R: Canonical Correlations (original) (raw)

cancor {stats}	R Documentation

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 they 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 RA, Chambers JM, Wilks AR (1988).The New S Language. Chapman and Hall/CRC, London.

⁠Hotelling H (1936). “Relations Between Two Sets of Variates.”Biometrika, 28(3–4), 321–377.doi:10.1093/biomet/28.3-4.321.

⁠Seber GAF (1984).Multivariate Observations. Wiley, New York.doi:10.1002/9780470316641. Page 506f.

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 4.6.0 Index]