Geographically Weighted Three-Parameters Bivariate Gamma Regression and Its Application

Abstract

This study discusses model development for response variables following a bivariate gamma distribution using three-parameters, namely shape, scale and location parameters, paying attention to spatial effects so as to produce different parameter estimator values for each location. This model is called geographically weighted bivariate gamma regression (GWBGR). The method used for parameter estimation is maximum-likelihood estimation (MLE) with the Berndt–Hall–Hall-Hausman (BHHH) algorithm approach. Parameter testing consisted of a simultaneous test using the maximum-likelihood ratio test (MLRT) and a partial test using Wald test. The results of GWBGR modeling three-parameters with fixed weight bisquare kernel showed that the variables that significantly affect the rate of infant mortality (RIM) and rate of maternal mortality (RMM) are the percentage of poor people, the percentage of obstetric complications treated, the percentage of pregnant mothers who received Fe3 and the percentage of first-time pregnant mothers under seventeen years of age. While the percentage of households with clean and healthy lifestyle only significant in several regencies and cities.

Keywords

• GWBGR with three-parameters
• RIM
• MLE
• RMM