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The Conway–Maxwell–Poisson (COMP) model is one of the count data regression models used in over- and underdispersion cases. Thus, COMP regression is a flexible model in the count data models. In the regression analysis, when the explanatory variables are correlated with each other, multicollinearity exists; this inflates the standard error of the maximum likelihood estimates. To handle the effect of multicollinearity, we proposed a new modified Liu estimator for the COMP regression model based on two shrinkage parameters. This estimator is proposed to reduce the effect of multicollinearity on the standard error of the estimates. To evaluate the performance of the proposed estimator, the mean squared error (MSE) criterion is employed. Theoretical comparison of the proposed estimator with existing estimators (ridge, Liu, and modified one-parameter Liu estimators) is made. The results of the simulation study and real-life application indicate the superiority of the proposed estimator.

New modified two-parameter Liu estimator for the Conway–Maxwell Poisson regression model