cancor {stats} R Documentation

## Canonical Correlations

### Description

Compute the canonical correlations between two data matrices.

### Usage

cancor(x, y, xcenter = TRUE, ycenter = TRUE)


### Arguments

 x numeric matrix (n \times p_1), containing the x coordinates. y numeric matrix (n \times p_2), containing the y coordinates. xcenter logical or numeric vector of length p_1, describing any centering to be done on the x values before the analysis. If TRUE (default), subtract the column means. If FALSE, do not adjust the columns. Otherwise, a vector of values to be subtracted from the columns. ycenter analogous to xcenter, but for the y values.

### Details

The canonical correlation analysis seeks linear combinations of the y variables which are well explained by linear combinations of the x variables. The relationship is symmetric as ‘well explained’ is measured by correlations.

### Value

A list containing the following components:

 cor correlations. xcoef estimated coefficients for the x variables. ycoef estimated coefficients for the y variables. xcenter the values used to adjust the x variables. ycenter the values used to adjust the x variables.

### References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988). The New S Language. Wadsworth & Brooks/Cole.

Hotelling H. (1936). Relations between two sets of variables. Biometrika, 28, 321–327. doi:10.1093/biomet/28.3-4.321.

Seber, G. A. F. (1984). Multivariate Observations. New York: Wiley. Page 506f.

### See Also

qr, svd.

### Examples

## signs of results are random
pop <- LifeCycleSavings[, 2:3]
oec <- LifeCycleSavings[, -(2:3)]
cancor(pop, oec)

x <- matrix(rnorm(150), 50, 3)
y <- matrix(rnorm(250), 50, 5)
(cxy <- cancor(x, y))
all(abs(cor(x %*% cxy$xcoef, y %*% cxy$ycoef)[,1:3] - diag(cxy $cor)) < 1e-15) all(abs(cor(x %*% cxy$xcoef) - diag(3)) < 1e-15)
all(abs(cor(y %*% cxy\$ycoef) - diag(5)) < 1e-15)


[Package stats version 4.4.1 Index]