Mitigating multicollinearity issues to improve the two-parameter estimators for a Beta regression model

The Maximum Likelihood Estimation (MLE) method is commonly used for parameter estimation in statistical models. However, it can be significantly affected by multicollinearity issues, which undermine the reliability of parameter estimates. In Beta regression models (BRMs) for continuous proportions in (0, 1), multicollinearity complicates estimation and produces unstable results when using MLE. To address this challenge, ridge-based and alternative regression estimators have been introduced for BRMs with logit links. Selecting a two-parameter estimator remains a challenge for obtaining reliable parameter estimates for the BRM. In this study, we proposed new two-parameter ridge estimators for the BRM that effectively mitigate multicollinearity. We evaluated the performance of our newly proposed estimators and existing methods based on the mean squared error (MSE) criterion as well as bias, variance, and predictive accuracy. Simulation results showed that the proposed estimators generally performed better than the existing methods across most scenarios. Furthermore, a real-world data application confirmed the simulation results, demonstrating that our proposed estimators provide reliable and robust parameter estimates compared to MLE and the other existing methods.