New Modified Liu Estimators to Handle the Multicollinearity in the Beta Regression Model: Simulation and Applications

Abstract

The beta regression model (BRM) is widely used for analyzingbounded response variables, such as proportions, percentages. How-ever, when multicollinearity exists among explanatory variables, theconventional maximum likelihood estimator (MLE) becomes unsta-ble and inefficient. To address this issue, we propose new modifiedLiu estimators for the BRM, designed to enhance estimation accu-racy in the presence of high multicollinearity among predictors. Theproposed estimators extend the traditional Liu estimator by incorpo-rating flexible biasing parameters, offering a more robust alternativeto the MLE. Theoretical comparisons demonstrate the superiority ofthe new estimators over existing methods. Additionally, Monte Carlosimulations and real-world applications evidence their improved per-formance in terms of mean squared error (MSE) and mean absoluteerror (MAE). The results indicate that the proposed estimators signif-icantly reduce estimation bias and variance under multicollinearity,providing more reliable regression coefficients.