[R-sig-ME] How to get dispersion parameter from a binomial mixed, model? (Ben Bolker)
Highland Statistics Ltd
highstat at highstat.com
Sat Dec 15 21:50:59 CET 2012
Date: Sat, 15 Dec 2012 03:13:30 +0000 (UTC)
From: Ben Bolker <bbolker at gmail.com>
To: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] How to get dispersion parameter from a
binomial mixed model?
Message-ID: <loom.20121215T034220-681 at post.gmane.org>
Content-Type: text/plain; charset=us-ascii
<v_coudrain at ...> writes:
> Thank you very much for this link. The implemented function
> "overdisp_fun" allowed me to get what I want.
> My data are indeed overdispersed and I think about adding an
> individual random effect, since
> quasi-binomial distribution are not supported by lmer. I may use
> penalized quasi likelihood, but I know that it is quite controverse.
> Maybe someone could give me some advice?
It's hard to give completely general advice. I don't know what
(for example) Zuur et al say in their books. I generally have a mild
AFZ: In our 2012 volume we carried out a simulation study (using the owl data) for a Poisson GLMM with
observation level random intercept epsilon. We were curious to see what happens if
the observation level random effect is much larger than the random effect that
was already in the model (for nests). Would it disappear...or would it stay as before?
And what happens if the observation level RE is the same magnitude, or smaller than the random
The method itself seems to perform ok. What I don't like of the observation level random intercept
is that quite often the observation level random intercept causes a perfect fit for the
model (assuming you use the fitted function...it includes the observation level RE). Well..
perhaps I should re-phrase this. I don't like that the fitted function in glmer includes
the observation level random intercept.
Because Pearson residuals are scaled you don't notice that you have a perfect fit.
My preference is to use an NB GLMM for overdispersed count data (assuming that the overdispersion
is not caused by something else). For binomial data, perhaps the beta-binomial?
preference for observation-level random effects because they have
a well-defined likelihood etc etc.. PQL is not awful; it's just known
to be biased in some cases (see Breslow's _Whither PQL?_ paper, I think
the ref is on the FAQ page). I believe there are several papers in the
medical literature arguing that it's OK in some typical biostats/clinical
stats setting (I haven't looked carefully). Note that the variance-mean
relationships are different for different choices:
standard quasibinomial: var=phi*n*p*(1-p)
beta-binomial: see http://en.wikipedia.org/wiki/Beta-binomial_distribution'
logistic-normal-binomial (i.e. observation-level random effect): ??
I worked out the comparison for the Poisson-overdispersion case at
one point and found that the Gamma-Poisson (neg binom) and lognormal-Poisson
have the same quadratic mean-variance relationship; my guess is that
there is a similar answer for this case but I'm not sure.
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