Scilab Function

concorGMREG - Regression of subsets Yj by subsets Xi.

Calling Sequence

[P,rx,u,v,varexp]=concorGMREG(X,Y,px,py,r)

Description

X and Y are 2 data matrices, n x p and n x q, of p variables and q variables (centered).

The row vector px contains the kx numbers of variables of the kx subsets of X.

The row vector py contains the ky numbers of variables of the ky subsets of Y. sum(px)=p and sum(py)=q.

When kx =1 (px=p), use concor.m

r is the wanted number of solutions (< 1+min(rank(Xi'Yj))), and thus often rmax = min(min(px),min(py),n).

The ky blocks vj (pyj x r) of v (q x r) are the orthonormed partial axes of Yj.

varexp (kx x ky x r) contains the explained variances.

The kx blocks ui (rx(i) x r) of u, are formed with r orthonormed vectors. P1=P(:,1:rx(1)), P2=P(:,rx(1)+1 : rx(1)+rx(2)), P3 =....

Each matrix Xi has been standardized for obtaining the matrix Pi and the standardized partial explanatory components Piui.

P1=P(:,1:rx(1)), P2=P(:,rx(1)+1 : rx(1)+rx(2)), P3 =....

P1u1=P(:,1:rx(1))*u(1:rx(1),:).

For each pair (Xi,Yj, and each solution k, varexp contains the explained variances varexpijk = rho2(Piui(:,k),Yjvj(:,k)) varYjvj(:,k).

For each solution k, sumi sumj varexpijk is the optimized criterion,

px+py orthogonality constraints for a new solution : ui'*ui=Ir and vj'*vj=Ir.

Authors

Hanafi & Lafosse (2004) in COMPSTAT 2004. hanafi@enitiaa-nantes.fr Roger.Lafosse@lsp.ups-tlse.fr