canocov: Canonical correlation analysis.

In ToolsForCoDa: Multivariate Tools for Compositional Data Analysis

Canonical correlation analysis.

Description

Function canocov performs a canonical correlation analysis. It operates on raw data matrices, which are only centered in the program. It uses generalized inverses and can deal with structurally singular covariance matrices.

Usage

canocov(X, Y)

Arguments

X	The n times p X matrix of observations
Y	The n times q Y matrix of observations

Details

canocov computes the solution by a singular value decomposition of the transformed between set covariance matrix.

Value

Returns a list with the following results

ccor	the canonical correlations
A	canonical weights of the X variables
B	canonical weights of the Y variables
U	canonical X variates
V	canonical Y variates
Fs	biplot markers for X variables (standard coordinates)
Gs	biplot markers for Y variables (standard coordinates)
Fp	biplot markers for X variables (principal coordinates)
Gp	biplot markers for Y variables (principal coordinates)
Rxu	canonical loadings, (correlations X variables, canonical X variates)
Rxv	canonical loadings, (correlations X variables, canonical Y variates)
Ryu	canonical loadings, (correlations Y variables, canonical X variates)
Ryv	canonical loadings, (correlations Y variables, canonical Y variates)
Sxu	covariance X variables, canonical X variates
Sxv	covariance X variables, canonical Y variates
Syu	covariance Y variables, canonical X variates
Syv	covariance Y variables, canonical Y variates
fitRxy	goodness of fit of the between-set correlation matrix
fitXs	adequacy coefficients of X variables
fitXp	redundancy coefficients of X variables
fitYs	adequacy coefficients of Y variables
fitYp	redundancy coefficients of Y variables

Author(s)

Jan Graffelman [e-mail]

References

Hotelling, H. (1935) The most predictable criterion. Journal of Educational Psychology (26) pp. 139-142.

Hotelling, H. (1936) Relations between two sets of variates. Biometrika (28) pp. 321-377.

Johnson, R. A. and Wichern, D. W. (2002) Applied Multivariate Statistical Analysis. New Jersey: Prentice Hall.

See Also

cancor

Examples

set.seed(123)
X <- matrix(runif(75),ncol=3)
Y <- matrix(runif(75),ncol=3)
cca.results <- canocov(X,Y)

ToolsForCoDa documentation built on April 3, 2025, 7:47 p.m.