An Almost Unbiased Ridge Estimator for the Conway-Maxwell-Poisson Regression Model

The Poisson model is the most widely used model for counts type response variables. It has a limitation of equal mean and variance, which undermines its application as compared to the Conway-Maxwell-Poisson-regression model (COMPRM). In general, the maximum likelihood estimator (MLE) is used to estimate the COMPRM, but when there is a high correlation among the explanatory variables, the MLE may not provides efficient estimates. In this situation, the ridge estimation technique provides a better alternative to the MLE but with a larger bias. In this work, we propose an almost unbiased ridge estimator for the estimation of COMPRM coefficients and derive its theoretical properties. The proposed estimator is compared with the available biased estimator as well as the MLE based on the mean squared error (MSE) and bias criteria. A Monte Carlo simulation analysis is performed for comparisons under various controlled conditions. A real application is considered to study the significance of the proposed estimator using MSE and cross-validation criteria. The simulation and real-world application results show that the proposed estimator outperforms the classical MLE and ridge estimators in terms of the minimum MSE and bias.

Automated summary

The Poisson model, commonly used for counts type response variables, has a limitation of equal mean and variance compared to the Conway-Maxwell-Poisson-regression model (COMPRM). This study proposes an almost unbiased ridge estimator for the estimation of COMPRM coefficients and derives its theoretical properties. The results show that the proposed estimator outperforms the classical MLE and ridge estimators in terms of the minimum MSE and bias.