Advanced outlier detection methods for enhancing beta regression robustness

Beta regression is a valuable statistical technique for modeling response variables within the standard unit interval (0, 1), where values represent rates, proportions, or probabilities. However, outliers in beta regression can severely impact parameter estimates and model performance, leading to predicted values that deviate significantly from actual observations. Detecting and managing these outliers is essential to ensure model reliability and accuracy. In this study, we propose three novel outlier detection methods: Tukey-Pearson Residual (TPR), Iterative Tukey-Pearson Residual (ITPR), and Iterative Tukey-MinMax Pearson Residual (ITMPR). These methods integrate the principles of Tukey’s boxplot with Pearson residuals, providing robust frameworks for detecting outliers in beta regression models. Extensive simulation studies and real-world data applications were conducted to evaluate their performance against existing outlier detection techniques in the literature. The results indicate that the ITPR method achieves the highest levels of precision and reliability, making it the most effective among the proposed methods. The TPR and ITMPR methods also exhibit strong performance, closely aligning with existing techniques. These findings highlight the potential of the proposed methods to enhance the robustness of beta regression analysis and its practical applications.