A Bayesian-Elastic net Hybrid for Estimating the Gamma Regression Model in the presence of Multicollinearity With Application

Abstract

Abstract. In this research, the Bayesian approach was employed to estimate the parameters of the Gamma regression model in the presence of the multicollinearity problem. As is well known, the Bayesian approach becomes inefficient in models suffering from multicollinearity, as the estimated parameters tend to be inefficient. Therefore, to enhance the performance of this approach, one of the penalization techniques, namely the Elastic Net technique, was utilized to estimate the parameters of the Gamma regression model under multicollinearity. The study aimed to investigate the behavior of the Bayesian approach in parameter estimation when this technique is applied, as well as to compare the proposed technique with classical methods. The results demonstrated the superiority and effectiveness of the employed technique in the estimation process. Simulation experiments were conducted in addition to real data analysis by computing the mean squared error at different levels of correlation among the independent variables and under varying sample sizes