Abstract:
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 coeffi cients. However, the variance of the MLE becomes high when the covari ates 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 sca lar 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.
