A Comparative Evaluation of Poisson, Negative Binomial, and Zero-Inflated Models for Count Data

Abstract

This study compares Poisson, Negative Binomial (NB), Zero-Inflated Poisson (ZIP), and Zero-Inflated Negative Binomial (ZINB) models for count data. Results show that the Poisson model performs poorly due to overdispersion, while the NB improves fit by relaxing the equidispersion assumption. The ZIP model better accounts for excess zeros but still underestimates variance. The ZINB model consistently outperforms all alternatives, achieving the lowest AIC, BIC, RMSE, and MAE, alongside the best goodness-of-fit statistics and residual diagnostics. Parameter estimates further confirm the significant effects of age, income, and education on count outcomes, with the zero-inflation component capturing structural zeros. Overall, findings establish the ZINB model as the most reliable approach for handling complex count data with overdispersion and zero inflation.