Simple Correspondence Analysis

Usage

corresp(tabl, nf=1, ...)

Arguments

tabl 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 crosstabs and formulae of the form ~ F1 + F2, where F1 and F2 are factors.
nf The number of factors to be computed. Note that although 1 is the most usual, one school of thought takes the first two singular vectors for a sort of biplot.
... If the principal argument is a formula, a data frame may be specified as well from which variables in the formula are preferentially satisfied.

Description

Find the principal canonical correlation and corresponding row- and column-scores from a correspondence analysis of a two-way contingency table.

Details

See the reference. The plot method produces a graphical representation of the table if nf=1, with the areas of circles representing the numbers of points. If nf is two or more the biplot method is called, which plots the second and third columns of the matrices A = Dr^(-1/2}) U L and B = Dc^(-1/2) U V where the singular value decomposition is U L V. Thus the x-axis is the canonical correlation times the row and column scores. Although this is called a biplot, it does not have any useful inner product relationship between the row and column scores. Think of this as an equally-scaled plot with two unrelated sets of labels.

Value

An list object of class correspondence for which print, plot and biplot methods are supplied. The main components are the canonical correlation(s) and the row and column scores.

References

Venables & Ripley (1997), chapter 13.

See Also

svd, princomp

Examples

data(quine)
ct <- corresp(~ Age + Eth, data=quine)
ct
plot(ct)

data(caith)
library(mva)
biplot(corresp(caith, nf=2))


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