A Huang–Yang-type Estimator to Reduce Multicollinearity in a Negative Binomial Regression Model

Abstract

Researchers often choose the Poisson distribution when analyzing count data. However, the Poisson distribution requires the constraint that the expected value and variance are equal, known as the “equidispersion” condition. Because this condition is rarely encountered in real life, the Negative Binomial distribution is used as an alternative to the Poisson distribution. In this study, a new biased estimator combining the properties of the Kibria–Lukman and Huang–Yang estimators is proposed as an alternative to existing estimators when the response variable follows a negative binomial distribution to reduce the effect of multicollinearity in regression models. Several estimators based on the mean square error have been proposed to estimate the optimal value of the biasing parameter(s). Furthermore, a simulation study is conducted to investigate the performance of the proposed biased estimators. Finally, the superiority of the proposed estimators is examined using real and experimental data.

Keywords

• Negative Binomial regression
• Mean squared error
• Multicollinearity
• Ridge estimator
• Liu estimator

References

1. Akay, K. U., Ertan, E., & Erkoç, A. (2023). A New biased estimator and variations based on the Kibria Lukman Estimator. Istanbul Journal of Mathematics, 1(2), 74-85. google scholar
2. Akay, K. U. & Ertan, E., (2022). A new Liu-type estimator in Poisson regression models, Hacet. J. Math. Stat., 51 (5), 1484-1503. google scholar
3. Almulhim, F. A., Nagy, M., Hammad, A. T., Mansi, A. H., Mekiso, G. T. & El-Raouf, M. A. (2025). New two parameter hybrid estimator for zero inflated negative binomial regression models. Scientific Reports, 15(1), 21239. google scholar
4. Alrweili, H. (2024). Kibria–Lukman Hybrid Estimator for Handling Multicollinearity in Poisson Regression Model: Method and Application. International Journal of Mathematics and Mathematical Sciences, 2024(1), 1053397. google scholar
5. Asar, Y. (2018) Liu-type negative binomial regression: A comparison of recent estimators and applications. In Trends and Perspectives in Linear Statistical Inference; Springer: Cham, Switzerland, pp. 23–39. google scholar
6. Ashraf, B., Amin, M., Emam, W., Tashkandy, Y., & Faisal, M. (2025). Negative Binomial Regression Model Estimation Using Stein Approach: Methods, Simulation, and Applications. Journal of Mathematics, 2025(1), 9134821. google scholar
7. Çetinkaya, M. K. & Kaçıranlar, S. (2019). Improved two-parameter estimators for the negative binomial and Poisson regression models. Journal of Statistical Computation and Simulation, 89(14), 2645-2660. google scholar
8. Çiçek, C., & Akay, K. U. (2024). A New Kibria-Lukman-Type Estimator for Poisson Regression Models. Acta Infologica, 8(2), 199-212. google scholar

9. Ertan, E., & Akay, K. U. (2023). A new class of Poisson Ridge-type estimator. Scientific Reports, 13(1), 4968. google scholar
10. Hilbe, J. M. (2011). Negative binomial regression. Cambridge University Press. google scholar
11. Hilbe, J. M. (2014) Modeling Count Data; Cambridge University Press: Cambridge. google scholar
12. Hoerl, A. E., & Kennard, R. W. (1970) Ridge regression: biased estimation for nonorthogonal problems. Technometrics, 12(1), 55-67. google scholar
13. Huang, J. & Yang, H. (2014). A two-parameter estimator in the negative binomial regression model. Journal of Statistical Computation and Simulation, 84 (1), 124-134. google scholar
14. Liu, K. (1993) A new class of biased estimate in linear regression. Commun Stat Theory Methods, 22(2), 393-402. google scholar
15. Liu, K. (2003) Using Liu-type estimator to combat collinearity. Commun Stat Theory Methods, 32(5), 1009-1020. google scholar
16. Jabur, D. M., Rashad, N. K., & Algamal, Z. Y. (2022). Jackknifed Liu-type estimator in the negative binomial regression model. International Journal of Nonlinear Analysis and Applications, 13(1), 2675-2684. google scholar
17. Jochmann, M. (2017) zic: Bayesian Inference for Zero-Inflated Count Models. R Package Version 0.9, 1. England. Available online: https://cran.r-project.org/web/packages/zic/zic.pdf (accessed on July 21, 2025). google scholar
18. Kaçıranlar, S. & Dawoud, I. (2018). On the performance of the Poisson and the negative binomial ridge predictors. Communications in Statistics-Simulation and Computation, 47(6), 1751-1770. google scholar
19. Kibria, B. M. G., & Lukman, A. F. (2020) A new ridge-type estimator for the linear regression model: simulations and applications. Scientifica https ://doi.org/10.1155/2020/9758378 google scholar
20. Koç, T., & Koç, H. (2023). A new effective jackknifing estimator in the negative binomial regression model. Symmetry, 15(12), 2107. google scholar
21. Månsson, K. (2012). On ridge estimators for the negative binomial regression model. Economic Modelling, 29(2), 178-184. google scholar
22. Månsson, K. (2013). Developing a Liu estimator for the negative binomial regression model: method and application. Journal of Statistical Computation and Simulation, 83(9), 1773-1780. google scholar
23. Michimae, H., Emura, T., & Furukawa, K. (2024). Bayesian ridge estimators based on a vine copula-based prior in Poisson and negative binomial regression models. Journal of Statistical Computation and Simulation, 94(18), 3979-4000. google scholar
24. Özkale, M.R. & Kaçıranlar, S. (2007) The restricted and unrestricted two-parameter estimators. Commun Stat Theory Methods, 36, 2707–2725. google scholar
25. Riphahn, R. T., Wambach, A., & Million, A. (2003). Incentive Effects in the Demand for Health Care: A Bivariate Panel Count Data Estimation. Journal of Applied Econometrics, 18, 387–405. google scholar
26. Türkan, S. & Özel, G. (2018). A Jackknifed estimators for the negative binomial regression model. Communications in Statistics-Simulation and Computation, 47(6), 1845-1865. google scholar
27. Yang, H., & Chang, X. (2010) A new two-parameter estimator in linear regression. Commun Stat Theory Methods, 39 (6), 923–934 google scholar