A Comparison of Bivariate Zero-Inflated Poisson Inverse Gaussian Regression Models with and without Exposure Variables

In this paper, we focus on the comparison of the bivariate zero-inflated Poisson inverse Gaussian regression (BZIPIGR) type II model in two cases: with and without exposure variables. The BZIPIGR type II model is applied to analyze the occurrence of maternal and early neonatal mortality in South Sulawesi Province, Indonesia using 2019 data, which contain many zero values and have the issue of overdispersion in the response variable. Furthermore, to analyze the number of deaths in various areas, the exposure variable is considered. The maximum likelihood estimation (MLE) is used in parameter estimation, which involves numerical iteration and application of the Berndt-Hall-Hall-Hausman (BHHH) algorithm. Sum square error (SSE) serves as the criterion of model selection when exposure variables are included. The existence of exposure variables strongly affects the model's accuracy, especially using the BZIPIGR type II model. According to the SSE and RMSE values, the BZIPIGR type II model with exposure variables performs better than the model without exposure variables in estimating parameter values. All predictors with exposure variables in this study had a significant influence on the number of maternal and early neonatal mortalities.