concorcano: Canonical analysis of several sets with another set

Description Usage Arguments Details Value References Examples

Description

Relative proximities of several subsets of variables Yj with another set X. SUCCESSIVE SOLUTIONS

Usage

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concorcano(x,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

py

is a row vector which contains the numbers qi, i=1,...,ky, of the ky subsets yi of y : ∑_i q_i=sum(py)=q. py is the partition vector of y

r

is the wanted number of successive solutions

Details

The first solution calculates a standardized canonical component cx[,1] of x associated to ky standardized components cyi[,1] of yi by maximizing ∑_i ρ(cx[,1],cy_i[,1])^2.

The second solution is obtained from the same criterion, with ky orthogonality constraints for having rho(cyi[,1],cyi[,2])=0 (that implies rho(cx[,1],cx[,2])=0). For each of the 1+ky sets, the r canonical components are 2 by 2 zero correlated.

The ky matrices (cx)'*cyi are triangular.

This function uses concor function.

Value

list with following components

cx

is n x r matrix of the r canonical components of x

cy

is n.ky x r matrix. The ky blocks cyi of the rows n*(i-1)+1 : n*i contain the r canonical components relative to Yi

rho2

is a ky x r matrix; each column k contains ky squared canonical correlations ρ(cx[,k],cy_i[,k])^2

References

Hanafi & Lafosse (2001) Generalisation de la regression lineaire simple pour analyser la dependance de K ensembles de variables avec un K+1 eme. Revue de Statistique Appliquee vol.49, n.1

Examples

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x<-matrix(runif(50),10,5);y<-matrix(runif(90),10,9)
x<-scale(x);y<-scale(y)
ca<-concorcano(x,y,c(3,2,4),2)
diag(t(ca$cx)%*%ca$cy[1:10,]/10)^2
ca$rho2[1,]


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