Developing a new modified two–parameter Liu estimator for the gamma regression model: Method, simulation and application to health data

The gamma regression model is one of the types of generalized linear models intended to work at the observation level and be able to handle the dependent variable, which is continuous, positive, and can often be skewed. This model is particularly beneficial in situations where the data distribution does not conform to the standard linear regression model's required normality. However, this model can suffer from multicollinearity. This paper develops a new two-parameter Liu (MTP-Liu) estimator for the gamma regression model. Further, we examine the mean squared errors of the proposed MTP-Liu estimator. In addition, we offer a few theorems to establish the relationship between the new estimators and the existing ones. To study the performance of the estimators under various forms of collinearity in the sense of the above definition, we undertake a Monte Carlo simulation exercise. In order to illustrate the practical applicability of the new estimator, we include two numerical examples using real data. The simulations and results of the real data show that the proposed MTP-Liu estimator performs better than its competitors.