Enhancing the accuracy of modeling highly multicollinear CO2 emission data using a novel generalized Poisson Liu regression method

Count data often exhibit dispersion patterns that the standard Poisson regression model struggles to handle, particularly in cases of overdispersion or underdispersion. The generalized Poisson regression model (GPRM) provides a more flexible alternative, extending the Poisson model to better accommodate such variations. However, parameter estimation in the GPRM typically relies on the generalized Poisson maximum likelihood estimator, which can be problematic when multicollinearity exists among explanatory variables. Biased estimation methods can be used to address this issue. This study explores the Liu estimator as a potential solution for reducing multicollinearity in the GPRM. We also propose different strategies for selecting the Liu parameter to improve estimation accuracy. The theoretical properties of the generalized Poisson Liu estimator are examined, and its performance is compared to that of the generalized Poisson maximum likelihood estimator using matrix mean squared error and scalar mean squared error as evaluation criteria. To assess its effectiveness, we conduct Monte Carlo simulations and apply the method to a carbon dioxide emission dataset in Canada. The results show that the generalized Poisson Liu estimator, particularly with an optimally chosen Liu parameter, outperforms the standard generalized Poisson maximum likelihood estimator in reducing estimation error in the presence of multicollinearity.