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

Masad A. Alrasheedi; Adewale F. Lukman; Rasha A. Farghali; Asamh Saleh M. Al Luhayb; Masad A. Alrasheedi; Adewale F. Lukman; Rasha A. Farghali; Asamh Saleh M. Al Luhayb

doi:10.3934/math.20251028

AIMS Mathematics

2025, Volume 10, Issue 10: 23169-23186. doi: 10.3934/math.20251028

Previous Article Next Article

Research article

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

1.
Department of Management Information Systems, College of Business Administration, Taibah University, Madinah, Saudi Arabia
2.
Department of Mathematics and Statistics, University of North Dakota, Grand Forks, North Dakota 58202, USA
3.
Department of Mathematics, Insurance and Applied Statistics, Helwan University, Cairo 11795, Egypt
4.
Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia

Received: 21 June 2025 Revised: 10 September 2025 Accepted: 29 September 2025 Published: 13 October 2025
MSC : 62J05, 62J07, 62J12

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.
- zero-inflated,
- negative binomial,
- multicollinearity,
- ridge regression,
- modified Kibria-Lukman estimator,
- simulation
Citation: Masad A. Alrasheedi, Adewale F. Lukman, Rasha A. Farghali, Asamh Saleh M. Al Luhayb. Mitigating multicollinearity in zero-inflated negative binomial regression using the modified Kibria-Lukman estimator[J]. AIMS Mathematics, 2025, 10(10): 23169-23186. doi: 10.3934/math.20251028

Related Papers:

Abstract

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.

References

[1]	A. Lukman, B. Aladeitan, K. Ayinde, M. Abonazel, Modified ridge-type for the Poisson regression model: simulation and application, J. Appl. Stat., 49 (2022), 2124–2136. https://doi.org/10.1080/02664763.2021.1889998 doi: 10.1080/02664763.2021.1889998
[2]	A. Lukman, O. Albalawi, M. Arashi, J. Allohibi, A. Alharbi, R. Farghali, Robust negative binomial regression via the Kibria-Lukman strategy: methodology and application, Mathematics, 12 (2024), 2929. https://doi.org/10.3390/math12182929 doi: 10.3390/math12182929
[3]	Z. Algamal, A. Lukman, M. Abonazel, F. Awwad, Performance of the ridge and Liu estimators in the zero‐inflated Bell regression model, J. Math., 2022 (2022), 9503460. https://doi.org/10.1155/2022/9503460 doi: 10.1155/2022/9503460
[4]	S. Seifollahi, H. Bevrani, Z. Algamal, Shrinkage estimators in zero-inflated Bell regression model with application, J. Stat. Theory Pract., 19 (2025), 1. https://doi.org/10.1007/s42519-024-00415-1 doi: 10.1007/s42519-024-00415-1
[5]	Y. Al-Taweel, Z. Algamal, Some almost unbiased ridge regression estimators for the zero-inflated negative binomial regression model, Periodicals of Engineering and Natural Sciences, 8 (2020), 248–255.
[6]	B. Kibria, K. Månsson, G. Shukur, Some ridge regression estimators for the zero-inflated Poisson model, J. Appl. Stat., 40 (2013), 721–735. https://doi.org/10.1080/02664763.2012.752448 doi: 10.1080/02664763.2012.752448
[7]	M. Akram, N. Afzal, M. Amin, A. Batool, Modified ridge-type estimator for the zero-inflated negative binomial regression model, Commun. Stat.-Simul. C., 53 (2024), 5305–5322. https://doi.org/10.1080/03610918.2023.2179070 doi: 10.1080/03610918.2023.2179070
[8]	M. Akram, M. Amin, N. Afzal, B. Kibria, Kibria-Lukman estimator for the zero-inflated negative binomial regression model: theory, simulation and applications, Commun. Stat.-Simul. C., 54 (2025), 1464–1480. https://doi.org/10.1080/03610918.2023.2286436 doi: 10.1080/03610918.2023.2286436
[9]	M. Akram, M. Abonazel, M. Amin, B. Golam Kibria, N. Afzal, A new Stein estimator for the zero-inflated negative binomial regression model, Concurr. Comp.-Pract. Expe., 34 (2022), e7045. https://doi.org/10.1002/cpe.7045 doi: 10.1002/cpe.7045
[10]	T. Omer, P. Sjölander, K. Månsson, B. Kibria, Improved estimators for the zero-inflated Poisson regression model in the presence of multicollinearity: simulation and application of maternal death data, Communications in Statistics: Case Studies, Data Analysis and Applications, 7 (2021), 394–412. https://doi.org/10.1080/23737484.2021.1952493 doi: 10.1080/23737484.2021.1952493
[11]	M. Zeeshana, A. Khana, M. Amanullaha, M. Bakrb, A. Alshangitib, O. Balogun, et al., A new modified biased estimator for Zero inflated Poisson regression model, Heliyon, 10 (2024), e24225. https://doi.org/10.1016/j.heliyon.2024.e24225 doi: 10.1016/j.heliyon.2024.e24225
[12]	M. Amin, B. Ashraf, S. Siddiqa, Liu estimation method in the zero-inflated Conway Maxwell Poisson regression model, J. Stat. Theory Appl., 24 (2025), 71–90. https://doi.org/10.1007/s44199-024-00101-y doi: 10.1007/s44199-024-00101-y
[13]	A. Dempster, M. Schatzoff, N. Wermuth, A simulation study of alternatives to ordinary least squares, J. Am. Stat. Assoc., 72 (1977), 77–91.
[14]	D. Lambert, Zero-inflated Poisson regression, with an application to defects in manufacturing, Technometrics, 34 (1992), 1–14.
[15]	G. Nanjundan, An EM algorithmic approach to maximum likelihood estimation in a mixture model, Vignana Bharathi, 18 (2006), 7–13.
[16]	A. Hoerl, R. Kennard, Ridge regression: biased estimation for nonorthogonal problems, Technometrics, 12 (1970), 55–67.
[17]	M. Amin, M. Akram, M. Amanullah, On the James-Stein estimator for the Poisson regression model, Commun. Stat.-Simul. C., 51 (2022), 5596–5608. https://doi.org/10.1080/03610918.2020.1775851 doi: 10.1080/03610918.2020.1775851
[18]	B. Kibria, A. Lukman, A new ridge‐type estimator for the linear regression model: simulations and applications, Scientifica, 2020 (2020), 9758378. https://doi.org/10.1155/2020/9758378 doi: 10.1155/2020/9758378
[19]	L. Kejian, A new class of blased estimate in linear regression, Commun. Stat.-Theor. M., 22 (1993), 393–402. https://doi.org/10.1080/03610929308831027 doi: 10.1080/03610929308831027
[20]	B. Aladeitan, O. Adebimpe, A. Lukman, O. Oludoun, O. Abiodun, Modified Kibria-Lukman (MKL) estimator for the Poisson regression model: application and simulation, F1000Res., 10 (2021), 548. https://doi.org/10.12688/f1000research.53987.2 doi: 10.12688/f1000research.53987.2
[21]	R. Farebrother, Further results on the mean square error of ridge regression, J. R. Stat. Soc. B, 38 (1976), 248–250.
[22]	G. Trenkler, H. Toutenburg, Mean squared error matrix comparisons between biased estimators—an overview of recent results, Stat. Pap., 31 (1990), 165–179. https://doi.org/10.1007/BF02924687 doi: 10.1007/BF02924687
[23]	R. Farghali, A. Lukman, A. Ogunleye, Enhancing model predictions through the fusion of Stein estimator and principal component regression, J. Stat. Comput. Sim., 94 (2024), 1760–1775. https://doi.org/10.1080/00949655.2024.2302011 doi: 10.1080/00949655.2024.2302011
[24]	A. Lukman, E. Adewuyi, K. Månsson, B. Kibria, A new estimator for the multicollinear Poisson regression model: simulation and application, Sci. Rep., 11 (2021), 3732. https://doi.org/10.1038/s41598-021-82582-w doi: 10.1038/s41598-021-82582-w
[25]	A. Zeileis, C. Kleiber, S. Jackman, Regression models for count data in R, J. Stat. Softw., 27 (2008), 1–25. https://doi.org/10.18637/jss.v027.i08 doi: 10.18637/jss.v027.i08

Reader Comments

Your name:*

Email:*
© 2025 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)