A Comparison of the Robust Zero-Inflated and Hurdle Models with an Application to Maternal Mortality

This study evaluates the performance of count regression models in the presence of zero inflation, outliers, and overdispersion using both simulated and real-world maternal mortality dataset. Traditional Poisson and Negative Binomial regression models often struggle to account for the complexities introduced by excess zeros and outliers. To address these limitations, this study compares the performance of robust zero-inflated (RZI) and robust hurdle (RH) models against conventional models using the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and the Vuong test to determine the best-fitting model. Results indicate that the robust zero-inflated Poisson (RZIP) model performs best overall. The simulation study considers various scenarios, including different levels of zero inflation (50%, 70%, and 80%), outlier proportions (0%, 5%, 10%, and 10 15%), dispersion values (1, 3, and 5), and sample sizes (50, 200, and 500). Based on AIC comparisons, the robust hurdle Poisson (RZIP) and robust hurdle Poisson (RHP) models demonstrate superior performance when outliers are absent or limited to 5%, particularly when dispersion is low (1 or 3). However, as outlier levels and dispersion increase, the robust zero-inflated negative binomial (RZINB) and robust hurdle negative binomial (RHNB) models outperform robust zero-inflated Poisson (RZIP) and robust hurdle Poisson (RHP) across all levels of zero inflation and sample sizes considered in the study.