Improved shrinkage estimators in the beta regression model with application in econometric and educational data

• Published in: Statistical papers (Berlin, Germany) Vol. 64; no. 6; pp. 1891 - 1912
• Main Authors: Arabi Belaghi, Reza, Asar, Yasin, Larsson, Rolf
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2023; Springer Nature B.V
• Subjects: Asymptotic distributional bias; Asymptotic distributional variances; Beta regression model; Continuity (mathematics); Data analysis; Economic analysis; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Estimators; Finance; Insurance; Management; Mathematics and Statistics; Maximum likelihood estimates; Monte Carlo simulation; Multicollinearity; Operations Research/Decision Theory; Parameters; Probability Theory and Stochastic Processes; Regression models; Regular Article; Shrinkage Liu estimators; Statistics; Statistics for Business; Beta regression model; Asymptotic distributional variances; Shrinkage Liu estimators; Monte Carlo simulation; Multicollinearity; Asymptotic distributional bias
• ISSN: 0932-5026; 1613-9798; 1613-9798
• DOI: 10.1007/s00362-022-01355-3

Although beta regression is a very useful tool to model the continuous bounded outcome variable with some explanatory variables, however, in the presence of multicollinearity, the performance of the maximum likelihood estimates for the estimation of the parameters is poor. In this paper, we propose improved shrinkage estimators via Liu estimator to obtain more efficient estimates. Therefore, we defined linear shrinkage, pretest, shrinkage pretest, Stein and positive part Stein estimators to estimate of the parameters in the beta regression model, when some of them have not a significant effect to predict the outcome variable so that a sub-model may be sufficient. We derived the asymptotic distributional biases, variances, and then we conducted extensive Monte Carlo simulation study to obtain the performance of the proposed estimation strategy. Our results showed a great benefit of the new methodologies for practitioners specifically in the applied sciences. We concluded the paper with two real data analysis from economics and education.