Modified two-parameter ridge estimator for the Beta logistic model to mitigate multicollinearity

Multicollinearity poses significant challenges to parameter estimation in regression models, often undermining the reliability of traditional methods like maximum likelihood estimation (MLE). This study addresses the issue by evaluating and enhancing regularization techniques, specifically the ridge-based regression (RBR), the Liu regression estimator (LRE), and a modified two-parameter ridge estimator (MTPRE) within the context of the Beta regression model (BRM). However, the selection of appropriate shrinkage parameters remains a persistent challenge. To address this limitation, we propose an MTPRE that eliminates the need for shrinkage parameter tuning, thereby improving estimation stability and accuracy. Through extensive simulation studies, the MTPRE consistently outperformed the MLE, RBR, and LRE under severe multicollinearity based on the mean squared error (MSE). The effectiveness of proposed estimators was further validated using a real-world gasoline yield dataset having multicollinearity issues, where the MTPRE demonstrated superior predictive accuracy and estimation precision. These results highlight the potential of the MTPRE as a practical and efficient method for handling multicollinearity in regression analysis.