Performance of the Ridge and Liu Estimators in the zero-inflated Bell Regression Model
The Poisson regression model is popularly used to model count data. However, the model suffers drawbacks when there is overdispersion—when the mean of the Poisson distribution is not the same as the variance. In this situation, the Bell regression model fits well to the data. Also, there is a high t...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/9503460 |
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| author | Zakariya Yahya Algamal Adewale F. Lukman Mohamed R. Abonazel Fuad A. Awwad |
| author_facet | Zakariya Yahya Algamal Adewale F. Lukman Mohamed R. Abonazel Fuad A. Awwad |
| author_sort | Zakariya Yahya Algamal |
| collection | DOAJ |
| description | The Poisson regression model is popularly used to model count data. However, the model suffers drawbacks when there is overdispersion—when the mean of the Poisson distribution is not the same as the variance. In this situation, the Bell regression model fits well to the data. Also, there is a high tendency of excess zeros in the count data. In this case, the zero-inflated Bell regression model is an alternative to the Bell regression model. The parameters of the zero-inflated Bell regression model are mostly estimated using the method of maximum likelihood. Linear dependency is a threat in a real-life application when modeling the relationship between the response variable and two or more explanatory variables in a generalized linear model such as the zero-inflated Bell regression model. It reduced the efficiency of the maximum likelihood estimator. Therefore, we developed the ridge and Liu estimators for the zero-inflated Bell regression model to deal with this issue. The simulation and application results support the dominance of the proposed methods over the conventional maximum likelihood estimator. |
| format | Article |
| id | doaj-art-143550da96d44c9db2e1ef9479e8d5b7 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-143550da96d44c9db2e1ef9479e8d5b72025-08-20T03:54:33ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/9503460Performance of the Ridge and Liu Estimators in the zero-inflated Bell Regression ModelZakariya Yahya Algamal0Adewale F. Lukman1Mohamed R. Abonazel2Fuad A. Awwad3Department of Statistics and InformaticsDepartment of Epidemiology and BiostatisticsDepartment of Applied Statistics and EconometricsDepartment of Quantitative AnalysisThe Poisson regression model is popularly used to model count data. However, the model suffers drawbacks when there is overdispersion—when the mean of the Poisson distribution is not the same as the variance. In this situation, the Bell regression model fits well to the data. Also, there is a high tendency of excess zeros in the count data. In this case, the zero-inflated Bell regression model is an alternative to the Bell regression model. The parameters of the zero-inflated Bell regression model are mostly estimated using the method of maximum likelihood. Linear dependency is a threat in a real-life application when modeling the relationship between the response variable and two or more explanatory variables in a generalized linear model such as the zero-inflated Bell regression model. It reduced the efficiency of the maximum likelihood estimator. Therefore, we developed the ridge and Liu estimators for the zero-inflated Bell regression model to deal with this issue. The simulation and application results support the dominance of the proposed methods over the conventional maximum likelihood estimator.http://dx.doi.org/10.1155/2022/9503460 |
| spellingShingle | Zakariya Yahya Algamal Adewale F. Lukman Mohamed R. Abonazel Fuad A. Awwad Performance of the Ridge and Liu Estimators in the zero-inflated Bell Regression Model Journal of Mathematics |
| title | Performance of the Ridge and Liu Estimators in the zero-inflated Bell Regression Model |
| title_full | Performance of the Ridge and Liu Estimators in the zero-inflated Bell Regression Model |
| title_fullStr | Performance of the Ridge and Liu Estimators in the zero-inflated Bell Regression Model |
| title_full_unstemmed | Performance of the Ridge and Liu Estimators in the zero-inflated Bell Regression Model |
| title_short | Performance of the Ridge and Liu Estimators in the zero-inflated Bell Regression Model |
| title_sort | performance of the ridge and liu estimators in the zero inflated bell regression model |
| url | http://dx.doi.org/10.1155/2022/9503460 |
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