A Statistical Approach Zero Inflated Negative Binomial and Hurdle Negative Binomial Modelling for Toddler Deaths due to Pneumonia

Abstract

The Generalized Linear Model (GLM) is an extension of the general regression model for response variables following an exponential family distribution, including normal, binomial, Poisson, negative binomial, exponential, and gamma. If the response variable is discrete and follows a Poisson distribution, then the Poisson regression model can be used for model formation. However, in its application, overdispersion often occurs, where the variance is greater than the mean. Overdispersion in Poisson regression can occur due to a large number of observations having zero values in the response variable (excess zeros). Data experiencing overdispersion and excess zeros are more suitable for using Zero Inflated Negative Binomial (ZINB) and Hurdle Negative Binomial (HNB) regressions. In this study, the models were further developed into ZINB and HNB regression models with transformed variables to improve model performance. Real-world issues related to these methods can be encountered in mortality cases, where the data used pertain to the number of toddler deaths due to pneumonia in East Java in 2022. The results of model selection using AIC show that the ZINB regression model with transformed variables is the best model in this study, with an AIC value of 58.63682. The results of the partial significance test of parameters in the ZINB regression  model with transformed variables indicate that the percentage of vitamin A supplementation (x₅), and the percentage of exclusive breastfeeding (x₇) significantly influence the number of toddler deaths due to pneumonia.