nbinom and nbinom1 in glmmADMB

Javier DelBarco Trillo <delbarcotrillo at ...> writes:

Hi,

I am trying to run some models using glmmADMB and I would like to
know what is the overall difference between the families nbinom and
nbinom1. I have tried to find this information but I still don?t
have a clear idea about which one would be more appropriate for my
models.

The difference is in the parameterization, and specifically in the
variance-to-mean relationship.  nbinom(2) uses the 'classical'
mean/variance parameterization, such that the variance is mu*(1+mu/k),
k>0 (i.e. variance is approx. equal to the mean for mu<<k and
proportional the mean squared for mu>>k); nbinom1 uses the
parameterization variance=mu*alpha, alpha>1, i.e. the variance is always
proportional to the mean.  There are various mechanistic
derivations of NB2 (e.g. a Poisson process compounded with
underlying Gamma-distributed heterogeneity); I am less clear
on the mechanistic foundation of NB1, but I have certainly seen
data sets where it fits the mean-variance relationship better.

You can look see for example
http://glmm.wdfiles.com/local--files/examples/Banta_2011_part1.pdf
pp 7-10 for some discussion of diagnostic plots.