Reducing The Influence of High Leverage Points in Beta Regression Using The Gm6 Robust Estimator

Hamza Lateef Katea  Al-Ayashy; Taha  Alshaybawee

Hamza Lateef Katea Al-Ayashy Department of Statistics, College of Administration and Economics, University of Al-Qadisiyah, Al-Qadisiyah, Iraq
Taha Alshaybawee Department of Statistics, College of Administration and Economics, University of Al-Qadisiyah, Al-Qadisiyah, Iraq

Keywords: Beta regression, GM6-BR-resistant estimation, high leverage points, outliers

Abstract

The problem of outliers and high leverage points is one of the most prominent challenges facing the design of statistical models, especially in regression models, as they have a significant impact on distorting the results of statistical estimation. This research aims to address the impact of high leverage points in a beta regression model using robustness estimation methods, specifically the GM6 multistage estimator (GM6-BR). A comparison of four estimation methods was studied: traditional estimation (BR), least discrete squares estimator (LTS-BR), generalized estimation (GM-BR), and GM6-BR. A simulation study was conducted on two models: one linear and the other nonlinear, with data contamination of 10% and 20% introduced to test the robustness of the different methods. The results demonstrated a clear superiority of the GM6-BR method in terms of reducing error (RMSE, MAE) and skewness (BIAS), while maintaining stability in the presence of contamination. Practical application on real data also showed that GM6-BR was least affected by outliers compared to other methods, while the traditional BR method exhibited the highest level of distortion. Therefore, the study recommends adopting GM6-BR as an effective and accurate option for analyzing data containing high leverage points or outliers, especially within beta regression models.

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