Mitigating multicollinearity in zero-inflated negative binomial regression using the modified Kibria-Lukman estimator

Multicollinearity presents a significant challenge in zero-inflated negative binomial (ZINB) regression, leading to unstable maximum likelihood estimates (MLEs) and inflated prediction errors. To address this issue, we investigated the performance of the Kibria-Lukman estimator (ZINB-KLE) and proposed a modified Kibria-Lukman estimator (ZINB-MKLE) that introduces an enhanced bias-adjustment mechanism for improved coefficient stability. Using extensive Monte Carlo simulations under varying degrees of multicollinearity and overdispersion, we demonstrated that the ZINB-MKLE consistently achieves substantially lower scalar mean squared error (SMSE) than MLEs, ZINB-KLEs, and other competing estimators. Application to the Blood Transfusion dataset further confirmed the practical advantages of the ZINB-MKLE, yielding an SMSE of 1.8568 compared to 14,638.75 for the MLE and 685.81 for the ZINB-KLE, highlighting dramatic improvements in predictive accuracy. These findings establish the ZINB-MKLE as a robust and efficient alternative for handling multicollinearity in zero-inflated regression models, with broad implications for statistical modeling in biomedical, epidemiological, and other applied data settings.