Analyzing a set of partial links between Xi and Yj

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Description

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

Usage

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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 <= min(min(px),min(py),n)

Details

For the first solution, ∑_i ∑_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.

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.

References

Kissita, Cazes, Hanafi & Lafosse (2004) Deux methodes d'analyse factorielle du lien entre deux tableaux de variables partitionn<e9>es. Revue de Statistique Appliqu<e9>e, Vol 52, n<b0> 3, 73-92.

Examples

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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,]