Negative Binomial Regression Model Estimation Using Stein Approach: Methods, Simulation, and Applications

The negative binomial regression model (NBRM) is popular for modeling count data and addressing overdispersion issues. Generally, the maximum likelihood estimator (MLE) is used to estimate the NBRM coefficients. However, when the explanatory variables in the NBRM are correlated, the MLE yields inaccurate estimates. To tackle this challenge, we propose a James-Stein estimator for the NBRM. The matrix mean squared error (MSE) and the scalar MSE properties are derived and compared with other estimators, including the ridge estimator (RE), Liu estimator (LE), and the MLE. We assess the performance of the suggested estimator using two real applications and a simulation study, with MSE serving as the assessment criterion. Results from both simulations and real applications demonstrate the superior performance of the proposed estimator over the RE, LE, and MLE.