Bivariate zero-inflated generalized Poisson regression on modelling stillbirth and maternal death

Abstract

Generalized Poisson regression is a common model used for over/underdispersion count data. However, excess zeros in the observed data can create difficulties for this model. The zero-inflation regression model is a model that can be used to handle excess zeros on data. If the observational data is over/underdispersion and excess zero, then the Zero-Inflated Generalized Poisson regression (ZIGPR) is the proper model to use. This study aims to obtain the estimator of the BZIGP regression through the EM algorithm and to model data on stillbirths and maternal deaths in 91 sub-districts in Pekalongan Residency, Central Java. Because there are two response variables, the regression analysis used is Bivariate ZIGPR (BZIGPR). The BZIGPR discussed in this study is BZIGPR type II, where the two BZIGP type II marginal distributions have their parameter of zero inflation to be applied in a broader range. BZIGPR parameter estimation is done using the EM algorithm, while the hypothesis testing of the BZIGPR model is derived using the Maximum Likelihood Ratio Test (MLRT). The model generated in the BZIGPR consists of two parts, the log model and the logit model. The results showed an overdispersion and an underdispersion in maternal deaths and stillbirths data, respectively. Based on empirical studies, all predictor variables affect the two response variables significantly.