**From:** Douglas Bates (*bates@stat.wisc.edu*)

**Date:** Fri 14 May 2004 - 00:57:49 EST

**Next message:**Jens Oehlschlägel: "RE: [R] please help with estimation of true correlations andreliabilities"**Previous message:**Thomas Lumley: "Re: [R] Explaining Survival difference between Stata and R"**In reply to:**Mark.Bravington@csiro.au: "[R] GLMMs & LMEs: dispersion parameters, fixed variances, design matrices"

Message-id: <6r3c64ml1u.fsf@bates4.stat.wisc.edu>

<Mark.Bravington@csiro.au> writes:

*> Three related questions on LMEs and GLMMs in R:
*

*>
*

*> (1) Is there a way to fix the dispersion parameter (at 1) in either
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*> glmmPQL (MASS) or GLMM (lme4)?
*

*>
*

*> Note: lme does not let you fix any variances in advance (presumably
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*> because it wants to "profile out" an overall sigma^2 parameter) and
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*> glmmPQL repeatedly calls lme, so I couldn't see how glmmPQL would be
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*> able to fix the dispersion parameter. The section on glmmPQL in V&R4
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*> says that the default is to estimate the dispersion parameter, but
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*> didn't seem to say how to change the default.
*

At the core of the lme calculations is the solution of a penalized

least squares problem defined by the relative dispersion matrix of the

random effects and the model matrices for the random effects and the

fixed effects. In versions 0.6-1 and later of the lme4 package (the

first release candidate is available from my web site

http://www.stat.wisc.edu/~bates/) the components of the log-likelihood

or the REML criterion are available as the devComp slot of the S4

object that represents the model and that is used to solve the

penalized least squares problem. If, using these components, you can

write the log-likelihood for the model that you wish to fit then you

can give it to an optimizer such as optim or nlm to fit.

In the notation of Bates and DebRoy (2004), "Linear mixed models and

penalized least squares" (to appear in J. of Multivariate Analysis,

available in preprint form from my web site), the components are

log(|Z'Z + \Omega|), log(|\Omega|), log(|R_{XX}|^2), and log(r_{yy}^2)

The C code that uses these to evaluate the deviance form of the

profiled log-likelihood criterion or the profiled REML criterion from

these components is in src/ssclme.c from the Matrix package.

Modifying the criteria for a fixed dispersion parameter may be trivial

or it may not.

*> (3) Are there any plans to allow some variances to be fixed in lme?
*

*> It would be useful e.g. for meta-analysis (and indeed for glmms with
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*> fixed dispersion).
*

The method = 'Laplacian' version of the GLMM function fixes the

dispersion parameter in those families where it should be fixed. As

we continue to develop lme4 we will provide a further enhancement

using an adaptive Gauss-Hermite evalution of the log-likelihood for

GLMMs that will also have this property.

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**Next message:**Jens Oehlschlägel: "RE: [R] please help with estimation of true correlations andreliabilities"**Previous message:**Thomas Lumley: "Re: [R] Explaining Survival difference between Stata and R"**In reply to:**Mark.Bravington@csiro.au: "[R] GLMMs & LMEs: dispersion parameters, fixed variances, design matrices"

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