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One of appropriate methods that could be used to model positive integers response and its corresponding predictors is Poisson regression. This method has a strict assumption to be achieved, that is the mean and variance of response variable must be equal (equidispersion). In many practical issues, sometimes, the variance is larger than the mean (overdispersion). Bivariate Poisson Inverse Gaussian Regression (BPIGR) is proposed to overcome the overdispersion issue. In this study, the BPIGR model is developed by adding the exposure variable as the weight of each sample unit. This study applies the proposed method to model the infant and maternal death data (as the responses) and the factors that influence them. The data of East Java 2017 are used for the application. Maximum Likelihood Estimation (MLE) method is used to estimate the parameters, while the hypothesis testing of the BPIGR model is derived using Maximum Likelihood Ratio Test (MLRT) approach. The results showed that the BPIGR model is a proper model for modeling the number of infant and maternal deaths. Furthermore, all predictor variables significantly influence those two responses.

Bivariate Poisson Inverse Gaussian Regression Model with Exposure Variable: Infant and Maternal Death Case Study