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.
Highlights
A study analyzing the causes of haze pollution in China, the results showed that the geographically weighted regression (GWR) model performed better than global models [7]
Researchers using the maximum-likelihood estimation method to find parameter estimation, but the results show that the MLE parameter estimation with no closed-form, the numerical optimization using algorithm Broyden–Fletcher–Goldfarb–Shanno (BFGS) [9]
In bivariate data, that is modeling the case of the rate of maternal mortality (RMM) and rate of infant mortality (RIM) in North Sumatra province in 2017 with geographically weighted bivariate gamma regression (GWBGR)
Summary
Rahayu, Purhadi, Sutikno and Prastyo [4] studied the theory of parameter estimation, hypothesis testing and its application to multivariate gamma regression. Research on parameter estimation and hypothesis testing models gamma geographically weighted regression (GWGR). In bivariate data, that is modeling the case of the rate of maternal mortality (RMM) and rate of infant mortality (RIM) in North Sumatra province in 2017 with geographically weighted bivariate gamma regression (GWBGR). The focus of this study is to determine the parameter estimator and test statistics BGR and GWBGR for three-parameters in the case of RIM and RMM in North Sulawesi, Gorontalo and Central Sulawesi. If the MLE method produces an equation that is not closed form, BHHH methods will be used
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