Background: I am building a count data model with an abundancy of zeros. More precesely, I am trying to estimate the number of competitors that will enter a certain market. 70% of my data consists of zeros (no entries). So, I am trying to model using a Zero-Inflated Poisson (or Neg. Binomial) model instead of a Poisson (or Neg. Binomial) model.
Problem: I got a nice ZIP model (smallest AIC, BIC, good p-values), and I did a Vuong test and got that it is better suited than a Poisson model. I want to compare this to the ZINB model (Stata can do that. I guess by testing if alpha = 0). But, when I run the same model as ZINB, the model fails to converge. What does this mean? Does this mean that this model should be discarded? Everytime I get a convergent ZINB model, it points out that it is similar to a ZIP model. My data has 112 entries (30 of which being non-zero entries). The models are very sensitive, adding a new variable to the model may lead to a non-convergent model. All in all, it was hard to find models that converge.
Sample of correlation matrix This is to give an example of the corr. matrix of one of the models I used.