On Estimation and Prediction in Mixed Poisson Regression Models for Overdispersed Count Data with Multicollinearity
Mixed Poisson regression models are widely used for analyzing count data across diverse disciplines, owing to their ability to accommodate overdispersion. A persistent challenge in such models, however, is multicollinearity among explanatory variables, which undermines the reliability of regression coefficient estimates obtained via the maximum likelihood estimator (MLE), inflates parameter variances, and substantially increases the mean squared error. The Poisson-modified Quasi-Lindley regression model (PMQLRM), a recently introduced mixed Poisson regression model, has demonstrated promising performance in analyzing overdispersed count data. This paper proposes a James-Stein estimator for the PMQLRM as a means of addressing multicollinearity. The theoretical superiority of the proposed estimator is established through analytical comparisons with competing estimators, and the conditions under which it outperforms the MLE, ridge, and Liu estimators with respect to the MSE criterion are derived. The finite-sample performance of the proposed estimator is further assessed through Monte Carlo simulation studies and a real data application. Both the simulation results and the empirical analyses consistently indicate that the James-Stein estimator outperforms the MLE and other biased estimators in the presence of multicollinearity, which provides more stable and reliable estimates, particularly in settings where multicollinearity is present among the explanatory variables.