New Modified Liu Estimators to Handle the Multicollinearity in the Beta Regression Model: Simulation and Applications
Ali Hammad, E. H. Hafez, Usman Shahzad, Elif Yıldırım, Ehab M. Almetwally, B. M. Golam Kibria
Abstract
The beta regression model (BRM) is widely used for analyzing bounded response variables, such as proportions, percentages. However, when multicollinearity exists among explanatory variables, the conventional maximum likelihood estimator (MLE) becomes unstable and inefficient. To address this issue, we propose new modified Liu estimators for the BRM, designed to enhance estimation accuracy in the presence of high multicollinearity among predictors. The proposed estimators extend the traditional Liu estimator by incorporating flexible biasing parameters, offering a more robust alternative to the MLE. Theoretical comparisons demonstrate the superiority of the new estimators over existing methods. Additionally, Monte Carlo simulations and real-world applications evidence their improved performance in terms of mean squared error (MSE) and mean absolute error (MAE). The results indicate that the proposed estimators significantly reduce estimation bias and variance under multicollinearity, providing more reliable regression coefficients.