New ridge parameter estimators for the quasi-Poisson ridge regression model

Abstract

The quasi-Poisson regression model is used for count data and is preferred over the Poisson regression model in the case of over-dispersed count data. The quasi-likelihood estimator is used to estimate the regression coefficients of the quasi-Poisson regression model. The quasi-likelihood estimator gives sub-optimal estimates if regressors are highly correlated—multicollinearity issue. Biased estimation methods are often used to overcome the multicollinearity issue in the regression model. In this study, we explore the ridge estimator for the quasi-Poisson regression model to mitigate the multicollinearity issue. Furthermore, we propose various ridge parameter estimators for this model. We derive the theoretical properties of the ridge estimator and compare its performance with the quasi-likelihood estimator in terms of matrix and scalar mean squared error. We further compared the proposed estimator numerically through a Monte Carlo simulation study and a real-life application. We found that both the simulation and application results show the superiority of the ridge estimator, particularly with the best ridge parameter estimator, over the quasi-likelihood estimator in the presence of multicollinearity issue.