Scilab Function

concor - Analyzing the contributions of each subset of variables Yj to its link with another set X

Calling Sequence

[u,v,V,cov2]=concor(X,Y,py,r)

Description

X and Y are 2 data matrices, n x p and n x q, of p variables and q variables (centered) measured on the same set of n cases. The row vector py contains the ky numbers of variables of each of the ky subsets of Y. sum(py)=q.

Y is the concatenated matrix of ky matrices Yj, j=1,...,ky.

r is the wanted number of solutions [0

u (p x r) are the orthonormed axes of X. They are associated to : V (q x r) the orthonormed global axes of Y, and to : the sub-blocks vj of v (q x r), the orthonormed partial axes of Yj. The ky x r matrix cri contains the values cov2(Yj vj(:,k), Xu(:,k)), k=1...r, which for each k are the measures of the relative links of Yj with X.

For each solution k, sumj cov2(Yjvj(:,k),Xu(:,k)) is equal to cov2(Xu(:,k),YV(:,k)), and that corresponds to these 2 independently optimized criteria, with respective norm constraints on the axes vj(:,k) and u(:,k), or on the axes u(:,k) and V(:,k);

Each column of YV represents a mean component of the respective partial components Yjvj.

For a set of r solutions, the matrix u'X'YV is diagonal and the matrices u'X'Yjvj are triangular.

Example of use : To make some "GPA" : so, by posing the compromise X = Y, "procrustes" rotations to the compromise X then are : Yj*(vj*u').

Examples


 

Authors

Lafosse & Hanafi (1997) in Revue de Statistique Appliquee. (concor.m corresponds to the svdcp.m function) hanafi@enitiaa-nantes.fr Roger.Lafosse@lsp.ups-tlse.fr