[R] Multivariate regression

From: Ravi Varadhan <rvaradhan_at_jhmi.edu>
Date: Fri 27 Oct 2006 - 16:54:08 GMT


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.  



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  


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