# The use of the negative binomial dispersion parameter in model selection…?

I'm doing model selection, analysing the effect of a number of variables on the number of shoots browsed by deer, using the number of shoots available as an offset variable. My data distribution is negative binomial.

Following the advices received during a course, I was first fitting a global model using glm.nb and noting the theta value obtained. After that, I was doing my model selection using the package AICcmodavg and glm. I specified the theta value for each model using the value of the first model in glm like this : family=negative.binomial(theta = ). My understanding here is that we specified a similar theta value to be able to compare the models.

So far, so good. But I needed to add a random effect to my model and my models didn't converged with glmer.nb. I thus switched to glmmadmb, where the theta value seems to have a different name, alpha, the negative binomial dispersion parameter. So, my questions:

1-Is alpha really the equivalent of theta ?

2-My models have very different alpha values (from 400 to 0.4000). Is there a range of "normal" negative binomial dispersion parameter value ?

EDIT: Running again my code this morning removed any values around 400. All alpha values are now similar. I think this was definitely a mistake and I think anyone obtaining very different values should be careful !

3-Should I still proceed with specifying a a same alpha values for all my models ? This can be achieve in glmmadmb, in my understanding, by using start= list(log_alpha = ).

Thanks everyone.