Model Selection in Generalized Linear Models
The problem of model selection in regression analysis through the use of forward selection, backward elimination, and stepwise selection has been well explored in the literature. The main assumption in this, of course, is that the data are normally distributed and the main tool used here is either a...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/10/1905 |
| _version_ | 1797572182557065216 |
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| author | Abdulla Mamun Sudhir Paul |
| author_facet | Abdulla Mamun Sudhir Paul |
| author_sort | Abdulla Mamun |
| collection | DOAJ |
| description | The problem of model selection in regression analysis through the use of forward selection, backward elimination, and stepwise selection has been well explored in the literature. The main assumption in this, of course, is that the data are normally distributed and the main tool used here is either a <i>t</i> test or an <i>F</i> test. However, the properties of these model selection procedures are not well-known. The purpose of this paper is to study the properties of these procedures within generalized linear regression models, considering the normal linear regression model as a special case. The main tool that is being used is the score test. However, the <i>F</i> test and other large sample tests, such as the likelihood ratio and the Wald test, the AIC, and the BIC, are included for the comparison. A systematic study, through simulations, of the properties of this procedure was conducted, in terms of level and power, for symmetric and asymmetric distributions, such as normal, Poisson, and binomial regression models. Extensions for skewed distributions, over-dispersed Poisson (the negative binomial), and over-dispersed binomial (the beta-binomial) regression models, are also given and evaluated. The methods are applied to analyze two health datasets. |
| first_indexed | 2024-03-10T20:51:43Z |
| format | Article |
| id | doaj.art-50b013a33715447e8f3188934cd39f41 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T20:51:43Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-50b013a33715447e8f3188934cd39f412023-11-19T18:18:31ZengMDPI AGSymmetry2073-89942023-10-011510190510.3390/sym15101905Model Selection in Generalized Linear ModelsAbdulla Mamun0Sudhir Paul1Department of Mathematics, Gonzaga University, Spokane, WA 99258-0102, USADepartment of Mathematics and Statistics, University of Windsor, Windsor, ON N9B 3P4, CanadaThe problem of model selection in regression analysis through the use of forward selection, backward elimination, and stepwise selection has been well explored in the literature. The main assumption in this, of course, is that the data are normally distributed and the main tool used here is either a <i>t</i> test or an <i>F</i> test. However, the properties of these model selection procedures are not well-known. The purpose of this paper is to study the properties of these procedures within generalized linear regression models, considering the normal linear regression model as a special case. The main tool that is being used is the score test. However, the <i>F</i> test and other large sample tests, such as the likelihood ratio and the Wald test, the AIC, and the BIC, are included for the comparison. A systematic study, through simulations, of the properties of this procedure was conducted, in terms of level and power, for symmetric and asymmetric distributions, such as normal, Poisson, and binomial regression models. Extensions for skewed distributions, over-dispersed Poisson (the negative binomial), and over-dispersed binomial (the beta-binomial) regression models, are also given and evaluated. The methods are applied to analyze two health datasets.https://www.mdpi.com/2073-8994/15/10/1905generalized linear modelover-dispersionscore testWald testlikelihood ratio test |
| spellingShingle | Abdulla Mamun Sudhir Paul Model Selection in Generalized Linear Models Symmetry generalized linear model over-dispersion score test Wald test likelihood ratio test |
| title | Model Selection in Generalized Linear Models |
| title_full | Model Selection in Generalized Linear Models |
| title_fullStr | Model Selection in Generalized Linear Models |
| title_full_unstemmed | Model Selection in Generalized Linear Models |
| title_short | Model Selection in Generalized Linear Models |
| title_sort | model selection in generalized linear models |
| topic | generalized linear model over-dispersion score test Wald test likelihood ratio test |
| url | https://www.mdpi.com/2073-8994/15/10/1905 |
| work_keys_str_mv | AT abdullamamun modelselectioningeneralizedlinearmodels AT sudhirpaul modelselectioningeneralizedlinearmodels |