A Liu estimator for the beta regression model and its application to chemical data. (8th September 2020) - Karlsson, Peter; Månsson, Kristofer; Kibria, B.M. Golam
Abstract: Beta regression has become a popular tool for performing regression analysis on chemical, environmental, or biological data in which the dependent variable is restricted to the interval [0, 1]. For the first time, in this paper, we propose a Liu estimator for the beta regression model with fixed dispersion parameter that may be used in several realistic situations when the degree of correlation among the regressors differs. First, we show analytically that the new estimator outperforms the maximum likelihood estimator (MLE) using the mean square error (MSE) criteria. Second, using a 'simulation study, we investigate the properties in finite samples of six different suggested estimators of the shrinkage parameter and compare it with the MLE. The simulation results indicate that in the presence of multicollinearity, the Liu estimator outperforms the MLE uniformly. Finally, using an empirical application on chemical data, we show the benefit of the new approach to applied researchers. Abstract : Beta regression is popular when the dependent variable is restricted to the interval [0, 1], such as rates and proportions. This paper suggests Liu estimators that may be used in the presence of multicollinearity. We show that the Liu estimator outperforms the MLE in a simulation study. Finally, using an empirical application on chemical data, we show the benefit of the new approach.