concorsreg {BMconcor}

Redundancy of sets yj by one set x

Description

Regression of several subsets of variables Yj by another set X. SUCCESSIVE SOLUTIONS

Usage

concorsreg(x, px, y, py, r)

Arguments

x

are the n times p and n times q matrices of p and q centered column

px

The row vector which contains the numbers pi, i = 1,...,kx, of the kx subsets xi of x : \sum_i p_i=sum(px)=p. px is the partition vector of x

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

Value

A list with following components:

cx

a n times rmatrix of the r explanatory components

v

is a q \times r matrix of ky row blocks v_i (q_i \times r) of axes in Rqi relative to yi; v_i'*v_i = \mbox{Id}

varexp

is a ky \times r matrix; each column k contains ky explained variances \rho(cx[,k],y_i*v_i[,k])^2 \mbox{var}(y_i*v_i[,k])

Author(s)

Lafosse, R.

Examples

x <- matrix(runif(50),10,5);y <- matrix(runif(90),10,9)
x <- scale(x);y <- scale(y)
crs <- concorsreg(x,c(2,3),y,c(3,2,4),2)
crs$varexp[1,1,]