Message-ID: <a05010404b7cf7dd7f230@[134.214.32.69]>
Date: 2001-09-20T11:18:07Z
From: Stéphane Dray
Subject: Two ?'s:Permuting a data matrix and projection operator
In-Reply-To: <Pine.A41.4.33.0109192024190.30574-100000@dante58.u.washington.edu>
>
>2. Is there a function which helps find a matrix... projection operator
>from p dimensional to p-1 dimensional subspace orthogonal to x, a real
>number?
I don't really understand what dou you want...
The expression of the projection operator on subspace engendered by a
matrix X is:
PX=X%*%(t(X)%*%Dn%*%X)-%*%t(X)%*%Dn
where Dn is a diagonal matrix of row weight and (t(X)%*%Dn%*%X)- is
generalized inverse of (t(X)%*%Dn%*%X).
In multivariate regression analysis you use:
y=PX%*%y+error=a+bX1+cX2+...+error
But if you want a regression without term a (i.e. orthogonal to
vector (1,1,...1), you must centered matrix X.
Is it what you want ?
--
St?phane DRAY
---------------------------------------------------------------
Biom?trie et Biologie ?volutive - Equipe "?cologie Statistique"
Universite Lyon 1 - Bat 711 - 69622 Villeurbanne CEDEX - France
Tel : 04 72 43 27 56 Fax : 04 78 89 27 19
04 72 43 27 57 E-mail : dray at biomserv.univ-lyon1.fr
---------------------------------------------------------------
ADE-4 http://pbil.univ-lyon1.fr/ADE-4/ADE-4F.html
---------------------------------------------------------------
-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-
r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html
Send "info", "help", or "[un]subscribe"
(in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch
_._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._