concor (version 1.0-0.1)

concorgm: Analyzing a set of partial links between Xi and Yj

Description

Analyzing a set of partial links between Xi and Yj, SUCCESSIVE SOLUTIONS

Usage

concorgm(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(pi)=sum(px)=p. px is the partition vector of x

py

is the partition vector of y with ky subsets yj, j=1,...,ky

r

is the wanted number of successive solutions rmax

Value

• list with following components
• u
  is a p x r matrix of kx row blocks ui (pi x r), the orthonormed partial axes of xi; associated partial components: xi*ui
• v
  is a q x r matrix of ky row blocks vj (qj x r), the orthonormed partial axes of yj; associated partial components: yj*vj
• cov2
  is a kx x ky x r array; for r fixed to k, the matrix contains kxky squared covariances $\mbox{cov2}(x_i*u_i[,k],y_j*v_j[,k])^2$, the partial links between xi and yj measured with the solution k.

Details

For the first solution, $\sum_i \sum_j \mbox{cov2}(x_i*u_i[,1],y_j*v_j[,1])$ is the optimized criterion. The second solution is calculated from the same criterion, but with $x_i-x_i*u_i[,1]*u_i[,1]'$ and $y_j-y_j*v_j[,1]*v_j[,1]'$ instead of the kx+ky matrices xi and yj. And so on for the other solutions. When kx=1 (px=p), take concor.m

This function uses the svdbip function.

References

Kissita, Cazes, Hanafi & Lafosse (2004) Deux methodes d'analyse factorielle du lien entre deux tableaux de variables partitionn�es. Revue de Statistique Appliqu�e, Vol 52, n� 3, 73-92.

Examples

x<-matrix(runif(50),10,5);y<-matrix(runif(90),10,9)
x<-scale(x);y<-scale(y)
cg<-concorgm(x,c(2,3),y,c(3,2,4),2)
diag(t(x[,1:2]%*%cg$u[1:2,])%*%y[,1:3]%*%cg$v[1:3,]/10)^2
cg$cov2[1,1,]