Comparison of Generalized Poisson Regression and Negative Binomial Regression Models Based on Akaike Information Criterion Values - Sinta Qorri Aina; Darnah; Meirinda Fauziyah; Wiwit Pura Nurmayanti (Statistika, 2025)
Abstract. Poisson regression models discrete data and assumes equidispersion, where the variance equals the mean. It is frequently observed that discrete data exhibits a variance exceeding its mean, a phenomenon known as over-dispersion. Over-dispersion may be addressed through various methodologies, such as Generalized Poisson Regression (GPR) and Negative Binomial Regression (NBR). Model selection is predicated on the smallest Akaike Information Criterion (AIC) value. This study aimed to identify the best model in the comparison of models between GPR and NBR based on the smallest AIC value so that it can be known what factors influence the number of cases of pulmonary tuberculosis (TB) in Indonesia in 2022. The results of the study showed that the NBR model was the best model, with an AIC value of 688.49. Factors that influence cases of pulmonary TB in Indonesia in 2022 are the percentage of households that have access to proper sanitation, nursing staff, and the percentage of education levels completed are high school or equivalent.