[R] GLMMs & LMEs: dispersion parameters, fixed variances, design matrices

[Prof Brian Ripley]

On Thu, 13 May 2004 Mark.Bravington at csiro.au wrote:

> Three related questions on LMEs and GLMMs in R:
> 
> (1) Is there a way to fix the dispersion parameter (at 1) in either
> glmmPQL (MASS) or GLMM (lme4)?

not glmmPQL in R (can be done in S-PLUS).

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

It's done in the same way as for lme via the control parameter (that is, 
not at all in R).

> (2) Is there a way to tell lme (either in nlme or lme4) to just use a
> specified design matrix Z for the random effects, rather than
> constructing one itself from factors? Sometimes I would really like to
> use my own funny-looking Z matrix (e.g. with non-integer coefficients),
> and even with contrasts() I haven't managed to do this.
> 
> (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 fixed
> dispersion).

It has been possible for a while in S-PLUS.

> Note: it has occurred to me that lme can possibly be tricked into fixing
> the measurement error variance (i.e. var[y|b] where b is the random
> effects and y the observed data) at some specified value e.g. 1 by
> adding two pseudo-observations at +/-1, with all zeros in the
> corresponding rows of the X and Z matrices, and with huge weights. Then
> sum( w*(y-E[y|b,params])^2) / sum(w) will be approximately 1, and any
> attempt to change the estimate of sigma^2 away from 1 will be "deterred"
> by a large penalty. Similar tricks might be possible for fixing other
> variances. However this approach is not nice and perhaps might cause
> computational problems-- and I haven't actually tried it yet.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595