Developing ridge estimators for the extended Poisson-Tweedie regression model: Method, simulation, and application

The extended Poisson-Tweedie (EPT) regression model is one of the count data regression models. It's a more flexible model in count data; since EPT model can be used in two situations: over-dispersion or under-dispersion but under assumption that this model uses second moment to be more flexible model. However, when the predictor (explanatory) variables of the EPT model are highly correlated, this means that there is the multicollinearity problem in the model. It causes inflation of the standard error of the maximum likelihood estimates and makes some of the significant variables insignificant. To handle and reduce the impact of the multicollinearity problem in the EPT model, we developed ridge estimators for this model. A theoretical comparison between the maximum likelihood and the proposed ridge estimators is done. The efficiency of the estimators is evaluated using the mean squared error (MSE). The simulation study and real-life application are used to evaluate the proposed estimators. We examined the performance of seven ridge estimators of the biasing parameter (k) to determine the most appropriate ridge estimator for this model. The simulation and application results showed that the proposed ridge estimator is superior to the maximum likelihood estimator, as it has the smallest MSE.