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Negative Binomial Regression Model Estimation Using Stein Approach: Methods, Simulation, and Applications

Author

Listed:
  • Bushra Ashraf
  • Muhammad Amin
  • Walid Emam
  • Yusra Tashkandy
  • Muhammad Faisal

Abstract

The negative binomial regression model (NBRM) is popular for modeling count data and addressing overdispersion issues. Generally, the maximum likelihood estimator (MLE) is used to estimate the NBRM coefficients. However, when the explanatory variables in the NBRM are correlated, the MLE yields inaccurate estimates. To tackle this challenge, we propose a James–Stein estimator for the NBRM. The matrix mean squared error (MSE) and the scalar MSE properties are derived and compared with other estimators, including the ridge estimator (RE), Liu estimator (LE), and the MLE. We assess the performance of the suggested estimator using two real applications and a simulation study, with MSE serving as the assessment criterion. Results from both simulations and real applications demonstrate the superior performance of the proposed estimator over the RE, LE, and MLE.

Suggested Citation

  • Bushra Ashraf & Muhammad Amin & Walid Emam & Yusra Tashkandy & Muhammad Faisal, 2025. "Negative Binomial Regression Model Estimation Using Stein Approach: Methods, Simulation, and Applications," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:9134821
    DOI: 10.1155/jom/9134821
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    References listed on IDEAS

    as
    1. Muhammad Amin & Muhammad Qasim & Muhammad Amanullah & Saima Afzal, 2020. "Performance of some ridge estimators for the gamma regression model," Statistical Papers, Springer, vol. 61(3), pages 997-1026, June.
    2. Royce A. Francis & Srinivas Reddy Geedipally & Seth D. Guikema & Soma Sekhar Dhavala & Dominique Lord & Sarah LaRocca, 2012. "Characterizing the Performance of the Conway‐Maxwell Poisson Generalized Linear Model," Risk Analysis, John Wiley & Sons, vol. 32(1), pages 167-183, January.
    3. B. Kibria & Kristofer Månsson & Ghazi Shukur, 2012. "Performance of Some Logistic Ridge Regression Estimators," Computational Economics, Springer;Society for Computational Economics, vol. 40(4), pages 401-414, December.
    4. Seth D. Guikema & Jeremy P. Goffelt, 2008. "A Flexible Count Data Regression Model for Risk Analysis," Risk Analysis, John Wiley & Sons, vol. 28(1), pages 213-223, February.
    5. Kibria, B. M. Golam & Månsson, Kristofer & Shukur, Ghazi, 2011. "A Ridge Regression estimator for the zero-inflated Poisson model," Working Paper Series in Economics and Institutions of Innovation 257, Royal Institute of Technology, CESIS - Centre of Excellence for Science and Innovation Studies.
    6. Månsson, Kristofer & Shukur, Ghazi, 2011. "A Poisson ridge regression estimator," Economic Modelling, Elsevier, vol. 28(4), pages 1475-1481, July.
    7. Ghazi Shukur & Kristofer Månsson & Pär Sjölander, 2015. "Developing Interaction Shrinkage Parameters for the Liu Estimator — with an Application to the Electricity Retail Market," Computational Economics, Springer;Society for Computational Economics, vol. 46(4), pages 539-550, December.
    8. Månsson, Kristofer, 2012. "On ridge estimators for the negative binomial regression model," Economic Modelling, Elsevier, vol. 29(2), pages 178-184.
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