mjca {ca}

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, ...)

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.

See Also

eigen, plot.mjca, summary.mjca, print.mjca

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)