ToolsForCoDa (version 1.1.0)

lrcco: Logratio Canonical Correlation Analysis

Description

Function lrcco is a wrapper function around canocov. It performs logratio canonical correlation analysis (LR-CCO) accepting two compositional data matrices as input.

Usage

lrcco(X, Y)

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

Arguments

X

The matrix of X compositions

Y

The matrix of Y compositions

Author

Jan Graffelman

Details

Matrices X and Y are assumed to contain positive elements only, and there rows sum to one.

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.

Graffelman, J. and Pawlowsky-Glahn, V. and Egozcue, J.J. and Buccianti, A. (2018) Exploration of geochemical data with compositional canonical biplots, Journal of Geochemical Exploration 194, pp. 120--133. tools:::Rd_expr_doi("10.1016/j.gexplo.2018.07.014")

See Also

cancor,canocov

Examples

set.seed(123)
X  <- matrix(runif(75),ncol=3)
Y  <- matrix(runif(75),ncol=3)
Xc <- X/rowSums(X) # create compositions by closure
Yc <- Y/rowSums(Y)
out.lrcco <- lrcco(X,Y)