Parameter estimation and hypothesis testing on geographically weighted gamma regression

Abstract

Having applied to observations from different location, the gamma regression yields global parameters which are assumed to be valid in any location. In fact, each location may have different characteristics such that the existence of spatial effect needs to be considered. In such a case the parameters of gamma regression are less representative. Thus, Geographically Weighted Gamma Regression (GWGR) plays into role. This study aims to estimate parameters of GWGR model using Maximum Likelihood Estimation (MLE) method and numerical optimization using Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. Once the parameter estimation done, the hypothesis testing procedure was used to test parameter similarity between gamma regression and GWGR as well as to test the significance of independent variables within the model, both partially using Z-test and simultaneously using Maximum Likelihood Ratio Test (MLRT).