Enhancing Poisson-inverse Gaussian ridge-type estimation for overdispersed and multicollinear data: Properties, estimation techniques, and application

The Poisson inverse Gaussian regression model (PIGRM) is widely used for modeling overdispersion in count data, outperforming baseline Poisson and negative binomial regression models, particularly when dealing with longer tails and higher kurtosis data. The PIGRM coefficients are usually estimated by the maximum likelihood estimator, but its performance deteriorates in the presence of multicollinearity. Multicollinearity means high correlation between explanatory variables, resulting in numerous interactions between variables, which lead to unreliable and unstable parameter estimates, inflated variances, and increased mean squared error. To handle this issue, this study proposes an alternative biased estimator for PIGRM, named the ridge-type estimator, which combines the advantages of the Liu-type and the ridge estimators to yield more reliable and stable parameter estimates. We evaluate the proposed method’s performance through a theoretical comparison, a Monte Carlo simulation study, and an application to real-world data. Simulation results demonstrate that the proposed estimator consistently outperforms existing estimators. The proposed estimator was further validated using a real-world dataset, where multicollinearity is common. The application results confirmed the estimator’s ability to handle multicollinearity while maintaining reliable estimates. This study provides an effective estimation method for researchers working with multicollinear and overdispersed count data.