On the Use of Zero-Inflated Mixed Models for Count Data: A Simulation and Empirical Evidence

Abstract

This paper evaluates the performance of classical count regression models (Poisson, Negative Binomial, Generalized Poisson), zero-inflated models (Zero-Inflated Poisson/ZIP, Zero-Inflated Negative Binomial/ZINB, Zero-Inflated Generalized Poisson/ZIGP), and zero-inflated mixed models (ZIPMM, ZINBMM, ZIGPMM) for over-dispersed count data, particularly due to excess zeros and unobserved heterogeneity. Using simulation and empirical studies, we evaluated the performance of the models based on their predictive capability and their ability to yield valid inferences through hypothesis testing. The simulation, replicated 1000 times, involves 27 scenarios that combine various sample sizes, proportions of zero counts, and response variable distributions. Our findings indicate that ZIGPMM and ZINBMM provide the smallest root mean square error (RMSE) values. Although the Poisson model yields a relatively small RMSE, it does not adequately account for overdispersion, leading to underestimated standard errors and potentially misleading significance tests. The negative binomial model yields dispersion estimates closest to 1, indicating good performance, whereas ZIGP, ZINB, ZIGPMM, and ZINBMM perform better when zero counts are extremely high. Empirical analysis of data on under-five mortality due to pneumonia in Java Island, Indonesia, indicates that ZINB, ZINBMM, and ZIGPMM have the smallest Akaike Information Criterion (AIC), making them the most suitable models. These models show that exclusive breastfeeding and vitamin A have no significant effect on under-five child mortality due to pneumonia, while severe malnutrition has a statistically significant impact (α=0.05).