From: Robin Hankin <r.hankin_at_noc.soton.ac.uk>

Date: Mon 30 Oct 2006 - 09:17:27 GMT

Date: Mon 30 Oct 2006 - 09:17:27 GMT

Hi

I discovered the other day that lm() does some of the work for you:

library(mvtnorm)

X <- matrix(rnorm(60),ncol=3)

beta <- matrix(1:6,ncol=2)

sig <- matrix(c(1,0.7,0.7,1),2,2)

Y <- X %*% beta + rmvnorm(n=20,sigma=sig)

lm(Y ~ X-1)

Call:

lm(formula = Y ~ X - 1)

Coefficients:

[,1] [,2]

X1 1.015 4.065 X2 2.483 5.366 X3 2.762 5.727

This gives an estimate for beta.

But I don't know of a ready-made R solution for estimating the covariance of the elements of beta, or the "sig" matrix for the covariance matrix of the observation errors.

Anyone?

On 30 Oct 2006, at 09:01, Andris Jankevics wrote:

> Also you can take a look on Partial Least Squares (PLS) regression.

*> http://www.statsoft.com/textbook/stpls.html
**> R-package: http://mevik.net/work/software/pls.html
**>
**> Andris Jankevics
**>
**> On Sestdiena, 28. Oktobris 2006 06:04, Ritwik Sinha wrote:
**>> You can use gee (
**>> http://finzi.psych.upenn.edu/R/library/geepack/html/00Index.html)
**>> or maybe
**>> the function gls in nlme.
**>>
**>> Ritwik.
**>>
**>> On 10/27/06, Ravi Varadhan <rvaradhan@jhmi.edu> wrote:
**>>> Hi,
**>>>
**>>>
**>>>
**>>> Suppose I have a multivariate response Y (n x k) obtained at a
**>>> set of
**>>> predictors X (n x p). I would like to perform a linear
**>>> regression taking
**>>> into consideration the covariance structure of Y within each unit
**>>> - this
**>>> would be represented by a specified matrix V (k x k), assumed to
**>>> be the
**>>> same
**>>> across units. How do I use "lm" to do this?
**>>>
**>>>
**>>>
**>>> One approach that I was thinking of is as follows:
**>>>
**>>>
**>>>
**>>> Flatten Y to a vector, say, Yvec (n*k x 1). Create Xvec (n*k,
**>>> p*k) such
**>>> that it is made up of block matrices Bij (k x k), where Bij is a
**>>> diagonal
**>>> matrix with X_ij as the diagonal (i = 1,.n, and j = 1,.,p). Now
**>>> I can
**>>> use "lm" in a univariate mode to regress Yvec against Xvec, with
**>>> covariance matrix Vvec (n*k x n*k). Vvec is a block-diagonal
**>>> matrix with
**>>> blocks of V along the diagonal. This seems like a valid
**>>> approach, but I
**>>> still don't know how to specify the covariance structure to do
**>>> weighted
**>>> least squares.
**>>>
**>>>
**>>>
**>>> Any help is appreciated.
**>>>
**>>>
**>>>
**>>> Best,
**>>>
**>>> Ravi.
**>>>
**>>>
**>>>
**>>>
**>>> --------------------------------------------------------------------
**>>> -----
**>>> --- -------
**>>>
**>>> Ravi Varadhan, Ph.D.
**>>>
**>>> Assistant Professor, The Center on Aging and Health
**>>>
**>>> Division of Geriatric Medicine and Gerontology
**>>>
**>>> Johns Hopkins University
**>>>
**>>> Ph: (410) 502-2619
**>>>
**>>> Fax: (410) 614-9625
**>>>
**>>> Email: rvaradhan@jhmi.edu
**>>>
**>>> Webpage:
**>>> http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
**>>>
**>>>
**>>>
**>>>
**>>> --------------------------------------------------------------------
**>>> -----
**>>> --- --------
**>>>
**>>>
**>>>
**>>>
**>>> [[alternative HTML version deleted]]
**>>>
**>>> ______________________________________________
**>>> R-help@stat.math.ethz.ch mailing list
**>>> https://stat.ethz.ch/mailman/listinfo/r-help
**>>> PLEASE do read the posting guide
**>>> http://www.R-project.org/posting-guide.html
**>>> and provide commented, minimal, self-contained, reproducible code.
**>
**> ______________________________________________
**> R-help@stat.math.ethz.ch mailing list
**> https://stat.ethz.ch/mailman/listinfo/r-help
**> PLEASE do read the posting guide http://www.R-project.org/posting-
**> guide.html
**> and provide commented, minimal, self-contained, reproducible code.
*

-- Robin Hankin Uncertainty Analyst National Oceanography Centre, Southampton European Way, Southampton SO14 3ZH, UK tel 023-8059-7743 ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.Received on Mon Oct 30 20:29:22 2006

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