Robust Regression Modelling using Generalized Maximum Likelihood Estimators and Generalized Scale Estimators on Indonesia’s Poverty Depth Index

Abstract

Poverty remains a critical issue that hinders both social and economic development by increasing the cost of growth and reducing the quality of human resources. One of the key indicators used to measure poverty is the Poverty Depth Index (PDI), which reflects the gap between poor individuals’ expenditures and the poverty line. This study aims to model the Poverty Depth Index Indonesia in 2023 using robust regression with the Generalized Maximum Likelihood (GM) estimator and the Generalized Scale (GS) estimator. The model is designed to identify the factors influencing the PDI, including the percentage of the poor population, gini ratio, poverty line, and Human Development Index. Robust regression was applied because the presence of outliers in the data violated the normality assumption of classical linear regression. The results show that the GS estimator provides a better model with an AIC value of –39.5507 and an adjusted R-squared of 98.048%, compared to the GM estimator, which yielded an AIC of –10.8284 and an adjusted R-squared of 95.058%.