| cancor {stats} | R Documentation |
Compute the canonical correlations between two data matrices.
cancor(x, y, xcenter = TRUE, ycenter = TRUE)
x |
numeric matrix (n * p1), containing the x coordinates. |
y |
numeric matrix (n * p2), containing the y coordinates. |
xcenter |
logical or numeric vector of length p1,
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. |
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.
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. |
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.
Seber, G. A. F. (1984). Multivariate Observations. New York: Wiley, p. 506f.
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)