Negative Binomial Regression Model Estimation Using Stein Approach: Methods, Simulation, and Applications
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 inacc...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2025-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/jom/9134821 |
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| _version_ | 1841524931642261504 |
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| author | Bushra Ashraf Muhammad Amin Walid Emam Yusra Tashkandy Muhammad Faisal |
| author_facet | Bushra Ashraf Muhammad Amin Walid Emam Yusra Tashkandy Muhammad Faisal |
| author_sort | Bushra Ashraf |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d389f7983a294afea26cb8d7d7584bad |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-d389f7983a294afea26cb8d7d7584bad2025-01-18T00:00:05ZengWileyJournal of Mathematics2314-47852025-01-01202510.1155/jom/9134821Negative Binomial Regression Model Estimation Using Stein Approach: Methods, Simulation, and ApplicationsBushra Ashraf0Muhammad Amin1Walid Emam2Yusra Tashkandy3Muhammad Faisal4Government Associate College for WomenDepartment of StatisticsDepartment of Statistics and Operations ResearchDepartment of Statistics and Operations ResearchCentre for Digital Innovations in Health & Social CareThe 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.http://dx.doi.org/10.1155/jom/9134821 |
| spellingShingle | Bushra Ashraf Muhammad Amin Walid Emam Yusra Tashkandy Muhammad Faisal Negative Binomial Regression Model Estimation Using Stein Approach: Methods, Simulation, and Applications Journal of Mathematics |
| title | Negative Binomial Regression Model Estimation Using Stein Approach: Methods, Simulation, and Applications |
| title_full | Negative Binomial Regression Model Estimation Using Stein Approach: Methods, Simulation, and Applications |
| title_fullStr | Negative Binomial Regression Model Estimation Using Stein Approach: Methods, Simulation, and Applications |
| title_full_unstemmed | Negative Binomial Regression Model Estimation Using Stein Approach: Methods, Simulation, and Applications |
| title_short | Negative Binomial Regression Model Estimation Using Stein Approach: Methods, Simulation, and Applications |
| title_sort | negative binomial regression model estimation using stein approach methods simulation and applications |
| url | http://dx.doi.org/10.1155/jom/9134821 |
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