boca Raton: Chapmann & Hall / CRC, pp. 523-551.
Greenacre, M.J. and Pardo, R. (2006), Subset correspondence analysis: visualizing relationships among a selected set of response categories from a questionnaire survey. Sociological Methods and Research, 35, pp. 193-218.

Examples

 
data("wg93")
mjca(wg93[,1:4])

# table input
data(UCBAdmissions)
mjca(UCBAdmissions)
## Not run: plot(mjca(UCBAdmissions))

### Different approaches to multiple correspondence analysis:
# Multiple correspondence analysis based on the indicator matrix:
## Not run: mjca(wg93[,1:4], lambda = "indicator")

# Multiple correspondence analysis based on the Burt matrix:
## Not run: mjca(wg93[,1:4], lambda = "Burt")

# "Adjusted" multiple correspondence analysis (default setting):
## Not run: mjca(wg93[,1:4], lambda = "adjusted")

# Joint correspondence analysis:
## Not run: mjca(wg93[,1:4], lambda = "JCA")


### Subset analysis and supplementary variables:
# Subset analysis:
## Not run: mjca(wg93[,1:4], subsetcat = (1:20)[-seq(3,18,5)])

# Supplementary variables:
## Not run: mjca(wg93, supcol = 5:7)

 data("wg93")
mjca(wg93[,1:4])

# table input
data(UCBAdmissions)
mjca(UCBAdmissions)
## Not run: plot(mjca(UCBAdmissions))

### Different approaches to multiple correspondence analysis:
# Multiple correspondence analysis based on the indicator matrix:
## Not run: mjca(wg93[,1:4], lambda = "indicator")

# Multiple correspondence analysis based on the Burt matrix:
## Not run: mjca(wg93[,1:4], lambda = "Burt")

# "Adjusted" multiple correspondence analysis (default setting):
## Not run: mjca(wg93[,1:4], lambda = "adjusted")

# Joint correspondence analysis:
## Not run: mjca(wg93[,1:4], lambda = "JCA")


### Subset analysis and supplementary variables:
# Subset analysis:
## Not run: mjca(wg93[,1:4], subsetcat = (1:20)[-seq(3,18,5)])

# Supplementary variables:
## Not run: mjca(wg93, supcol = 5:7)

Draw lines for groups distinguished by a factor

Description

This is a convenience function for drawing a set of lines distinguished by the levels of a factor. It can be used to make more attractive plots than available via plot.mjca.

Usage

multilines(XY, group=NULL, which=1:nf, sort=1, type='l', col=palette(), lwd=1, ...) 
multilines(XY, group=NULL, which=1:nf, sort=1, type='l', col=palette(), lwd=1, ...)

Arguments

`XY`	A two-column data frame or matrix
`group`	A factor; a separate line is drawn for each level included in `which`
`which`	An integer vector used to select the factors for which lines are drawn. By default, all lines are drawn.
`sort`	Column of `XY` to sort upon before drawing the line for each group
`type`	Line type: `"l"` for line, `"b"` for line and points
`col`	A vector of colors to be used for the various lines, in the order of the levels in `group`; recycled as necessary.
`lwd`	A vector of line widths to be used for the various lines; recycled as necessary
`...`	Other graphic parameters passed to `lines`, e.g., `lty`

Value

none

Author(s)

Michael Friendly

Examples

if (require(vcd)) {
  data(PreSex, package="vcd")
  presex.mca <- mjca(PreSex)
  res <- plot(presex.mca, labels=0, pch='.', cex.lab=1.2)
  coords <- data.frame(res$cols, presex.mca$factors)      
  nlev <- rle(as.character(coords$factor))$lengths
  fact <- unique(as.character(coords$factor))
  
  cols <- c("blue", "red", "brown", "black")
  lwd <- c(2, 2, 2, 4)
  
  plot(Dim2 ~ Dim1, type='n', data=coords)
  points(coords[,1:2], pch=rep(16:19, nlev), col=rep(cols, nlev), cex=1.2)
  text(coords[,1:2], labels=coords$level, col=rep(cols, nlev), pos=3, cex=1.2, xpd=TRUE)
  
  multilines(coords[, c("Dim1", "Dim2")], group=coords$factor, col=cols, lwd=lwd)
}

if (require(vcd)) {
  data(PreSex, package="vcd")
  presex.mca <- mjca(PreSex)
  res <- plot(presex.mca, labels=0, pch='.', cex.lab=1.2)
  coords <- data.frame(res$cols, presex.mca$factors)      
  nlev <- rle(as.character(coords$factor))$lengths
  fact <- unique(as.character(coords$factor))
  
  cols <- c("blue", "red", "brown", "black")
  lwd <- c(2, 2, 2, 4)
  
  plot(Dim2 ~ Dim1, type='n', data=coords)
  points(coords[,1:2], pch=rep(16:19, nlev), col=rep(cols, nlev), cex=1.2)
  text(coords[,1:2], labels=coords$level, col=rep(cols, nlev), pos=3, cex=1.2, xpd=TRUE)
  
  multilines(coords[, c("Dim1", "Dim2")], group=coords$factor, col=cols, lwd=lwd)
}

Listing the set of available symbols.

Description

A plot of the available symbols for use with the option pch.

Usage

pchlist() pchlist()

Details

This function generates a numbered list of the plotting symbols available for use in the functions plot.ca and plot3d.ca.

Examples

pchlist()
pchlist()

Plotting 2D maps in correspondence analysis

Description

Graphical display of correspondence analysis results in two dimensions

Usage

## S3 method for class 'ca'
plot(x, dim = c(1,2), map = "symmetric", what = c("all", "all"), 
               mass = c(FALSE, FALSE), contrib = c("none", "none"), 
               col = c("blue", "red"), 
               pch = c(16, 21, 17, 24), 
               labels = c(2, 2), 
               arrows = c(FALSE, FALSE), 
               lines = c(FALSE, FALSE), 
               lwd=1,
               xlab = "_auto_", ylab = "_auto_",
               col.lab = c("blue", "red"), ...) ## S3 method for class 'ca'
plot(x, dim = c(1,2), map = "symmetric", what = c("all", "all"), 
               mass = c(FALSE, FALSE), contrib = c("none", "none"), 
               col = c("blue", "red"), 
               pch = c(16, 21, 17, 24), 
               labels = c(2, 2), 
               arrows = c(FALSE, FALSE), 
               lines = c(FALSE, FALSE), 
               lwd=1,
               xlab = "_auto_", ylab = "_auto_",
               col.lab = c("blue", "red"), ...)

Arguments

`x`	Simple correspondence analysis object returned by `ca`
`dim`	Numerical vector of length 2 indicating the dimensions to plot on horizontal and vertical axes respectively; default is first dimension horizontal and second dimension vertical.
`map`	Character string specifying the map type. Allowed options include `"symmetric"` (default) `"rowprincipal"` `"colprincipal"` `"symbiplot"` `"rowgab"` `"colgab"` `"rowgreen"` `"colgreen"`
`what`	Vector of two character strings specifying the contents of the plot. First entry sets the rows and the second entry the columns. Allowed values are `"all"` (all available points, default) `"active"` (only active points are displayed) `"passive"` (only supplementary points are displayed) `"none"` (no points are displayed) The status (active or supplementary) of rows and columns is set in `ca` using the options `suprow` and `supcol`.
`mass`	Vector of two logicals specifying if the mass should be represented by the area of the point symbols (first entry for rows, second one for columns)
`contrib`	Vector of two character strings specifying if contributions (relative or absolute) should be represented by different colour intensities. Available options are `"none"` (contributions are not indicated in the plot). `"absolute"` (absolute contributions are indicated by colour intensities). `"relative"` (relative contributions are indicated by colour intensities). If set to `"absolute"` or `"relative"`, points with zero contribution are displayed in white. The higher the contribution of a point, the closer the corresponding colour to the one specified by the `col` option.
`col`	Vector of length 2 specifying the colours of row and column point symbols, by default blue for rows and red for columns. Colours can be entered in hexadecimal (e.g. `"\#FF0000"`), rgb (e.g. `rgb(1,0,0)`) values or by R-name (e.g. `"red"`).
`pch`	Vector of length 4 giving the type of points to be used for row active and supplementary, column active and supplementary points. See `pchlist` for a list of symbols.
`labels`	Vector of length two specifying if the plot should contain symbols only (`0`), labels only (`1`) or both symbols and labels (`2`). Setting `labels` to `2` results in the symbols being plotted at the coordinates and the labels with an offset.
`arrows`	Vector of two logicals specifying if the plot should contain points (`FALSE`, default) or arrows (`TRUE`). First value sets the rows and the second value sets the columns.
`lines`	Vector of two logicals specifying if the plot should join the points with lines (`FALSE`, default) or arrows (`TRUE`). First value sets the rows and the second value sets the columns.
`lwd`	Line width for `arrows` and `lines`
`xlab`, `ylab`	Labels for horizontal and vertical axes. The default, `"_auto_"` means that the function auto-generates a label of the form `Dimension X (xx.xx %`
`col.lab`	Vector of length 2 specifying the colours of row and column point labels
`...`	Further arguments passed to `plot` and `points`.

Details

The function plot.ca makes a two-dimensional map of the object created by ca with respect to two selected dimensions. By default the scaling option of the map is "symmetric", that is the so-called symmetric map. In this map both the row and column points are scaled to have inertias (weighted variances) equal to the principal inertia (eigenvalue or squared singular value) along the principal axes, that is both rows and columns are in pricipal coordinates. Other options are as follows:

-"rowprincipal" or "colprincipal" - these are the so-called asymmetric maps, with either rows in principal coordinates and columns in standard coordinates, or vice versa (also known as row-metric-preserving or column-metric-preserving respectively). These maps are biplots;

-"symbiplot" - this scales both rows and columns to have variances equal to the singular values (square roots of eigenvalues), which gives a symmetric biplot but does not preserve row or column metrics;

-"rowgab" or "colgab" - these are asymmetric maps (see above) with rows (respectively, columns) in principal coordinates and columns (respectively, rows) in standard coordinates multiplied by the mass of the corresponding point. These are also biplots and were proposed by Gabriel & Odoroff (1990);

-"rowgreen" or "colgreen" - these are similar to "rowgab" and "colgab" except that the points in standard coordinates are multiplied by the square root of the corresponding masses, giving reconstructions of the standardized residuals.

This function has options for sizing and shading the points. If the option mass is TRUE for a set of points, the size of the point symbol is proportional to the relative frequency (mass) of each point. If the option contrib is "absolute" or "relative" for a set of points, the colour intensity of the point symbol is proportional to the absolute contribution of the points to the planar display or, respectively, the quality of representation of the points in the display. To globally resize all the points (and text labels), use par("cex"=) before the plot.

Value

In addition to the side effect of producing the plot, the function invisibly returns the coordinates of the plotted points, a list of two components, with names rows and cols. These can be used to further annotate the plot using base R plotting functions.

References

Gabriel, K.R. and Odoroff, C. (1990). Biplots in biomedical research. Statistics in Medicine, 9, pp. 469-485.
Greenacre, M.J. (1993) Correspondence Analysis in Practice. London: Academic Press.
Greenacre, M.J. (1993) Biplots in correspondence Analysis, Journal of Applied Statistics, 20, pp. 251 - 269.

Examples

data("smoke")

# A two-dimensional map with standard settings
plot(ca(smoke))

# Mass for rows and columns represented by the size of the point symbols
plot(ca(smoke), mass = c(TRUE, TRUE))

# Displaying the column profiles only with masses represented by size of point
# symbols and relative contributions by colour intensity.
# Since the arguments are recycled it is sufficient to give only one argument 
# for mass and contrib.
data("author")
plot(ca(author), what = c("none", "all"), mass = TRUE, contrib = "relative")

data("smoke")

# A two-dimensional map with standard settings
plot(ca(smoke))

# Mass for rows and columns represented by the size of the point symbols
plot(ca(smoke), mass = c(TRUE, TRUE))

# Displaying the column profiles only with masses represented by size of point
# symbols and relative contributions by colour intensity.
# Since the arguments are recycled it is sufficient to give only one argument 
# for mass and contrib.
data("author")
plot(ca(author), what = c("none", "all"), mass = TRUE, contrib = "relative")

Plotting 2D maps in multiple and joint correspondence analysis

Description

Graphical display of multiple and joint correspondence analysis results in two dimensions

Usage

## S3 method for class 'mjca'
plot(x, dim = c(1,2), map = "symmetric", centroids = FALSE, 
     what = c("none", "all"), mass = c(FALSE, FALSE), 
     contrib = c("none", "none"), col = c("#000000", "#FF0000"), 
     pch = c(16, 1, 17, 24), 
     labels = c(2, 2), collabels = c("both", "level", "factor"),
     arrows = c(FALSE, FALSE), xlab = "_auto_", ylab = "_auto_", ...) ## S3 method for class 'mjca'
plot(x, dim = c(1,2), map = "symmetric", centroids = FALSE, 
     what = c("none", "all"), mass = c(FALSE, FALSE), 
     contrib = c("none", "none"), col = c("#000000", "#FF0000"), 
     pch = c(16, 1, 17, 24), 
     labels = c(2, 2), collabels = c("both", "level", "factor"),
     arrows = c(FALSE, FALSE), xlab = "_auto_", ylab = "_auto_", ...)

Arguments

`x`	Multiple or joint correspondence analysis object returned by `mjca`
`dim`	Numerical vector of length 2 indicating the dimensions to plot on horizontal and vertical axes respectively; default is first dimension horizontal and second dimension vertical.
`map`	Character string specifying the map type. Allowed options include `"symmetric"` (default) `"rowprincipal"` `"colprincipal"` `"symbiplot"` `"rowgab"` `"colgab"` `"rowgreen"` `"colgreen"`
`centroids`	Logical indicating if column centroids should be added to the plot
`what`	Vector of two character strings specifying the contents of the plot. First entry sets the rows and the second entry the columns. Allowed values are `"all"` (all available points, default) `"active"` (only active points are displayed) `"passive"` (only supplementary points are displayed) `"none"` (no points are displayed) The status (active or supplementary) of columns is set in `mjca` using the option `supcol`.
`mass`	Vector of two logicals specifying if the mass should be represented by the area of the point symbols (first entry for rows, second one for columns)
`contrib`	Vector of two character strings specifying if contributions (relative or absolute) should be represented by different colour intensities. Available options are `"none"` (contributions are not indicated in the plot). `"absolute"` (absolute contributions are indicated by colour intensities). `"relative"` (relative contributions are indicated by colour intensities). If set to `"absolute"` or `"relative"`, points with zero contribution are displayed in white. The higher the contribution of a point, the closer the corresponding colour to the one specified by the `col` option.
`col`	Vector of length 2 specifying the colours of row and column point symbols, by default black for rows and red for columns. Colours can be entered in hexadecimal (e.g. `"#FF0000"`), rgb (e.g. `rgb(1,0,0)`) values or by R-name (e.g. `"red"`).
`pch`	Vector of length 4 giving the type of points to be used for row active and supplementary, column active and supplementary points. See `pchlist` for a list of symbols.
`labels`	Vector of length two specifying if the plot should contain symbols only (`0`), labels only (`1`) or both symbols and labels (`2`). Setting `labels` to `2` results in the symbols being plotted at the coordinates and the labels with an offset.
`collabels`	Determines the format used for column labels, when the columns are labeled in the plot. `"both"` uses the factor names and level value, in the form `"factor:level"` `"level"` uses the factor level value only `"factor"` uses the factor name only
`arrows`	Vector of two logicals specifying if the plot should contain points (`FALSE`, default) or arrows (`TRUE`). First value sets the rows and the second value sets the columns.
`xlab`, `ylab`	Labels for horizontal and vertical axes. The default, `"_auto_"` means that the function auto-generates a label of the form `Dimension X (xx.xx %)`
`...`	Further arguments passed to `plot` and `points`.

Details

The function plot.mjca makes a two-dimensional map of the object created by mjca with respect to two selected dimensions. By default the scaling option of the map is "symmetric", that is the so-called symmetric map. In this map both the row and column points are scaled to have inertias (weighted variances) equal to the principal inertia (eigenvalue) along the principal axes, that is both rows and columns are in pricipal coordinates. Other options are as follows:

-"rowprincipal" or "colprincipal" - these are the so-called asymmetric maps, with either rows in principal coordinates and columns in standard coordinates, or vice versa (also known as row-metric-preserving or column-metric-preserving respectively). These maps are biplots;

-"symbiplot" - this scales both rows and columns to have variances equal to the singular values (square roots of eigenvalues), which gives a symmetric biplot but does not preserve row or column metrics;

-"rowgab" or "colgab" - these are asymmetric maps (see above) with rows (respectively, columns) in principal coordinates and columns (respectively, rows) in standard coordinates multiplied by the mass of the corresponding point. These are also biplots and were proposed by Gabriel & Odoroff (1990);

-"rowgreen" or "colgreen" - these are similar to "rowgab" and "colgab" except that the points in standard coordinates are multiplied by the square root of the corresponding masses, giving reconstructions of the standardized residuals.

Value

References

Examples

data("wg93")

# A two-dimensional map with standard settings
plot(mjca(wg93[,1:4]))

data("wg93")

# A two-dimensional map with standard settings
plot(mjca(wg93[,1:4]))

Plotting 3D maps in correspondence analysis

Description

Graphical display of correspondence analysis in three dimensions

Usage

## S3 method for class 'ca'
plot3d(x, dim = c(1, 2, 3), map = "symmetric", what = c("all", "all"), 
             contrib = c("none", "none"), col = c("#6666FF","#FF6666"), 
             labcol = c("#0000FF", "#FF0000"), pch = c(16, 1, 18, 9), 
             labels = c(2, 2), sf = 0.00001, arrows  = c(FALSE, FALSE),
             axiscol = "#333333", axislcol = "#333333",
			 laboffset = list(x = 0, y = 0.075, z = 0.05), ...) ## S3 method for class 'ca'
plot3d(x, dim = c(1, 2, 3), map = "symmetric", what = c("all", "all"), 
             contrib = c("none", "none"), col = c("#6666FF","#FF6666"), 
             labcol = c("#0000FF", "#FF0000"), pch = c(16, 1, 18, 9), 
             labels = c(2, 2), sf = 0.00001, arrows  = c(FALSE, FALSE),
             axiscol = "#333333", axislcol = "#333333",
			 laboffset = list(x = 0, y = 0.075, z = 0.05), ...)

Arguments

`x`	Simple correspondence analysis object returned by ca
`dim`	Numerical vector of length 2 indicating the dimensions to plot
`map`	Character string specifying the map type. Allowed options include `"symmetric"` (default) `"rowprincipal"` `"colprincipal"` `"symbiplot"` `"rowgab"` `"colgab"` `"rowgreen"` `"colgreen"`
`what`	Vector of two character strings specifying the contents of the plot. First entry sets the rows and the second entry the columns. Allowed values are `"none"` (no points are displayed) `"active"` (only active points are displayed, default) `"supplementary"` (only supplementary points are displayed) `"all"` (all available points) The status (active or supplementary) is set in `ca`.
`contrib`	Vector of two character strings specifying if contributions (relative or absolute) should be indicated by different colour intensities. Available options are `"none"` (contributions are not indicated in the plot). `"absolute"` (absolute contributions are indicated by colour intensities). `"relative"` (relative conrributions are indicated by colour intensities). If set to `"absolute"` or `"relative"`, points with zero contribution are displayed in white. The higher the contribution of a point, the closer the corresponding colour to the one specified by the `col` option.
`col`	Vector of length 2 specifying the colours of row and column profiles. Colours can be entered in hexadecimal (e.g. `"\#FF0000"`), rgb (e.g. `rgb(1,0,0)`) values or by R-name (e.g. `"red"`).
`labcol`	Vector of length 2 specifying the colours of row and column labels.
`pch`	Vector of length 2 giving the type of points to be used for rows and columns.
`labels`	Vector of length two specifying if the plot should contain symbols only (`0`), labels only (`1`) or both symbols and labels (`2`). Setting `labels` to `2` results in the symbols being plotted at the coordinates and the labels with an offset.
`sf`	A scaling factor for the volume of the 3d primitives.
`arrows`	Vector of two logicals specifying if the plot should contain points (FALSE, default) or arrows (TRUE). First value sets the rows and the second value sets the columns.
`axiscol`	Colour of the axis line.
`axislcol`	Colour of the axis labels.
`laboffset`	List with 3 slots specifying the label offset in x, y, and z direction.
`...`	Further arguments passed to the rgl functions.

Printing ca objects

Description

Printing method for correspondence analysis objects

Usage

## S3 method for class 'ca'
print(x, ...) ## S3 method for class 'ca'
print(x, ...)

Arguments

`x`	Simple correspondence analysis object returned by `ca`
`...`	Further arguments are ignored

Details

The function print.ca gives the basic statistics of the ca object. First the eigenvalues (that is, principal inertias) and their percentages with respect to total inertia are printed. Then for the rows and columns respectively, the following are printed: the masses, chi-square distances of the points to the centroid (i.e., centroid of the active points), point inertias (for active points only) and principal coordinates on the first nd dimensions requested (default = 2 dimensions). The function summary.ca gives more detailed results about the inertia contributions of each point on each principal axis.
For supplementary points, masses and inertias are not applicable.

Examples

data("smoke")
print(ca(smoke))
data("smoke")
print(ca(smoke))

Printing mjca objects

Description

Printing method for multiple and joint correspondence analysis objects

Usage

## S3 method for class 'mjca'
print(x, ...) ## S3 method for class 'mjca'
print(x, ...)

Arguments

`x`	Multiple or joint correspondence analysis object returned by `mjca`
`...`	Further arguments are ignored

Details

The function print.mjca gives the basic statistics of the mjca object. First the eigenvalues (that is, principal inertias) and their percentages with respect to total inertia are printed. Then for the rows and columns respectively, the following are printed: the masses, chi-square distances of the points to the centroid (i.e., centroid of the active points), point inertias (for active points only) and principal coordinates on the first nd dimensions requested (default = 2 dimensions). The function summary.mjca gives more detailed results about the inertia contributions of each point on each principal axis.
For supplementary points, masses and inertias are not applicable.

Examples

data("wg93")
print(mjca(wg93[,1:4]))
# equivalent to:
mjca(wg93[,1:4])
data("wg93")
print(mjca(wg93[,1:4]))
# equivalent to:
mjca(wg93[,1:4])

Printing summeries of ca objects

Description

Printing method for summaries of correspondence analysis objects

Usage

## S3 method for class 'summary.ca'
print(x, ...) ## S3 method for class 'summary.ca'
print(x, ...)

Arguments

`x`	Summary of a simple correspondence analysis object returned by `summary.ca`
`...`	Further arguments are ignored

Printing summeries of mjca objects

Description

Printing method for summaries of multiple and joint correspondence analysis objects

Usage

## S3 method for class 'summary.mjca'
print(x, ...) ## S3 method for class 'summary.mjca'
print(x, ...)

Arguments

`x`	summary of a multiple or joint correspondence analysis object returned by `summary.mjca`
`...`	Further arguments are ignored

Smoke dataset

Description

Artificial dataset in Greenacre (1984)

Usage

data(smoke)data(smoke)

Format

Table containing 5 rows (staff group) and 4 columns (smoking categories), giving the frequencies of smoking categories in each staff group in a fictional organization.

References

Greenacre, M.J. (1984). Theory and Applications of Correspondence Analysis. London: Academic Press.

Summarizing simple correspondence analysis

Description

Printed output summarizing the results of ca, including a scree-plot of the principal inertias and row and column contributions.

Usage

## S3 method for class 'ca'
summary(object, scree = TRUE, rows=TRUE, columns=TRUE, ...)## S3 method for class 'ca'
summary(object, scree = TRUE, rows=TRUE, columns=TRUE, ...)

Arguments

`object`	Simple correspondence analysis object returned by `ca`.
`scree`	Logical flag specifying if a scree-plot should be included in the output.
`rows`	Logical: should row contribution summaries be included?
`columns`	Logical: should column contribution summaries be included?
`...`	Further arguments (ignored)

Details

The function summary.ca gives the detailed numerical results of the ca function. All the eigenvalues (principal inertias) are listed, their percentages with respect to total inertia, and a bar chart (also known as a scree plot). Then for the set of rows and columns a table of results is given in a standard format, where quantities are either multiplied by 1000 or expressed in permills (thousandths): the mass of each point (x1000), the quality of display in the solution subspace of nd dimensions, the inertia of the point (in permills of the total inertia), and then for each dimension of the solution the principal coordinate (x1000), the (relative) contribution COR of the principal axis to the point inertia (x1000) and the (absolute) contribution CTR of the point to the inertia of the axis (in permills of the principal inertia).
For supplementary points, masses, inertias and absolute contributions (CTR) are not applicable, but the relative contributions (COR) are valid as well as their sum over the set of chosen nd dimensions (QLT).

Examples

data("smoke")
summary(ca(smoke))
data("smoke")
summary(ca(smoke))

Summarizing multiple and joint correspondence analysis

Description

Textual output summarizing the results of mjca, including a scree-plot of the principal inertias and row and column contributions.

Usage

## S3 method for class 'mjca'
summary(object, scree = TRUE, rows = FALSE, columns = TRUE, ...)## S3 method for class 'mjca'
summary(object, scree = TRUE, rows = FALSE, columns = TRUE, ...)

Arguments

`object`	Multiple or joint correspondence analysis object returned by `mjca`.
`scree`	Logical flag specifying if a scree-plot should be included in the output.
`rows`	Logical specifying whether the results for the rows should be included in the output (default = `FALSE`).
`columns`	Logical specifying whether the results for the columns should be included in the output (default = `TRUE`).
`...`	Further arguments (ignored)

Details

The function summary.mjca gives the detailed numerical results of the mjca function. All the eigenvalues (principal inertias) are listed, their percentages with respect to total inertia, and a bar chart (also known as a scree plot). Then for the set of rows and columns a table of results is given in a standard format, where quantities are either multiplied by 1000 or expressed in permills (thousandths): the mass of each point (x1000), the quality of display in the solution subspace of nd dimensions, the inertia of the point (in permills of the total inertia), and then for each dimension of the solution the principal coordinate (x1000), the (relative) contribution COR of the principal axis to the point inertia (x1000) and the (absolute) contribution CTR of the point to the inertia of the axis (in permills of the principal inertia).
For supplementary points, masses, inertias and absolute contributions (CTR) are not applicable, but the relative contributions (COR) are valid as well as their sum over the set of chosen nd dimensions (QLT).

Examples

 data("wg93")
 summary(mjca(wg93[,1:4]))
data("wg93")
 summary(mjca(wg93[,1:4]))

International Social Survey Program on Environment 1993 - western German sample

Description

This data frame contains records of four questions on attitude towards science with responses on a five-point scale (1=agree strongly to 5=disagree strongly) and three demographic variables (sex, age and education).

Usage

data(wg93)data(wg93)

Format

Data frame (871x7).

Source

ISSP (1993). International Social Survey Program: Environment. http://www.issp.org

Package 'ca'

Help Index

Author dataset

Description

Usage

Format

Source

Simple correspondence analysis

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Converting data types in CA and MCA

Description

Usage

Arguments

Details

Value

See Also

Extracting coordinates from ca and mjca objects.

Description

Usage

Arguments

Details

Value

See Also

Updating a Burt matrix in Joint Correspondence Analysis

Description

Usage

Arguments

Details

Value

See Also

Multiple and joint correspondence analysis

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Draw lines for groups distinguished by a factor

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Listing the set of available symbols.

Description

Usage

Details

See Also

Examples

Plotting 2D maps in correspondence analysis

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Plotting 2D maps in multiple and joint correspondence analysis

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Plotting 3D maps in correspondence analysis

Description