Comparison of GLM, GLMM and HGLM in Identifying Factors that Influence the District or City Poverty Level in Aceh Province

Abstract

Abstract The purpose of research is to evaluate the GLM, GLMM and HGLM models to poverty data in Aceh Province and then identify the best model. The response variable is the percentage of district or city poverty while the fixed effect is population density, sex ratio, the number of populations, the number of industries, area types, percentage of PLN user, poverty line and percentage of productive age group. The random effect for the GLMM and HGLM models is the average monthly expenditure. The data in 2019 were taken from website of the Aceh Central Statistics Agency (BPS) on April 13, 2020. For aggregate, the response variable and the random effect met the normal and gamma distribution. the results showed that the population density has an influence on the percentage of poverty in the GLM and HGLM, while in the GLMM, there are no factors that affect it. The scores of determination coefficient (R2) for GLM, GLMM and HGLM were 75.795%, 68.441% and 75.881%, respectively whereas scores of RMSE of them were 0.121, 1.917 and 0.120, respectively. Because the HGLM model has the largest R2 and the smallest RMSE, the HGLM was said to be the best model for the case.