[R-sig-ME] making inferences about overdispersion in nbinom glmmabmb

[Paul Johnson]

Hi,

I'm fitting negative binomial GLMMs in glmmadmb using  glmmabmb(…, family = "nbinom"). I'm interested in making inferences about the amount of overdispersion in each model, and comparing overdispersion between models. The outcome is mosquito count and the different models are different designs of mosquito trap. Each model fit gives an estimate of alpha (the [inverse] overdispersion parameter) and sd_alpha, the standard error of alpha. It's tempting to use the standard error of alpha to construct CIs, test for differences, etc, but I have no idea if this is justified. It seems over-optimistic to assume that sampling error in alpha is approximately normally distributed. Are there conditions (e.g large sample size) where this assumption is justified?

Thanks for your help,
Paul Johnson