MASS (version 7.3-60.0.1)

corresp: Simple Correspondence Analysis

Description

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

Usage

```corresp(x, ...)# S3 method for matrix
corresp(x, nf = 1, ...)# S3 method for factor
corresp(x, y, ...)# S3 method for data.frame
corresp(x, ...)# S3 method for xtabs
corresp(x, ...)# S3 method for formula
corresp(formula, data, ...)```

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.

Arguments

x, 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"` 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.

y

a second factor for a cross-classification.

data

an optional data frame, list or environment against which to preferentially resolve variables in the formula.

...

If the principal argument is a formula, a data frame may be specified as well from which variables in the formula are preferentially satisfied.

Details

See Venables & Ripley (2002). 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) V L` 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. The origin is marked on the plot with a cross. (For other versions of this plot see the book.)

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Gower, J. C. and Hand, D. J. (1996) Biplots. Chapman & Hall.

`svd`, `princomp`.

Examples

Run this code
``````## IGNORE_RDIFF_BEGIN
## The signs can vary by platform
(ct <- corresp(~ Age + Eth, data = quine))
plot(ct)

corresp(caith)
biplot(corresp(caith, nf = 2))
## IGNORE_RDIFF_END
``````

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