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, ...)

    ## S3 method for class 'matrix':
    corresp(x, nf = 1, ...)

    ## S3 method for class 'factor':
    corresp(x, y, ...)

    ## S3 method for class 'data.frame':
    corresp(x, ...)

    ## S3 method for class 'xtabs':
    corresp(x, ...)

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

### 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` | a data frame 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) 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. The origin is marked on the plot with a cross.

### 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, 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.

### See Also

`svd`, `princomp`

### Examples

    (ct <- corresp(~ Age + Eth, data = quine))
    ## Not run: plot(ct)

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

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