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Robust Negative Binomial Regression via the Kibria–Lukman Strategy: Methodology and Application

Author

Listed:
  • Adewale F. Lukman

    (Department of Mathematics and Statistics, University of North Dakota, Grand Forks, ND 58202, USA)

  • Olayan Albalawi

    (Department of Statistics, Faculty of Science, University of Tabuk, Tabuk 47512, Saudi Arabia)

  • Mohammad Arashi

    (Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad 9177948974, Razavi Khorasan, Iran
    Department of Statistics, Faculty of Natural and Agricultural Sciences, University of Pretoria, Pretoria 0002, South Africa)

  • Jeza Allohibi

    (Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah Al-Munawara 42353, Saudi Arabia)

  • Abdulmajeed Atiah Alharbi

    (Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah Al-Munawara 42353, Saudi Arabia)

  • Rasha A. Farghali

    (Department of Mathematics, Insurance and Applied Statistics, Helwan University, Cairo 11795, Egypt)

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.

Suggested Citation

  • Adewale F. Lukman & Olayan Albalawi & Mohammad Arashi & Jeza Allohibi & Abdulmajeed Atiah Alharbi & Rasha A. Farghali, 2024. "Robust Negative Binomial Regression via the Kibria–Lukman Strategy: Methodology and Application," Mathematics, MDPI, vol. 12(18), pages 1-16, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:18:p:2929-:d:1482092
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    References listed on IDEAS

    as
    1. Månsson, Kristofer & Shukur, Ghazi, 2011. "A Poisson ridge regression estimator," Economic Modelling, Elsevier, vol. 28(4), pages 1475-1481, July.
    2. William H. Aeberhard & Eva Cantoni & Stephane Heritier, 2014. "Robust inference in the negative binomial regression model with an application to falls data," Biometrics, The International Biometric Society, vol. 70(4), pages 920-931, December.
    3. B. Kibria & Kristofer Månsson & Ghazi Shukur, 2013. "Some ridge regression estimators for the zero-inflated Poisson model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(4), pages 721-735.
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