Tree-Based Random Effects Models for Poverty Analysis in Indonesia

Abstract

Poverty is a multidimensional phenomenon influenced by socioeconomic factors and regional heterogeneity. This study aims to compare the predictive performance of the Linear Mixed Model (LMM), Mixed-Effects Regression Trees (MERT), Random Effects Expectation Maximization Tree (RE-EM Tree), and 3Trees in modeling district- and city-level poverty rates in Indonesia, accounting for clustering by province. The analysis uses data from Statistics Indonesia and evaluates model performance through within-cluster repeated two-fold cross-validation with 50 repetitions, yielding 100 model evaluations. Predictive accuracy is assessed using the Mean Squared Error (MSE) on training data and the Prediction Mean Squared Error (PMSE) on testing data. The results show that 3Trees achieves the lowest average MSE of 7.46 (standard deviation: 1.02) and the lowest average PMSE of 13.97 (standard deviation: 1.70). In comparison, LMM, MERT, and RE-EM Tree produce higher average PMSE values of 14.62, 19.38, and 17.86, respectively. These findings indicate that 3Trees provides the best predictive performance among the four methods under the evaluation procedure used in this study