Kibria-Lukman Hybrid Estimator for the Conway–Maxwell–Poisson Regression Model

Abstract

The Conway-Maxwell-Poisson regression (CMPR) model provides a flexi- ble framework for analyzing count data in cases of over- and under-dispersion. Estimating the parameter in CMPR typically relies on the maximum likeli- hood estimator (MLE), which can be challenging, mainly when multicollinear- ity exists. In such cases, many estimators offer alternatives to MLE, but often with a more considerable bias. This paper introduces a new hybrid estimator, combining the modified ridge-type estimator’s robustness with the Kibria- Lukman estimator’s efficiency, named the Kibria-Lukman hybrid estimator (KLHE). We propose that KLHE address multicollinearity in CMPR, demon- strating its performance through Monte Carlo simulations. The effectiveness of KLHE is highlighted by its ability to handle multicollinearity, resulting in improved estimation accuracy compared to other estimators. We illustrate the practical application of KLHE using a real dataset, demonstrating its potential to enhance parameter estimation in CMPR models, particularly in settings with prevalent multicollinearity. KLHE is a valuable addition to the statistical toolkit, providing researchers with a robust and efficient means to address multicollinearity in CMPR modeling.