corresp {MASS} | R Documentation

## 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, nf=1, ...)

### Arguments

`x` | 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.

### 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 (1999), chapter 11.

### See Also

`svd`, `princomp`

### Examples

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

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