[R-sig-ME] How to get dispersion parameter from a binomial mixed model?

Ben Bolker bbolker at gmail.com
Sat Dec 15 04:13:30 CET 2012

 <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
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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