concor (version 1.0-0.1)

concorgmreg: Regression of subsets Yj by subsets Xi

Description

Regression of subsets Yj by subsets Xi for comparing all the explanatory-explained pairs (Xi,Yj). SUCCESSIVE SOLUTIONS

Usage

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

Arguments

x

is a n x p matrix of p centered variables

y

is a n x q matrix of q centered variables

px

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

py

is the partition vector of y with ky subsets yj, j=1,...,ky. sum(py)=q

r

is the wanted number of successive solutions rmax

Value

• list with following components
• cx
  is a n.kx x r matrix of kx row blocks cxi (n x r). Each row block contains r partial explanatory components
• v
  is a q x r matrix of ky row blocks vj (qj x r), the orthonormed partial axes of yj; The components yj*vj are the explained components
• varexp
  is a kx x ky x r array; for a fixed solution k, the matrix varexp[,,k] contains kxky explained variances obtained by a simultaneous regression of all the yj by all the xi, so the values $\mbox{rho2}(cx[n*(i-1)+1:n*i,k],y_j*v_j[,k]) var(y_j*v_j[,k])$

Details

For the first solution, $\sum_i \sum_j \mbox{rho2}(cx_i[,1],y_j*v_j[,1]) \mbox{var}(y_j*v_j[,1])$ is the optimized criterion. The second solution is calculated from the same criterion, but with $y_j-y_j*v_j[,1]*v_j[,1]'$ instead of the matrices yj and with orthogonalities for having two by two zero correlated the explanatory components defined for each matrix xi. And so on for the other solutions. One solution k associates kx explanatory components (in cx[,k]) to ky explained components. When kx =1 (px=p), take concoreg function

This function uses the concorgm function

References

Hanafi & Lafosse (2004) Regression of a multi-set by another based on an extension of the SVD. COMPSTAT'2004 Symposium

Examples

x<-matrix(runif(50),10,5);y<-matrix(runif(90),10,9)
x<-scale(x);y<-scale(y)
cr<-concorgmreg(x,c(2,3),y,c(3,2,4),2)
diag(t(cr$cx[1:10,])%*%y[,1:3]%*%cr$v[1:3,]/10)^2
cr$varexp[1,1,]