Abstract:
Count regression models, particularly negative binomial regression (NBR), are widely
used in various fields, including biometrics, ecology, and insurance. Over-dispersion is likely
when dealing with count data, and NBR has gained attention as an effective tool to address this
challenge. However, multicollinearity among covariates and the presence of outliers can lead
to inflated confidence intervals and inaccurate predictions in the model. This study proposes a
comprehensive approach integrating robust and regularization techniques to handle the simultaneous
impact of multicollinearity and outliers in the negative binomial regression model (NBRM). We
investigate the estimators’ performance through extensive simulation studies and provide analytical
comparisons. The simulation results and the theoretical comparisons demonstrate the superiority of
the proposed robust hybrid KL estimator (M-NBKLE) with predictive accuracy and stability when
multicollinearity and outliers exist. We illustrate the application of our methodology by analyzing a
forestry dataset. Our findings complement and reinforce the simulation and theoretical results.
