[Lme4-authors] Underdispersion in GLMM

[I'm taking the liberty of forwarding this to r-sig-mixed-models,
where I think it is more appropriate.]

  A few thoughts about underdispersion:

 * underdispersed _count_ data (e.g. litter sizes for large mammals) are
often better captured by an ordinal model (e.g. ordinal::clmm)
 * you _might_ be able to fit underdispersed binomial data by allowing
negative correlation structure within groups: this could be tricky,
though, depending on the size and complexity of your data set.  (The
standard approach of nested random effects is essentially a compound
symmetry structure, but only allows positive/non-negative correlations.
 The nlme package enabled fitting models with a more general CS
structure, but that's not implemented in lme4, and slightly harder to do
in GLMMs in general).
 * the standard 'quasi-likelihood' approach, i.e. taking the estimated
level of underdispersion and shrinking all the confidence intervals
accordingly, might be a reasonable first/hackish approach.  The thing to
be careful about there is that I have yet to read any good treatment (or
figure out for myself) how quasi-likelihood estimates of 'residual'
variance interact with the estimates of the random effects variances ...

  good luck,
  Ben Bolker

Dear Mr Bates, Mr Maechler, Mr Bolker, Mr Walker, Mr Christensen, and
Mr Singmann,

My name is Eva Reindl and I am a Phd student at the University of
Birmingham working with your lme4 package to analyse my data. I am
running GLMMs with a binomial error structure and found that my full
model is heavily underdispersed. I am writing you because I would
like to ask whether your package offers any strategy to deal with
underdispersion. Any help or reference to resources would be greatly
appreciated.

I would like to thank you very much in advance for your efforts.

Yours sincerely,

Eva Reindl

Eva Reindl MSc Doctoral Researcher at School of Psychology University
of Birmingham Edgbaston Birmingham B15 2TT United Kingdom

phone: 0121 414 7209 E-mail: EMR328 at bham.ac.uk 

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