Analysis of Classical Spatial Regression Models for Human Development Index (HDI) in Sumatra Island

This study applies classical spatial regression models (C-SRM) to analyze the determinants of the Human Development Index (HDI) across 154 cities in Sumatra Island. Unlike standard regression, C-SRM accounts for spatial dependence—where neighboring regions influence each other’s development outcomes. Three C-SRM specifications are evaluated: Spatial Autoregressive (SAR), Spatial Error Model (SEM), and Spatial Autoregressive Moving Average (SARMA). HDI, measuring education, income, and health, is inherently spatial due to interregional mobility, infrastructure spillovers, and policy diffusion. Using data from 2019, 2020, and their average (2019–2020), 13 potential predictors were tested, with variable selection yielding 12, 11, and 11 final variables, respectively. Results show HDI in Sumatra improved steadily from 2010 to 2020, with most cities classified as medium development. Among C-SRMs, the SEM model consistently outperformed SAR and SARMA based on AIC and log-likelihood values, indicating that unobserved spatially correlated factors significantly affect HDI variation. Key significant determinants include poverty rate, poverty gap index, population density, unemployment rate, labor force size, average years of schooling, access to school facilities, sanitation coverage, prevalence of health complaints, and nurse density. The findings confirm that classical spatial models provide a robust, interpretable framework for understanding regional development patterns without requiring complex modern specifications. This study supports the use of SEM as an effective tool for policymakers targeting equitable human development across spatially interconnected regions in Sumatra.