dave fournier otter at otter-rsch.com
Wed Oct 27 06:05:35 PDT 2010

``` >  Fair enough.  Perhaps glmmADMB could be extended to make it easier to
>test this; not looking at it at the moment, but I suspect that it only
>allows a single parameterization?  I wonder if one could build
>exploratory graphical tools that showed residuals/nonparametric
>estimates of the mean/variance relationship and superimposed
>quasi-Poisson (var=phi*mu), NB (var=mu*(1+mu/k)), etc. ... >relationships?

>   Ben Bolker

The idea that you paramerterize the NB so that var=mu*(1+mu/k)
is also a misconception. As I understand it this is done
so that the limited GLMM approach can be used in R.
If youembrace the ADMB-RE formulation for nonlinear
mixed models there is no need to restrict yourself to
that parameterization.  So you can try

var = mu * (1+a+b*mu) = tau*mu

for a>=0 b>=0 for example
this applies whether or not one has RE's so also for
a simple NB regression model.  A nice test for
remaining overdispersion is to fit the model as a mixture

(1-p)NB(y,mu,tau*mu) + p* NB(y,mu,taumult*tau*mu)

where one thinks of p as the percent contamination by
outliersso normally p is "close" to .05 or maybe .10
and taumult is "close" to 9.0. Of course p and taumult
can be estimated in the model.

For the NB data in your book (I think its the book,
I got the data from Hans.) the estimates are

# p:
0.100752588412
# log_tmult:
2.55001219536

which produces a big improvement in the LL over p=0.0
and chooses the model

var = mu *(1+a)

that is it completely rejects the b>0 part of the
overdispersion.

Anyway the problem lies not with the ADMB part
of glmmADMB. It is is the kludgey R interface.
R's real legacy to date seems to be
that it makes serious nonlinear parameter estimation
difficult or impossible.

```