Geographically Weighted Negative Binomial Regression Modeling using Adaptive Kernel on the Number of Maternal Deaths during Childbirth

Abstract

The standard model that is used for count data is Poisson Regression. In fact, most of the count data is overdispersed, which means that the response variable has greater variance than the mean. So the Poisson Regression cannot be used because overdispersion can cause inaccurate parameter estimators. One of the most widely used methods to overcome overdispersion is Negative Binomial Regression. If there are spatial effects such as spatial heterogeneity that are taken into Negative Binomial model, the appropriate method to analyze is Geographically Weighted Negative Binomial Regression (GWNBR). A spatial weighting matrix is required in the GWNBR model. In this study, three weighting functions were used, that is Adaptive Gaussian Kernel, Adaptive Bisquare Kernel, and Adaptive Tricube Kernel. From the three weighting functions, a model will be formed and the best model will be selected based on the smallest AIC. Count data used in this study is maternal deaths during childbirth in West Java Province, which is the highest case in Indonesia. The results of the analysis show that based on the smallest AIC, the best modeling in maternal deaths during childbirth in West Java is the GWNBR model using the Adaptive Gaussian Kernel weight. The results of the best model were obtained from three groups based on the predictor variables that had a significant effect.