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 at jhmi.edu
Webpage:
http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
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