Stein estimation in the Conway-Maxwell Poisson model with correlated regressors

Abstract

The Poisson regression model (PRM) is widely used for count data, applicable when the response variable follows a Poisson distribution with equal dispersion. The Conway-Maxwell Poisson regression model (COMPRM) is more flexible and can handle both under-dispersion and over-dispersion. However, the COMPRM may involve correlated regressors, leading to multicollinearity, which makes the maximum likelihood estimator (MLE) inefficient. Biased estimation methods can address multicollinearity in data. This study proposes a Stein estimator, a biased estimation method, for the COMPRM that can simultaneously address correlated regressors and dispersion issues. The estimated mean square error (EMSE) is used to evaluate performance. The proposed estimator's performance is assessed both theoretically and numerically. The numerical evaluations include a simulation study under various parametric conditions and a real-world application. The results from both the simulation study and the real application demonstrate that the Stein estimator outperforms the MLE.