Two parameter estimators for the Conway-Maxwell-Poisson regression model

The two-parameter estimator (TPE) was proposed for the Poisson regression model. It has the limitation of a single parameter. Contrary to this, count data models often exhibit the problems of dispersion and multicollinearity. The Conway-Maxwell-Poisson regression model (COMPRM) is suitable to handle both the dispersion and the multicollinearity issues simultaneously. The TPE for COMPRM is proposed to overcome these issues. In order to estimate the COMPRM co-efficient, the method of iterative reweighted least square (IRLS) is used. The efficiency of the estimator is evaluated in terms of mean square error (MSE) through a Monte Carlo simulation study. In the presence of multicollinearity, mostly the Asar and Genc's two-parameter estimator (AGTPE) gives more efficient results for COMPRM as compared to the maximum likelihood (MLE), the Ridge estimator, the Liu estimator and the TPE by Huang and Yang (HYTPE). The proposed estimator is also being studied for real-life application.

Automated summary

The two-parameter estimator (TPE) is proposed for the Poisson regression model, but it has the limitation of a single parameter. The count data models often suffer from the problems of dispersion and multicollinearity. The Conway-Maxwell-Poisson regression model (COMPRM) is suitable for handling both issues simultaneously. To estimate the COMPRM coefficients, the iterative reweighted least square (IRLS) method is used. Through a Monte Carlo simulation study, the efficiency of the estimator is evaluated based on the mean square error (MSE). In the presence of multicollinearity, the Asar and Genc's two-parameter estimator (AGTPE) shows better efficiency for COMPRM compared to other estimators like maximum likelihood (MLE), Ridge estimator, Liu estimator, and the TPE by Huang and Yang (HYTPE). The proposed estimator is also being studied for real-life applications.