Liu Estimation Method in the Zero-Inflated Conway Maxwell Poisson Regression Model

The Zero-Inflated Conway-Maxwell Poisson Regression Model (ZICPRM) is developed specifically for overdispersed, underdispersed, and excessive zeros in the count data. The ZICMPRM is estimated by the maximum likelihood estimator (MLE). The estimation through MLE can be affected by the presence of multicollinearity among regressors. Hence, the Liu estimator is brought forth to effectively deal with the effect of multicollinearity and to solve the problems of overdispersion, equal dispersion, and underdispersion. A theoretical and numerical comparison of the Liu estimator and MLE has been performed, and biasing parameters for the Liu estimator have been incorporated into the ZICPRM. A Monte Carlo simulation study is performed to compare the performance of the proposed estimator, where mean squared error (MSE) is utilized to demonstrate its superiority. Further, application to real-world data from West Nile Virus surveillance demonstrate that the Liu estimator outperforms the MLE, with smaller MSE in the situation of multicollinearity.