A Bias-Reduced Estimator for Negative Binomial Regression with an Application to CO2 Emissions Data

The negative binomial regression model (NBRM) is a widely used approach for analyzing non-negative count data, particularly when overdispersion is present. Parameter estimation in this model typically relies on the maximum likelihood estimator (MLE), which can produce unstable and unreliable results under multicollinearity. To address this issue, we present a hybrid version of the Kibria-Lukman estimator adapted for NBRM. We evaluate the efficacy of our proposed estimator compared to established methods via simulation studies and a practical application for estimating CO₂ emissions from vehicles in Canada. Our results show that the hybrid Kibria-Lukman estimator is more accurate and stable than traditional methods. This makes it a promising way to deal with multicollinearity in count data analysis.