Ridge estimator in a mixed Poisson regression model

The generalized linear model approach of the mixed Poisson regression models (MPRM) is suitable for over-dispersed count data. The maximum likelihood estimator (MLE) is adopted to estimate their regression coefficients. However, the variance of the MLE becomes high when the covariates are collinear. The Poisson-Modification of Quasi Lindley (PMQL) regression model is a recently introduced model as an alternative MPRM. The variance of the proposed MLE for the PMQL regression model is high in the presence of multicollinearity. This paper adopts the ridge regression method for the PMQL regression model to combat such an issue, and we use several notable methods to estimate its ridge parameter. A Monte Carlo simulation study was designed to evaluate the performance of the MLE and the different PMQL ridge regression estimators by using their scalar mean square (SMSE) values. Further, we analyzed a simulated data and a real-life applications to show the consistency of the simulation results. The simulation and applications results indicate that the PMQL ridge regression estimators dominate the MLE when multicollinearity exists.