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

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  • Nimra Ilyas

  • Muhammad Amin

  • Muhammad Nauman Akram

  • Syeda Maryam Siddiqa

Abstract

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.

Suggested Citation

  • Nimra Ilyas & Muhammad Amin & Muhammad Nauman Akram & Syeda Maryam Siddiqa, 2025. "Improved Liu estimator for the beta regression model: Methods, simulation and applications," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 35(1), pages 21-43.
    • Handle: RePEc:wut:journl:v:35:y:2025:i:1:p:21-43:id:2
    DOI: 10.37190/ord250102
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