[R] syntax and package for generalized linear mixed models

[Jeff Evans]

Thanks Doug,

I appreciate your response. I'm not a statistician and didn't realize this
limitation of the distribution and model I chose. This may be getting beyond
the scope of this help list, but I'll try anyway: 

If the variance of the response variable (survival) is, in fact, a function
of a covariate as it appears to be, is there a different model or
distribution I should explore that could account for it without a
transformation? I think it is a biologically important feature of the data.



-----Original Message-----
From: dmbates at gmail.com [mailto:dmbates at gmail.com] On Behalf Of Douglas
Bates
Sent: Friday, November 21, 2008 11:28 AM
To: Jeff Evans
Cc: r-help at r-project.org
Subject: Re: [R] syntax and package for generalized linear mixed models

On Thu, Nov 20, 2008 at 2:54 PM, Jeff Evans <evansj18 at msu.edu> wrote:

> I am making the switch to R and uncertain which of the several packages
for
> mixed models is appropriate for my analysis. I am waiting for Pinheiro and
> Bates' book to arrive via inter-library loan, but it will be a week or
more
> before it arrives.

> I am trying to fit a generalized linear mixed model of survival data
> (successes/trials) as a function of several categorical fixed and nested
> random effects and a covariate. Additionally, the residual variance in the
> data is a negative function of the covariate, which I would like to model
as
> well. Working in SAS, I was able to do this on transformed data in PROC
> MIXED, but ran into trouble trying to run it as a logistic regression in
the
> original scale in GLIMMIX.

> Can glmer in lme4 do this? It seems that "weights" in lme4 refers to
> weighting of observations rather than modeling the variance-covariate, as
it
> does in nlme. I tried running nlme, but I'm stuck on syntax, particularly
> with regards to how the fixed and random statements should be constructed
> separate from the model statement (not sure how this is supposed to work).
> Generally, I believe my model in lme4 should look like this:

> gm1 = glmer(cbind(#successes,#trials) ~ A*B + covariate + (1|B/C),
> family = binomial, link="logit", data=mydata,
> weights=varExp(form = ~covariate))

I'm sorry to say that this is not a valid model specification for
glmer.  As you have surmised, lme4 does not allow a general weights
specification like this.

Failure to accept a specification like this is not just an oversight
or an unimplemented feature.  This isn't a valid model specification
because this isn't a valid model. If the conditional distribution of
the response, given the value of the random effects, is Bernoulli (or
Poisson) then it is completely specified by the conditional mean.  You
can't separately specify the mean and the variance for a Bernoulli or
a Poisson distribution as you can for a Gaussian distribution.

As tempting as it may be to want to have several dials and knobs on
statistical models to tune their behavior we still need to be careful
to specify a mathematical model that is consistent.

>
>
>
> where #trials is the number of subjects at the beginning of the experiment
> in each experimental unit, #successes is the number of survivors, A and B
> are fully crossed fixed categorical factors, C is a categorical random
> factor nested within B (i.e. random site within year), and covariate is a
> continuous numerical variable ranging from 1- +inf.
>
>
>
> Can someone please suggest (a) which package to use for this analysis and
> (b) perhaps share some dummy code using my mock variables above?
>
>
>
> Many thanks,
>
>
>
> Jeff Evans
>
>
>
> PhD Candidate
>
> Department of Entomology
>
> EEBB Graduate Program
>
> Michigan State University
>
>
>
>
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>
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