Modeling Maternal Mortality in East Java: A GWBZIGPR Approach with Spatial Weighting

Abstract

Maternal mortality remains a critical indicator of health development, reflecting the quality of maternal health services and the socio-geographic conditions of a region. Data on maternal deaths during pregnancy and childbirth in East Java Province in 2025 exhibit characteristics of correlated bivariate count data, excess zeros relative to the Poisson specification, overdispersion, and spatial heterogeneity. This study applies the Geographically Weighted Bivariate Zero-Inflated Generalized Poisson Regression (GWBZIGPR) model to 38 districts and cities in East Java Province, with parameter estimation employing Maximum Likelihood Estimation and the Berndt–Hall–Hall–Hausman (BHHH) numerical iteration. Significance testing uses the Maximum Likelihood Ratio Test (MLRT) for simultaneous testing and the Z-test for partial testing, and MLRT confirms that the model is significant overall, while the partial tests show that no individual parameter is statistically significant at the 5% level. The optimal weighting function is selected by comparing four kernels, namely Fixed Gaussian, Fixed Bisquare, Adaptive Gaussian, and Adaptive Bisquare, based on the lowest Akaike Information Criterion Corrected value (AICc). The results show that, among the four kernels, the GWBZIGPR model with the Adaptive Bisquare kernel yields the smallest AICc value of 575.2514. Because the effective degrees of freedom of the local GWBZIGPR model (23 parameters estimated separately at each of the 38 locations) differ fundamentally from those of the global BZIGPR model, the AICc values of the two models are not on a strictly equivalent penalty basis and are therefore not used to rank one model as superior to the other. Model preference is instead based on estimation precision and inferential reliability. The standard errors of the local estimates are substantially larger than the parameter estimates across locations, indicating that the GWBZIGPR model suffers from low estimation precision for this dataset and that the BZIGPR model, which estimates parameters globally, remains the preferred model for this dataset.