What percentage of zeros in the data should make us consider trying the sequence of models: Poisson -> Negative Binomial -> Zinf-Poisson -> Zinf-Negative Binomial, etc? I have two datasets with about 1/4-1/3 of zeros (about 250-350 out of a 1000 data points) and the zeros are not generated by two different underlying phenomena. They're just true zeros. I'm trying to use wilcox test to make comparisons between two treatment groups in the data. But I'm concerned if I should use one of the above models. Any guidance is appreciated.
First, you can check whether the observed and expected zeros from a simple model like Poisson or NB look alike. A nice graphical check for this is to use a rootogram (see http://econpapers.repec.org/RePEc:inn:wpaper:2014-20). But then you can also easily go on and fit a zero-inflated or hurdle model to check whether this improves the model fit (e.g., judging by AIC or BIC).
The fact that all zeros are true zeros does not mean that the effect of the regressors on the zeros and non-zeros has to be the same. Possibly you obtain better predictions if you use a two-part model.