lrcco: Logratio Canonical Correlation Analysis

In ToolsForCoDa: Multivariate Tools for Compositional Data Analysis

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)

Arguments

X	The matrix of X compositions
Y	The matrix of Y compositions

Details

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

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.

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. \Sexpr[results=rd]{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)

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