[6509] in s-news-athena
Re: Summary of response to varcomp question
daemon@ATHENA.MIT.EDU (Douglas Bates)
Fri Feb 24 12:46:59 1995
Date: Fri, 24 Feb 95 10:53:43 -0600
From: bates@stat.wisc.edu (Douglas Bates)
To: hughes@diamond.mcis.washington.edu
Cc: s-news@utstat.toronto.edu
In-Reply-To: <9502231808.AA01802@diamond.mcis.washington.edu> (hughes@diamond.mcis.washington.edu)
>>>>> Jim Hughes <hughes@diamond.mcis.washington.edu> writes:
> 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.
Sorry I didn't participate in this discussion previously but I have
been out of town all this week.
The model you wish to fit is exactly the model that is fit through the
lme function in the nlme software Jose' Pinheiro, Mary Lindstrom, and
I contributed to statlib. We sent a new, maintenance version to
statlib recently. I haven't checked if it has been installed yet.
The new version is available for both Unix and Windows systems at
ftp://ftp.stat.wisc.edu/src/NLME
