concoreg function

Redundancy of sets yj by one set x

Regression of several subsets of variables Yj by another set X. SUCCESSIVE SOLUTIONS

concoreg(x, y, py, r)

Arguments

• x: are the n times p and n times q matrices of p and q centered column
• y: See x
• py: The partition vector of y. A row vector containing the numbers qi for i = 1,...,ky of the ky subsets yi of y : sum(qi)=sum(py)=q.
• r: The number of wanted successive solutions

Returns

A list with following components: - cx: a n times rmatrix of the r explanatory components

• v: is a $q x r$ matrix of ky row blocks $v_i$ ($q_i x r$) of axes in Rqi relative to yi; $v_i'*v_i = \mbox{Id}$

• V: is a $q x r$ matrix of axes in Rq relative to y; $V'*V = \mbox{Id}$

• varexp: is a $ky x r$ matrix; each column k contains ky explained variances $\rho(cx[,k],y_i*v_i[,k])^2 \mbox{var}(y_i*v_i[,k])$

Examples

x <- matrix(runif(50),10,5);y <- matrix(runif(90),10,9)
x <- scale(x);y <- scale(y)
co <- concoreg(x,y,c(3,2,4),2)

References

Lafosse R. & Hanafi M.(1997) Concordance d'un tableau avec K tableaux: Definition de K+1 uples synthetiques. Revue de Statistique Appliquee vol.45,n.4.

Chessel D. & Hanafi M. (1996) Analyses de la Co-inertie de K nuages de points. Revue de Statistique Appliquee vol.44, n.2. (this ACOM analysis of one multiset is obtained by the command : concoreg(Y,Y,py,r))

Author(s)