concorcano: Canonical analysis of several sets with another set

In BMconcor: CONCOR for Structural- And Regular-Equivalence Blockmodeling

Canonical analysis of several sets with another set

Description

Relative proximities of several subsets of variables Yj with another set X. SUCCESSIVE SOLUTIONS

Usage

concorcano(x, y, py, r)

Arguments

x	are the n times p and n times q matrices of p and q centered column
y	See x
py	The partition vector of y. A row vector containing the numbers qi for i = 1,...,ky of the ky subsets yi of y : sum(qi)=sum(py)=q.
r	The number of wanted successive solutions

Details

The first solution calculates a standardized canonical component cx[,1] of x associated to ky standardized components cyi[,1] of yi by maximizing \sum_i \rho(cx[,1],cy_i[,1])^2. The second solution is obtained from the same criterion, with ky orthogonality constraints for having rho(cyi[,1],cyi[,2])=0 (that implies rho(cx[,1],cx[,2])=0). For each of the 1+ky sets, the r canonical components are 2 by 2 zero correlated. The ky matrices (cx)'*cyi are triangular. This function uses concor function.

Value

A list with following components:

cx	a n times r matrix of the r canonical components of x
cy	a n.ky times r matrix. The ky blocks cyi of the rows n*(i-1)+1 : n*i contain the r canonical components relative to Yi
rho2	a ky times r matrix; each column k contains ky squared canonical correlations \rho(cx[,k],cy_i[,k])^2

Author(s)

Lafosse, R.

References

Hanafi & Lafosse (2001) Generalisation de la regression lineaire simple pour analyser la dependance de K ensembles de variables avec un K+1 eme. Revue de Statistique Appliquee vol.49, n.1

Examples

x <- matrix(runif(50),10,5);y <- matrix(runif(90),10,9)
x <- scale(x);y <- scale(y)
ca <- concorcano(x,y,c(3,2,4),2)

BMconcor documentation built on May 29, 2024, 8:21 a.m.