Pardomuan Robinson Sihombing, Erfiani, Khairil Anwar Notodiputro, Anang Kurnia

Comparative Performance of GLMM and GEE for Longitudinal Beta Regression in Economic Inequality Modelling

Introduction

Comparative performance of glmm and gee for longitudinal beta regression in economic inequality modelling. Compare GLMM & GEE for longitudinal beta regression in modeling economic inequality in Indonesia. GLMM outperforms GEE, offering more accurate estimates for economic and social research.

Abstract

Due to the shortcomings of conventional Gaussian methods, specialized models are frequently needed for longitudinal data analysis with bounded outcomes, such as the Gini ratio. In order to model economic inequality in Indonesia, this study compares the effectiveness of Generalized Linear Mixed Models (GLMM) and Generalized Estimating Equations (GEE) for beta-distributed longitudinal data. Root Mean Square Error (RMSE) and pseudo R-squared values are used to assess model performance using panel data from 10 provinces between 2018 and 2024 as well as important socioeconomic indicators. With lower RMSE and higher explanatory power across all provincial subsets, the results consistently demonstrate that GLMM performs better than both GEE and generalized linear models (GLM). ANOVA tests verify that modeling methodologies, not data heterogeneity in GRDP or Gini values, are responsible for the differences in model performance. These results demonstrate how well GLMM handles complex data structures and within-subject correlations, providing more accurate and effective estimates in longitudinal beta regression scenarios. The study encourages the use of GLMM for more precise longitudinal analysis in economic and social research and offers insightful information for researchers modeling inequality indices.

Review

This study addresses a critical methodological challenge in economic and social research: the appropriate modeling of bounded longitudinal outcomes, such as the Gini ratio, where conventional Gaussian assumptions are violated. By undertaking a direct comparison between Generalized Linear Mixed Models (GLMM) and Generalized Estimating Equations (GEE) for beta-distributed longitudinal data, the authors provide timely and relevant insights. The clear objective of evaluating model effectiveness in the context of economic inequality in Indonesia using a well-defined dataset and robust performance metrics (RMSE and pseudo R-squared) is a significant strength, offering valuable guidance for researchers dealing with similar data structures. The methodology employed is sound, leveraging panel data from 10 Indonesian provinces over a six-year period (2018-2024) and incorporating relevant socioeconomic indicators. The findings unequivocally demonstrate GLMM's superior performance, consistently yielding lower RMSE and higher explanatory power compared to both GEE and generalized linear models (GLM). A particularly strong aspect of the study is the use of ANOVA tests to validate that these performance differences are attributable to the modeling methodologies themselves, rather than inherent data heterogeneity in GRDP or Gini values. This robust conclusion reinforces the assertion that GLMM is better equipped to handle complex data structures and within-subject correlations, which are common in longitudinal studies of economic phenomena. The implications of this research are substantial for the field of economic and social sciences. By providing compelling evidence for the efficacy of GLMM in longitudinal beta regression scenarios, the study offers a clear recommendation for more precise and effective estimation of inequality indices and other bounded outcomes. This will undoubtedly encourage the adoption of GLMM for more rigorous and accurate longitudinal analyses, enhancing the quality and reliability of research in these domains. The paper serves as an insightful guide, empowering researchers to make more informed methodological choices when modeling complex, bounded data over time.

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