A New Conway Maxwell–Poisson Liu Regression Estimator—Method and Application
Poisson regression is a popular tool for modeling count data and is applied in medical sciences, engineering and others. Real data, however, are often over or underdispersed, and we cannot apply the Poisson regression. To overcome this issue, we consider a regression model based on the Conway–Maxwel...
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| Main Authors: | , , , , , |
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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/10.1155/2022/3323955 |
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| author | Muhammad Nauman Akram Muhammad Amin Faiza Sami Adam Braima Mastor Omer Mohamed Egeh Abdisalam Hassan Muse |
| author_facet | Muhammad Nauman Akram Muhammad Amin Faiza Sami Adam Braima Mastor Omer Mohamed Egeh Abdisalam Hassan Muse |
| author_sort | Muhammad Nauman Akram |
| collection | DOAJ |
| description | Poisson regression is a popular tool for modeling count data and is applied in medical sciences, engineering and others. Real data, however, are often over or underdispersed, and we cannot apply the Poisson regression. To overcome this issue, we consider a regression model based on the Conway–Maxwell Poisson (COMP) distribution. Generally, the maximum likelihood estimator is used for the estimation of unknown parameters of the COMP regression model. However, in the existence of multicollinearity, the estimates become unstable due to its high variance and standard error. To solve the issue, a new COMP Liu estimator is proposed for the COMP regression model with over-, equi-, and underdispersion. To assess the performance, we conduct a Monte Carlo simulation where mean squared error is considered as an evaluation criterion. Findings of simulation study show that the performance of our new estimator is considerably better as compared to others. Finally, an application is consider to assess the superiority of the proposed COMP Liu estimator. The simulation and application findings clearly demonstrated that the proposed estimator is superior to the maximum likelihood estimator. |
| format | Article |
| id | doaj-art-bc13d14ea7b94198a4f9a447afc62b98 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-bc13d14ea7b94198a4f9a447afc62b982025-02-03T06:14:14ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/3323955A New Conway Maxwell–Poisson Liu Regression Estimator—Method and ApplicationMuhammad Nauman Akram0Muhammad Amin1Faiza Sami2Adam Braima Mastor3Omer Mohamed Egeh4Abdisalam Hassan Muse5Department of StatisticsDepartment of StatisticsUniversity of Management and TechnologyPan African UniversityDepartment of Mathematics and StatisticsJomo Kenyatta University of Agriculture and Technology (JKUAT)Poisson regression is a popular tool for modeling count data and is applied in medical sciences, engineering and others. Real data, however, are often over or underdispersed, and we cannot apply the Poisson regression. To overcome this issue, we consider a regression model based on the Conway–Maxwell Poisson (COMP) distribution. Generally, the maximum likelihood estimator is used for the estimation of unknown parameters of the COMP regression model. However, in the existence of multicollinearity, the estimates become unstable due to its high variance and standard error. To solve the issue, a new COMP Liu estimator is proposed for the COMP regression model with over-, equi-, and underdispersion. To assess the performance, we conduct a Monte Carlo simulation where mean squared error is considered as an evaluation criterion. Findings of simulation study show that the performance of our new estimator is considerably better as compared to others. Finally, an application is consider to assess the superiority of the proposed COMP Liu estimator. The simulation and application findings clearly demonstrated that the proposed estimator is superior to the maximum likelihood estimator.http://dx.doi.org/10.1155/2022/3323955 |
| spellingShingle | Muhammad Nauman Akram Muhammad Amin Faiza Sami Adam Braima Mastor Omer Mohamed Egeh Abdisalam Hassan Muse A New Conway Maxwell–Poisson Liu Regression Estimator—Method and Application Journal of Mathematics |
| title | A New Conway Maxwell–Poisson Liu Regression Estimator—Method and Application |
| title_full | A New Conway Maxwell–Poisson Liu Regression Estimator—Method and Application |
| title_fullStr | A New Conway Maxwell–Poisson Liu Regression Estimator—Method and Application |
| title_full_unstemmed | A New Conway Maxwell–Poisson Liu Regression Estimator—Method and Application |
| title_short | A New Conway Maxwell–Poisson Liu Regression Estimator—Method and Application |
| title_sort | new conway maxwell poisson liu regression estimator method and application |
| url | http://dx.doi.org/10.1155/2022/3323955 |
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