Inequality Restricted Estimator for Gamma Regression: Bayesian approach as a solution to the Multicollinearity

• Main Authors: Seifollahi, Solmaz, Bevrani, Hossein, Kamary, Kaniav
• Format: Journal Article
• Language: English
• Published: 09-03-2023
• Subjects: Statistics - Methodology
• DOI: 10.48550/arxiv.2303.05120

In this paper, we consider the multicollinearity problem in the gamma
regression model when model parameters are linearly restricted. The linear
restrictions are available from prior information to ensure the validity of
scientific theories or structural consistency based on physical phenomena. In
order to make relevant statistical inference for a model any available
knowledge and prior information on the model parameters should be taken into
account. This paper 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 term of pertinence and accuracy through Monte Carlo simulations
and application to a real dataset.