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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.

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    $\begingroup$ Try the "difficult" option in stata; it often brings convergence when the normal likelihood maximizer doesn't. Apart from that, in a zero inflated model you jointly estimate a logit and a (say) poisson model. This might be difficult with few observations, especially when you have dummies as covariates. Do you get "xx predicts success perfectly" messages? If so, you have no variation in your data and that might be why it doesn't converge. $\endgroup$ – Nameless Apr 1 '13 at 19:09
  • $\begingroup$ Dear Nameless, thanks a lot for letting me know about the "difficult" option. I didn´t get the message you mentioned, because the computer keep iterating for such a long time that I stop the computations. Thanks again! $\endgroup$ – JJ O Apr 1 '13 at 19:27
  • $\begingroup$ Are you getting the "backed up" or the "not concave" message? $\endgroup$ – Dimitriy V. Masterov Apr 1 '13 at 20:30
  • $\begingroup$ Also, how many explanatory variables are you trying to use? Are they collinear? $\endgroup$ – Dimitriy V. Masterov Apr 1 '13 at 20:35
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    $\begingroup$ I don't see the matrix up there, but that seems like a lot of variables for this little data. I would try looking at the VIFs after a simple regress. Anything above ~10 might be problematic collinearity. Also, you can try tightening up the convergence criterion, or try ltol(0) tol(1e-7) to see if the optimizer can work its way out of the bad flat region (in addition to using difficult). $\endgroup$ – Dimitriy V. Masterov Apr 1 '13 at 21:26

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