Issue: 2025/Vol.35/No.1, Pages 21-43
IMPROVED LIU ESTIMATOR FOR THE BETA REGRESSION MODEL: METHODS, SIMULATION AND APPLICATIONS
Nimra Ilyas
, Muhammad Amin 
, Muhammad Nauman Akram , Syeda Maryam Siddiqa
Cite as: N. Ilyas, M. Amin, M. N. Akram, S. M. Siddiqa. Improved Liu estimator for the beta regression model: Methods, simulation and applications. Operations Research and Decisions 2025: 35(1), 21-43. DOI 10.37190/ord250102
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 there is a high degree of multicollinearity in the data. 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 Squared 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.
Keywords: Beta regression, beta ridge regression estimator, beta Liu estimator, multicollinearity
Received: 1 May 2024 Accepted: 16 November 2024
Published online: 8 February 2025