Alternatives to zero inflated negative binomial regression?

[Maliha Ali]

Hi all,
I have a dataset that contains counts of preventable ED visits (outcome variable), with over dispersion and skewed to right, making this appropriate for a negative binomial regression, except that I have 18% of the dataset (85 visits) that are 0 counts, and 18% of the dataset (87 visits) with count of 1.
I attempted zero inflated nbreg but the models do not converge.
I compared participants with counts 0 and 1, and do not find them significantly different from each other.
My question regarding the next best alternative to zero inflated nbreg is which of the following would you recommend:
a) conduct nbreg with the outcome variable as it is (with 18% zeros)
b) or, conduct nbreg with the outcome variable transformed by adding +1 to the counts to turn the zeros into 1.

Please advise!

Thanks

[John Mullahy]

Maliha: Without more information it is difficult to know, but as you describe the data there is nothing that would a priori motivate me to think about a zero-inflated model.

Between choices (a) and (b) that you pose, I would — in light of the information you provide — cast a strong vote for (a).

Once you've estimated your model you can, of course, pursue goodness-of-fit questions that may be relevant to your analysis and then consider other estimation strategies if your model's fit is unsatisfactory.

P.S. In a regression context, a claim about overdispersion—presumably overdispersed relative to a Poisson model?—can't in general be advanced based simply on an examination of the marginal or unconditional distribution of the outcome variable. In such contexts, overdispersion typically corresponds to a situation where the conditional variance exceeds the conditional mean, i.e. var(y|x)>E(y|x).

[Maliha Ali]

Thank you John!