Developed first-order approximated estimators for the gamma distributed response variable

Abstract

Generalized linear models (GLM) applications have become very popular in recent years. However, if there is a high degree of relationship between the independent variables, the problem of multicollinearity arises in these models. In this paper, we introduce new first-order approximated (FOA) estimators in the case of gamma distributed response variables in GLMs. Also, the generalization of some estimation methods for ridge and Liu parameters in gamma regression models (GRM) are provided. The superiority of these estimators is assessed by the estimated mean squared error (EMSE) via Monte Carlo simulation study where the response follows a gamma distribution with the log link function. We finally consider a real data application. The proposed estimators are compared and interpreted.

Keywords:

• Gamma regression models
• Generalized linear models
• First-order approximated estimators
• Log link
• Monte Carlo
• Multicollinearity

Acknowledgments

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions which were helpful in improving the paper.