canocov {ToolsForCoDa}

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)