Kibria–Lukman estimator for the Conway–Maxwell Poisson regression model: Simulation and applications

Abstract

The Conway–Maxwell Poisson (COMP) regression model is one of the count data models to account for over– and under–dispersion. In regression analysis, when the explanatory variables are correlated, when there is multicollinearity problem, this inflates the standard error of the maximum likelihood estimates. The Kibria–Lukman estimator was provided to handle the effect of multicollinearity in the linear regression model. Therefore, we proposed to extend this estimator to the COMP model to overcome this problem in the COMP model. The proposed estimator mitigates the adverse effect of multicollinearity on the standard error of the estimates. We used the mean squared error (MSE) as the performance assessment criterion to assess the performance of the proposed estimator and others. Also, we compared the proposed estimator theoretically with other estimators (the ridge and Liu estimators). We employed a simulation study and two life applications to study the performance of the proposed estimator. The simulation study and applications results showed the superiority of the proposed estimator because the MSE of the proposed estimator is smaller than the other estimators.

Keywords

• Biased estimator
• Conway–maxwell poisson model
• Kibria–lukman estimator
• Liu estimator
• Multicollinearity
• Ridge regression