[6502] in s-news-athena
Summary of response to varcomp question
daemon@ATHENA.MIT.EDU (Jim Hughes)
Thu Feb 23 13:39:39 1995
Date: Thu, 23 Feb 95 10:08:49 -0800
From: hughes@diamond.mcis.washington.edu (Jim Hughes)
To: s-news@utstat.toronto.edu
Yesterday I posted the question
> Does anyone know if it is possible to recover the off-diagonal elements
> of the matrix of variance components from the varcomp() function? That is,
> varcomp() uses the model
>
> Y_i = aX_i + b_iZ_i + e_i
>
> where Y_i is the vector response for the i'th individual, a is a vector of
> fixed effects parameters, b_i is a vector of random effects for the i'th
> individual, X and Z are design matricies and the e's are random errors. The
> assumption is that b_i is multivariate normal, mean = 0, variance = sigma.
> I would like the full matrix sigma, rather than just the diagonal elements.
The definitive response comes from Chris Fraley at Statsci:
> Varcomp assumes that the covariance matrices between groups of random effects
> are of the form \gamma^2 I, so that there are no off diagonal elements. It
> solves the standard `variance-component' problem. The more general problem of
> computing covariance components is much harder. An implementation would have
> to have users input how they want the covariance matrices parameterized, and
> (optionally) give the corresponding derivatives to facilitate the optimization.
> There would be no easy way to guarantee positive-definiteness unless it was
> implicit in the parameterization.
>
> Chris Fraley (fraley@statsci.com)
> Statistical Sciences, 1700 Westlake Ave N, Suite 500, Seattle, WA 98109 USA
Jim Hughes
hughes@biostat.washington.edu
