Geographically Weighted Regression and Bayesian Geographically Weighted Regression Modelling with Adaptive Gaussian Kernel Weight Function on the Poverty Level in West Java Province

Ikin Sodikin, Henny Pramoedyo, and Suci Astutik

Abstract

GWR analysis is an expansion of a global regression analysis that generates parameter estimators to predict each point or location where the data is observed and collected. This analysis can accommodate spatial influence in an estimation of the regression model. One of the important issues that arise in GWR modeling is the non-constant variety between observations. Bayesian GWR analysis (BGWR) is considered as one of the best solutions to address the problems that arise in GWR modeling. Through the Bayesian approach, observations that potentially generate a non-constant variety can be detected and weighted directly so as to reduce their effect on model parameter estimation. In this study, the weights used are the adaptive Gaussian Kernel function, where the resulting bandwidth varies for each location of observation. This weighting is applied to compare the estimation results of GWR and BGWR model parameters. The results of the analysis show that the BGWR model is better than the GWR model in explaining the variables of literacy rate (%), percentage of households with joint latrine (%), and percentage of households receiving poor rice (%) to district poverty level in West Java Province. This is shown based on the Mean Square Error (MSE) value that is used as the model goodness criterion. The MSE value for the BGWR model is less than MSE for the GWR model of .

Keywords: spatial, bayesian, Geographically Weighted Regression, adaptive gaussian kernel, non-constant variance, poverty
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