Developing a ridge estimator for the gamma regression model

• Published in: Journal of chemometrics Vol. 32; no. 10
• Main Author: Algamal, Zakariya Yahya
• Format: Journal Article
• Language: English
• Published: Chichester Wiley Subscription Services, Inc 01-10-2018
• Subjects: Computer simulation; Economic models; gamma regression model; jackknife estimator; Maximum likelihood estimators; Monte Carlo simulation; multicollinearity; Regression coefficients; Regression models; ridge estimator; Shrinkage
• ISSN: 0886-9383; 1099-128X
• DOI: 10.1002/cem.3054

The ridge regression model has been consistently demonstrated to be an attractive shrinkage method to reduce the effects of multicollinearity. The gamma regression model is a very popular model in the application when the response variable is positively skewed. However, it is known that multicollinearity negatively affects the variance of maximum likelihood estimator of the gamma regression coefficients. To address this problem, a gamma ridge regression model has been proposed. In this study, a new estimator is developed by proposing a modification of Jackknife estimator with gamma ridge regression model. Our Monte Carlo simulation results and the real data application suggest that the proposed estimator can bring significant improvement relative to other competitor estimators, in absolute bias and mean squared error.
This study deals with the problem of the presence of multicollinearity in regression modeling. The gamma regression model is a very popular model in the application when the response variable is positively skewed. In this study, a new estimator is developed by proposing a modification of Jackknife estimator with gamma ridge regression model. The simulation results and the real data application reveal that the proposed estimator can bring significant improvement relative to other competitor estimators, in absolute bias and mean squared error.