Dispersion parameter calculation for Poisson glmer

I think a response is in order!

Whether one believes in it or not, the variance ratio that the dispersion
estimate is designed to accommodate is, probably more often than not
with allegedly binomial or poisson errors, real.  The dispersion estimate
that can be obtained from glm() fits provides important clues, that users
ignore at peril to the credibility of the analysis.  In the common
situation where a dispersion substantially greater than 1 is identified,
the variance adjustment is a simple ad hoc recourse that generally
does a good job in allowing calculation of SEs that are plausible.  One
can set down models for which the dispersion variance correction is
pretty much right.  Sussing out the details of models that would lead
to something very close to the dispersion correction would surely be
a good PhD project.  

As an aside, I do not myself find what comes out of the magic world of 
negative binomial distributions more plausible than the way that I
understand the dispersion "correction". 

GLMMs with observation level random effects are another way to
handle the matter -- albeit the dispersion correction is different.
I have data where results for most species (there were quite a
number of species) suggested to me that a GLM type dispersion
correction did a better job than observation level random effects
in a GLMM.  This tentative conclusion does though need careful
checking.  If I live to be 99 with my faculties pretty much intact, 
maybe I will sometime make a stab at investigating further and 
writing it up.

John Maindonald             email: john.maindonald at anu.edu.au
phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
Centre for Mathematics & Its Applications, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.
http://www.maths.anu.edu.au/~johnm

On Wed, Feb 27, 2013 at 4:31 PM, Ben Bolker <bbolker at gmail.com> wrote:

<juwb08 at ...> writes:

Hi All,

I would like to calculate a dispersion parameter for a glmer with a
Poisson family (in lme4). I found a function posted on this mailing
list that had been suggested to use for calculating a dispersion
parameter for a glmer with a binomial family. (Found on
https://stat.ethz.ch/pipermail/r-sig-mixed-models/2011q1/015383.html )

[snip]

 Please see slightly more robust code at

http://glmm.wikidot.com/faq#overdispersion_est

It should be applicable to GLMMs generally, although please note all the
boldface warnings about this being a crude approximation of the
overdispersion parameter.

As you know, my opinion is that you can approximate it however you want
because it doesn't exist :-)

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