Zero-inflated and overdispersed: what's one to do?

TLDR

Zero‑inflated Poisson and negative binomial models are recommended to handle excessive zeros in count data, yet many researchers ignore zero inflation. The study aims to educate researchers on the importance of accounting for zero inflation and the consequences of misspecifying models, and to provide guidance on when to use ZIP versus ZINB. Simulations show that ignoring zero inflation or overdispersion yields poor estimation, missed significant findings, and inflated Type I errors, and that a two‑step selection procedure correctly identifies the ZIP model only under moderate means and sample sizes, failing to detect the ZINB model or zero inflation.

Abstract

Zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) models are recommended for handling excessive zeros in count data. For various reasons, researchers may not address zero inflation. This paper helps educate researchers on (1) the importance of accounting for zero inflation and (2) the consequences of misspecifying the statistical model. Using simulations, we found that when the zero inflation in the data was ignored, estimation was poor and statistically significant findings were missed. When overdispersion within the zero-inflated data was ignored, poor estimation and inflated Type I errors resulted. Recommendations on when to use the ZINB and ZIP models are provided. In an illustration using a two-step model selection procedure (likelihood ratio test and the Vuong test), the ZIP model was correctly identified only when the distributions had moderate means and sample sizes and did not correctly identify the ZINB model or the zero inflation in the ZIP and ZINB distributions.