Spatial Analysis of the Human Development Index in Central Java Using Geographically Weighted Generalized Log-Gamma Regression

¹ Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, 60111 Surabaya, Indonesia
² Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro, 50275 Semarang, Indonesia

^* Corresponding author: purhadi@its.ac.id

Abstract

The Human Development Index in Central Java ranks 15th in Indonesia; however, some specific districts and cities receive high categories while others are categorized as low. The uneven conditions among these regions need to be analysed to identify the factors influencing the HDI in the districts and cities of Central Java. The HDI data in this province exhibits an asymmetric pattern, identified as having a Generalized log-gamma distribution and contains spatial effects. A more in-depth analysis can be conducted using the Geographically Weighted Generalized Log-Gamma Regression (GWGLGR) model, which is a point-based spatial regression model that requires the response variable to be distributed as Generalized Log-Gamma. The Generalized Log-Gamma (GLG) distribution is an extension of the Log Gamma distribution. GWGLGR model is capable of specifically depicting the HDI conditions in Central Java with different models for each area. The variable X₁ is the most consistently significant variable across all regions, while other variables (X₂, X₃, X₄) are only significant in some areas. The improvement of the HDI in Batang and Banjarnegara districts specifically needs poverty reduction, equitable development, and better access to quality upper secondary education. GWGLGR performs better than GLG regression, with a much lower AICc (67.44 vs. 183.61).