Comparison of some methods for estimating a (COM-Poisson) regression model using simulation

Abstract

     The Conway Maxwell Poisson Regression (COMPR) model is highly flexible due to its ability to adapt to different data dispersion cases, both increasing and decreasing, due to the presence of the smoothing constant and the dispersion parameter within the (COMP) distribution function, which makes it suitable for modeling economic, health, traffic accidents, and other phenomena with varying dispersion. In this research, a regression model (COMPR) was estimated in the case of data with over and underdispersion, where a Monte Carlo simulation study was conducted, to compare between the maximum likelihood estimator (MLE) and the weighted maximum likelihood estimator (WMLE) and the quasi-likelihood estimator (QLE), where the simulation results showed based on the trade-off criteria (MSE) (R²) and for sample sizes (50, 100, 150) and explanatory variables (6) and for the cases of underdispersion at values ​​of the dispersion parameter (0.5, 0.85) and overdispersion at values ​​of the dispersion parameter (3, 9), that the weighted maximum likelihood estimator (WMLE) is more efficient than the maximum likelihood estimator (MLE) and the quasi-likelihood estimator (QLE) in estimating the Conway Maxwell Poisson regression model for all sample sizes and for the cases of over and underdispersion.