Robust Modeling of Over Dispersed Count Data Using an Outlier-Weighted Poisson Regression Approach

Poisson regression serves as a crucial method for modeling count data; however, it encounters challenges when the data display overdispersion, frequently due to outliers, which can lead to biased inferences and underestimated standard errors. This research introduces an Outlier-Weighted Poisson Model (OWPM) that utilizes robust weights derived from Cook’s distance to reduce the impact of outliers. By employing enhanced simulation designs that account for heteroscedasticity, zero inflation, and correlated predictors, we assess the performance of OWPM in comparison to standard Poisson and Negative Binomial models through various metrics and tests. The findings indicate that OWPM effectively addresses overdispersion, resulting in lower prediction errors and more dependable inferences, akin to those obtained from Negative Binomial regression. Statistical evaluations reveal significant enhancements over the conventional Poisson model, particularly in scenarios with moderate to high levels of outliers. This study offers a practical and computationally efficient method for robust regression of count data, demonstrating wide-ranging applicability.