[R] Multivariate regression

[Pfaff, Bernhard Dr.]

Hello Ravi,

have you considered the SUR method proposed by Zellner? An
implementation of it is provided in CRAN-package 'systemfit' (see
?systemfit for more information).

Best,
Bernhard

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