On some beta ridge regression estimators: method, simulation and application

• Published in: Journal of statistical computation and simulation Vol. 91; no. 9; pp. 1699 - 1712
• Main Authors: Qasim, Muhammad, Månsson, Kristofer, Golam Kibria, B. M.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 13-06-2021; Taylor & Francis Ltd
• Subjects: Beta regression model; Empirical analysis; Error analysis; Maximum likelihood estimators; mean Squared error; median Squared error; Monte Carlo simulation; multicollinearity; Parameter estimation; Primary 62J12; Regression models; Secondary 62J07; Simulation; simulation study; Statistical analysis
• ISSN: 0094-9655; 1563-5163; 1563-5163
• DOI: 10.1080/00949655.2020.1867549

The classic statistical method for modelling the rates and proportions is the beta regression model (BRM). The standard maximum likelihood estimator (MLE) is used to estimate the coefficients of the BRM. However, this MLE is very sensitive when the regressors are linearly correlated. Therefore, this study introduces a new beta ridge regression (BRR) estimator as a remedy to the problem of instability of the MLE. We study the mean squared error properties of the BRR estimator analytically and then based on the derived MSE, we suggest some new estimators of the shrinkage parameter. We also suggest a median squared error (SE) performance criterion, which can be used to achieve strong evidence in favour of the proposed method for the Monte Carlo simulation study. The performance of BRR and MLE is appraised through Monte Carlo simulation. Finally, an empirical application is used to show the advantages of the proposed estimator.