[ADMB Users] Estimating the dispersion parameter of the negative binomial

[Ben Bolker]

On 11-12-26 09:42 PM, dave fournier wrote:
>>Is it possible to estimate the dispersion parameter of the negative
> binomial GLM using maximum >Likelihood in ADMB (i.e. admbglmm) and if so
> why is this possible given others use two component >iterative methods
> such as the EM algorithm or profiling over the dispersion parameter?
> 
>>Thanks,
> 
>>Mark
> 
> 
> Yes you could make the overdispersion any kind of function of the mean
> and other
> parameters/covariates that you want.  R sucks.
> 

  The current iteration of glmmADMB fits a single global value of the
overdispersion parameter.  It would of course be possible to incorporate
(most easily) a linear model/design matrix for the overdispersion
parameter, but it will depend on demand.

  Of course you can do this yourself by coding it in ADMB.

  In mle2() from the bbmle package you can do something like:

  mle2(response~dnbinom(mu=exp(logmu),size=exp(logk)),
           parameters=list(logmu=~x,logk~f), data=..., start=...))

   where x is a continuous predictor and f is a categorical predictor.
  You will have to specify starting values, and it won't be as fast or
as robust as doing it in ADMB.

  I think the main reason that most existing methods use an iterative or
two-stage procedure is that they are using the GLM machinery in the
inner (i.e. fitting with known k) part of the estimation -- the
quadratic-form (NB2) negative binomial falls within the exponential
family when k is known, which allows use of off-the-shelf iteratively
reweighted least squares code for the fitting ... (this is also I think
why NB2 is so much more widely available than NB1, which is
parameterized with a linear mean-variance relationship) since ADMB and
mle2 are using general-purpose maximum likelihood rather than something
like IRLS, they aren't constrained in this way.

  cheers
    Ben