# corresp: Simple Correspondence Analysis In MASS: Support Functions and Datasets for Venables and Ripley's MASS

## Description

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

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```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` 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.)

## 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

 ```1 2 3 4 5``` ```(ct <- corresp(~ Age + Eth, data = quine)) plot(ct) corresp(caith) biplot(corresp(caith, nf = 2)) ```

### Example output  ```First canonical correlation(s): 0.05317534

Age scores:
F0         F1         F2         F3
-0.3344445  1.4246090 -1.0320002 -0.4612728

Eth scores:
A          N
-1.0563816  0.9466276
First canonical correlation(s): 0.4463684

Row scores:
blue       light      medium        dark
-0.89679252 -0.98731818  0.07530627  1.57434710

Column scores:
fair         red      medium        dark       black
-1.21871379 -0.52257500 -0.09414671  1.31888486  2.45176017
```

MASS documentation built on May 3, 2021, 5:08 p.m.