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1 2025

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Improved Liu estimator for the beta regression model: methods, simulation and applications

Ilyas Nimra, Amin Muhammad, Akram Muhammad Nauman, Siddiqa Syeda Maryam

Operations Research and Decisions

2025

Vol. 35, No. 1

21--43

The beta regression model (BRM) is a well-known approach to modeling a response variable that has a beta distribution. The maximum likelihood estimator (MLE) does not produce accurate results for the BRM when the data has a high degree of multicollinearity. We propose a one-parameter beta Liu estimator (OPBLE) for the BRM to tackle the weaknesses of the available Liu estimator in dealing with the issue of multicollinearity. Using the mean square error (MSE), we analytically show that the proposed estimator performs more efficiently than the MLE, beta ridge regression estimator (BRRE), and beta Liu estimator (BLE). We conduct a simulation study and use two practical examples to investigate the performance of the OPBLE. Using the findings from the simulations and empirical studies, we demonstrate the superiority of the proposed estimator over the MLE, BRRE, and BLE in the presence of multicollinearity in the regressors.