On a Mixed Poisson Liu Regression Estimator for Overdispersed and Multicollinear Count Data

The mixed Poisson regression models are commonly employed to analyze the overdispersed count data. However, multicollinearity is a common issue when estimating the regression coefficients by using the maximum likelihood estimator (MLE) in such regression models. To deal with the multicollinearity, a Liu estimator was proposed by Liu (1993). The Poisson-Modification of the Quasi Lindley (PMQL) regression model is a mixed Poisson regression model introduced recently. The primary interest of this paper is to introduce the Liu estimator for the PMQL regression model to mitigate the multicollinearity issue. To estimate the Liu parameter, some exiting methods are used, and the superiority conditions of the new estimator over the MLE and PMQL ridge regression estimator are obtained based on the mean square error (MSE) criterion. A Monte Carlo simulation study and applications are used to assess the performance of the new estimator in the scalar mean square error (SMSE) sense. Based on the simulation study and the results of the applications, it is shown that the PMQL Liu estimator performs better than the MLE and some other existing biased estimators in the presence of multicollinearity.