Robust estimation methods for addressing multicollinearity and outliers in beta regression models

Beta regression has emerged as a valuable tool in regression analysis, particularly for data constrained within the [0, 1] interval, commonly encountered in chemistry, environmental studies, and biology. However, challenges such as multicollinearity and the influence of outliers persist, affecting the reliability of estimators, particularly the maximum likelihood estimator (MLE). This study addresses these challenges by proposing estimators that combine ridge estimation with robust beta estimators to mitigate the impact of multicollinearity and outliers. We evaluated the performance of the proposed estimators through a comprehensive simulation study and real-life applications involving gasoline yield data, firm cost data, and education data. Results indicate that the robust estimators, especially the Logit Surrogate Maximum Likelihood Estimator (BR-LSMLE), demonstrate greater resilience against outliers and multicollinearity than traditional MLE, making them suitable choices for datasets prone to such issues. These findings underscore the importance of robust estimation techniques in enhancing the reliability and accuracy of beta regression models in empirical research.