Implementation of Gamma Regression and Gamma Geographically Weighted Regression on Case Poverty in Bengkulu Province

Abstract

Spatial analysis involves leveraging spatial references inherent in the data being analyzed. The method to be used in spatial analysis is the Geographically Weighted Regression (GWR) method. GWR is an extension of the linear regression model at each location by adding a weighting function to the model. Generally, the GWR model uses residuals with a normal distribution in its analysis. One distribution that can be used is the gamma distribution. With the development of methods in statistics, when a response variable follows a gamma distribution, analysis is performed using Gamma Regression (GR). GR analysis is conducted because the response variable meets the gamma distribution assumption. One method used for spatial effects with a gamma-distributed response variable is the Gamma Geographically Weighted Regression (GGWR) method. In 2022, Bengkulu Province was among the ten poorest provinces in Indonesia. Therefore, the main objective is to compare the GR and GGWR models and analyze the factors affecting poverty in Bengkulu Province using these models. The results of this study show that the GR model has an R² accuracy of 87.93%, while the GGWR model has an R² accuracy of 95.87%. This indicates that the best model for the analysis is the GGWR. An example of the GGWR model equation for poverty in Bengkulu Province is Y=exp⁡(-6.039+3.15×〖10〗^(-6) X_1-0.055X_2+0.156X_4-0.00021X_5+0.004X_7-0.021X_8-0.006X_9+4.794×〖10〗^(-5) X_10). The factors influencing the GGWR model in Bengkulu Province are Population, Life Expectancy, Average Years of Schooling, Adjusted Per Capita Expenditure, School Participation Rate, Per Capita Expenditure on Food, Households Receiving Rice for the Poor, and Gross Regional Domestic Product. The benefit of this research is to serve as a reference for the provincial government of Bengkulu regarding the variables that influence poverty. It is expected that this will help the government reduce the poverty rate in Bengkulu Province.

Keywords

• spatial analysis
• poverty
• gamma regression
• gamma geographically
• weighted regression.