A Modified Inverse Gaussian Poisson Regression with an Exposure Variable to Model Infant Mortality

Infant mortality has generally been increasing and has become an issue that urgently needs to be addressed. As the number of infant deaths is count data, a Poisson regression model is needed to determine the causal factors. However, the assumption of equidispersion in Poisson regression is rarely satisfied. The overdispersion issue is frequently found in real data. Thus, this research employs mixed Poisson distribution modeling to overcome the overdispersion issue, namely, the inverse Gaussian Poisson regression (IGPR) model. In this study, a simple IGPR model, a modified IGPR model, and the negative binomial regression (NBR) model are compared. The results show that the modified IGPR model and the NBR model with an exposure variable outperform the benchmark, based on the global deviance and Akaike Information Criteria (AIC) value, to model the number of infant deaths in East Nusa Tenggara, Indonesia. The significant predictors that affect the number of infant mortalities are the percentage of complete basic immunization, the percentage of low birth weight (LBW), the percentage of babies under six months who receive exclusive breastfeeding, the percentage of infants who receive vitamin A, and the percentage of births assisted by health workers in the district.