Beta ridge regression estimators: simulation and application

• Published in: Communications in statistics. Simulation and computation Vol. 52; no. 9; pp. 4280 - 4292
• Main Authors: Abonazel, Mohamed R., Taha, Ibrahim M.
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 02.09.2023; Taylor & Francis Ltd
• Subjects: Beta regression model; Empirical analysis; Fisher scoring; Maximum likelihood; Maximum likelihood estimators; Mean absolute error; Mean squared error; Monte Carlo simulation; Multicollinearity; Regression models; Ridge regression
• ISSN: 0361-0918; 1532-4141
• DOI: 10.1080/03610918.2021.1960373

The beta regression model is commonly used when analyzing data that come in the form of rates or percentages. However, a problem that may encounter when analyzing these kinds of data that has not been investigated for this model is the multicollinearity problem. It is well known that the maximum likelihood (ML) method is very sensitive to high inter-correlation among the explanatory variables. Therefore, this paper proposes some ridge estimators for the beta regression model to remedy the problem of instability of the traditional ML method and increase the efficiency of estimation. The performance of ridge estimators is compared to the ML estimator through the mean squared error (MSE) and the mean absolute error (MAE) criteria by conducting a Monte-Carlo simulation study and through an empirical application. According to the simulation and application results, the proposed estimators outperform the ML estimator in terms of MSE and MAE.