A Data-Driven Shrinkage for Efficient Estimation in the Generalized Poisson Regression Model: Simulation and Application
Abstract
Count data in practice rarely conform to the equidispersion assumption that the standard Poisson regression model imposes. When counts are overdispersed or underdispersed, the generalized Poisson regression model (GPRM) steps in as a more accommodating alternative, extending the classical framework to handle such variation. Like other generalized regression models, GPRM is typically fitted via maximum likelihood estimation (MLE). The problem is that MLE becomes unreliable when predictors are highly correlated, a condition known as multicollinearity, producing unstable coefficients, inflated standard errors, and predictors that appear statistically insignificant even when they are not. This paper introduces a new two-parameter estimator for GPRM specifically designed to handle multicollinearity. We establish its theoretical properties and evaluate it against existing methods through Monte Carlo simulations. We also apply the estimator to Canadian carbon dioxide emissions data. The realdata results mirror the simulation findings: the proposed estimator yields more stable parameter estimates with smaller standard errors, making it a practical tool when correlated predictors threaten inferential quality.OPEN ACCESS Received: 14/04/2026 Accepted: 03/06/2026 Published: 24/07/2026