[R] Mixed model for negative binomial distribution (glmm.ADMB)

[nflynn@ualberta.ca]

Dear R-list,

I thought that I would let some of you know of a free R package, glmm.ADMB, that
can handle mixed models for overdispersed and zero-inflated count data
(negativebinomial and poisson).
It was built using AD Model Builder software (Otter Research) for random effects
modeling and is available (for free and runs in R) at:

 http://otter-rsch.com/admbre/examples/glmmadmb/glmmADMB.html

I have been using this package for a split plot design along streams
(my  M.Sc thesis).  My response data was best described by a negative binomial
distribution (without zero-inflation) (beaver dam counts).

The model worked very well for my dataset and appeared to handle the
random effect (stream section).  Although I only had one random effect, 
glmm.ADMB can handle at least two nested random effects.  The output and
functions  available in glmm.ADMB are similar to those available in GLM.

One of my criteria for a mixed-model was that is provided the correct estimate
of the log-likelihood so that I could use an information theoretic approach for
 model selection, based on AIC values.  To my knowledge the maximum likelihood 
estimate for glmm.ADMB is appropriate for AIC model selection (*see comment
below), unlike glmmPQL.

Other packages that correctly estimate the log likelihood estimate,
such  as, Lindsey´s Repeated Measures Package (glmm)  and glmmML
do not accept the negative binomial family.  However glmm and glmmML do
accept the poisson family to describe the distribution of the response variable,
which may be adequate for modeling negative binomial data. The glmmML does not
allow for more than one random effect but glmmADMB is more flexible, in terms
of both random effects (allows nesting) and model output.

If any of you try glmm.ADMB, I would be very interested in your
feedback, especially in the realm of model verification, i.e. how is
the random effect really being handled.

You can also contact the creators at otter at otter-rsch.com.  I found
them to be very helpful in explaining their software, both its benefits and 
limitations. They have also run some tests comparing glmm.ADMB to other 
software packages like SAS NLMIXED and arrived at similar solutions.

If any of you are interested in my model comparisons (glmm.admb,
glmm and glmmML)  I can send you some of my test data and results.

 Best Regards, Nadele Flynn

 *  "maximizing is the approximate likelihood obtained by integrating
    out the random effects via the laplace approximation."
  (Otter Research Ltd)  This is not the exact maximum likelihood
   estimate, but I accepted any small error in the estimate and used
   it to calculate AIC values.