What is the appropriate strategy for deciding which model to use with count data? I have count data that i need to model as a multilevel model and it was recommended to me (on this site) that the best way to do so this is through bugs or MCMCglmm. However i am still trying to learn about bayesian statistics, and i thought i should first try to fit my data as generalized linear models and ignore the nested structure of the data (just so i can get a vague idea of what to expect).
About 70% of the data are 0 and the ratio of variance to the mean is 33. So the data is quite over-dispersed.
After trying a number of different options (including poisson, negative binomial, quassi and zero inflated model) i see very little consistency in the results (varying from everything is significant to nothing is significant).
How can i go about making an informed decision about which type of model to choose based on the 0 inflation and over-dispersion? For instance, how can i infer that quassi-poisson is more appropriate than negative binomial (or vise versa) and how can i know that using either has dealt adequately (or not) with the excess zeros? Similarly, how do i evaluate that there is no more over-dispersion if a zero-inflated model is used? or how should i decide between a zero inflated poisson and a zero inflated negative binomial?