A new method of Poisson regression estimator in the presence of a Multicollinearity problem: Simulation and application

Abstract

A new estimator for the Poisson model is introduced in this study. Poisson regression model is an important log- Linear models which is the tool of modeling the dependent variable when its values are positive and as a form of count data or rates additional to be the appropriate model for analyzing rare events. The maximum likelihood estimator (MLE) suffers from the instability problem in the presence of multicollinearity for a Poisson regression model (PRM). The purpose of this study is to make a comparison of parameters estimation methods for the Poisson regression model when that model suffer from semi multicollinearity problem through the possible methods with proposed method and also propositions for the biased parameter. A Monte Carlo simulation experiment used to generate data follows Poisson regression model and suffer from multicollinearity problem according to variation factors like sample size, the value of simple correlation coefficient and the number of independent variables. So mean squared error and relative efficiency is adopted as a criteria to the comparison of the parameters estimation methods for the model. The simulation results and the real-life application evidenced that the proposed estimator performs better than the rest of the estimators.