ZINB Model Convergence Issue in Stata with Panel Data

[Nick Baradar]

Hello everyone,

I’m seeking advice on a convergence issue I’m encountering while running a zero-inflated negative binomial (ZINB) model in Stata for my panel data analysis.

I have an unbalanced panel dataset spanning 20 years with around 1,100 entities. My dependent variable is a count variable with approximately 56% zero values, and it shows a standard deviation about three times higher than its mean (all count variables are log-transformed). Given this distribution, ZINB seemed like the most suitable approach. However, when I attempt to run the full ZINB model in Stata, the process enters an endless iteration loop and does not converge.

To troubleshoot, I tried adding independent variables and controls sequentially to see if a particular variable was causing the issue, but I haven’t identified any clear pattern or logic that explains the endless iterations. In the meantime, I’ve been using a regular negative binomial regression and panel data fixed effects regression for preliminary analysis, though results vary significantly depending on the model, with coefficient signs shifting depending on which methodology I use.

Does anyone have suggestions on how to address ZINB convergence issues in Stata, or insights into which strategies might help identify the source of this iteration problem? Any tips or alternative modeling recommendations would also be greatly appreciated.

Thank you very much for your help!

[John Mullahy]

In many instances the absence of conditional-on-x overdispersion (relative to a Poisson baseline) creates convergence problems for negative binomial specifications. The overdispersion of the marginal distribution that you report is not relevant.

Also, I am curious about the log-transformation. In general one would not transform the outcome variable in a count-data regression specification (negbin, poisson, etc.).

I might consider beginning with a much simpler model, e.g. a Poisson panel specification with no zero-inflation and no log transformation.

[Nick Baradar]

Thank you for your response, Prof. Mullahy (and I’ve really enjoyed being your student, by the way).

I ran a negative binomial regression without log transformation successfully. However, when switching to a ZINB model, it fails to converge. I converted my dependent variable to binary and ran a logit model to identify predictors of observations greater than zero. I then included these variables (2 variables) in the inflated part of the ZINB model, but the iterations still don't converge.

I’d really appreciate any strategies or insights from your experience on resolving ZINB convergence issues. If ZINB remains unfeasible, what alternative models would you suggest?

Thank you again for your help.

[John Mullahy]

Nick, From your description I'm not convinced that there's a compelling case for estimating a zero-inflated model, unless you had some theoretical basis for maintaining that there's a zero-inflation process influencing your outcomes.

A high fraction of zero outcomes in the marginal distribution of your outcome is not per se a rationale for a zero-inflated model.

I wrote about zero-inflated models in section 2.10.1 of this recent paper. Perhaps its discussion would be helpful https://pubmed.ncbi.nlm.nih.gov/38598916/