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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan Jurnal Teknik Informatika (JUTIF)
Khairil Anwar Notodiputro
School of Data Science, Mathematics and Informatics, IPB University, Indonesia
Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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DEVELOPMENT STUDY OF GLMM-GEE-TREE REGRESSION MODELLING FOR BETA DISTRIBUTION RESPONSE DATA (IMPLICATIONS OF GINI RATIO MODELING IN INDONESIA, 2018-2024) Pardomuan Robinson Sihombing; Erfiani Erfiani; Khairil Anwar Notodiputro; Anang Kurnia
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss3pp2085-2098

Abstract

Economic inequality remains one of the most persistent challenges faced by Indonesia as a developing country. Previous studies have predominantly employed conventional models such as Ordinary Least Squares (OLS) or Panel Least Squares. However, these models are often inappropriate, as they fail to account for the bounded nature of inequality indices such as the Gini ratio, which ranges between 0 and 1. Beta regression offers a more appropriate alternative. In the context of panel data, Generalized Linear Mixed Models (GLMM) and Generalized Estimating Equations (GEE) are commonly used to handle correlated data; however, their integration with nonlinear models for longitudinal Beta-distributed responses remains limited. This study proposes a novel GLMM-GEE-Tree modeling approach for Beta-distributed response data. The proposed model combines GLMM (to capture individual random effects), GEE (to handle temporal correlation and provide robust marginal estimates), and Regression Trees (to address nonlinear relationships and complex interactions). The aim is to simultaneously tackle the challenges of proportional responses, panel structure, random effects, correlation, and nonlinearity. Empirical validation uses Gini ratio data from 34 Indonesian provinces spanning 2018 to 2024. The findings reveal that in this empirical data, the GLMM-GEE-Tree model outperforms alternative models, achieving an R² of 0.472 and a QIC of 13.435 and yielding the lowest AIC and BIC values.
A Comparative Study of Generalized Linear Mixed Model and Mixed Effects Random Forest for Analyzing Data with Outliers Reza Arianti; Khairil Anwar Notodiputro; Yenni Angraini
Jurnal Teknik Informatika (Jutif) Vol. 7 No. 2 (2026): JUTIF Volume 7, Number 2, April 2026
Publisher : Informatika, Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.52436/1.jutif.2026.7.2.5407

Abstract

This study compares MERF and GLMM-NB in analyzing hierarchical data and focusing on the role of residual outliers and the application of winsorization. A two-stage analytical pipeline was implemented: (1) winsorization to reduce extreme residual values, and (2) model training using MERF and GLMM-NB. The dataset comes from the 2021 National Socio-Economic Survey (Susenas) in West Java Province, measuring tobacco consumption intensity. Two statistical approaches are compared, MERF and GLMM with a Negative Binomial distribution (GLMM-NB). Models were trained under two conditions: without winsorization (WIN0) and with two-sided 5% winsorization (WIN5). Winsorization was applied to the training data, and the test data were adjusted using thresholds from the training set. Model performance was assessed using Root Mean Squared Error (RMSE) and the train-test ratio. Under WIN0, GLMM recorded an RMSE of 49.65 for training and 42.27 for testing, while MERF achieved 35.96 and 39.94, respectively. After WIN5, GLMM showed a larger error reduction, with RMSE values of 34.90 (train) and 30.20 (test), while MERF dropped to 26.63 (train) and 28.64 (test). These results indicate that MERF provides higher predictive accuracy, whereas GLMM benefits more from winsorization. Household expenditure, employment status, age, and gender consistently emerged as key variables linked to tobacco consumption intensity. This study is the first to compare MERF and GLMM-NB with winsorization using Indonesia’s hierarchical data. The analytical framework helps inform public health policies aligned with SDG 3: Good Health and Well-being, particularly in reducing tobacco-related health risks.
Co-Authors Anang Kurnia Erfiani Erfiani Pardomuan Robinson Sihombing Reza Arianti Yenni Angraini