Inequality restricted estimator for gamma regression: Bayesian approach as a solution to the multicollinearity

Abstract

In this article, we consider the multicollinearity problem in the gamma regression model when model parameters are bounded linearly restricted. The linear restrictions are available from prior information to ensure the validity of scientific theories or structural consistency based on physical phenomena. To make relevant statistical inference for a model, any available knowledge and prior information on the model parameters should be taken into account. This article proposes therefore an algorithm to acquire Bayesian estimator for the parameters of a gamma regression model subjected to some linear inequality restrictions. We then show that the proposed estimator outperforms the ordinary estimators such as the maximum likelihood and ridge estimators in terms of pertinence and accuracy through Monte Carlo simulations and application to a real dataset.