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.

 

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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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