An Evaluation of Overall Goodness-of-Fit Tests for the Rasch Model
For assessing the fit of item response theory models, it has been suggested to apply overall goodness-of-fit tests as well as tests for individual items and item pairs. Although numerous goodness-of-fit tests have been proposed in the literature for the Rasch model, their relative power against seve...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2019-01-01
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| Series: | Frontiers in Psychology |
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| Online Access: | https://www.frontiersin.org/article/10.3389/fpsyg.2018.02710/full |
| _version_ | 1818127733543141376 |
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| author | Rudolf Debelak |
| author_facet | Rudolf Debelak |
| author_sort | Rudolf Debelak |
| collection | DOAJ |
| description | For assessing the fit of item response theory models, it has been suggested to apply overall goodness-of-fit tests as well as tests for individual items and item pairs. Although numerous goodness-of-fit tests have been proposed in the literature for the Rasch model, their relative power against several model violations has not been investigated so far. This study compares four of these tests, which are all available in R software: T10, T11, M2, and the LR test. Results on the Type I error rate and the sensitivity to violations of different assumptions of the Rasch model (unidimensionality, local independence on the level of item pairs, equal item discrimination, zero as a lower asymptote for the item characteristic curves, invariance of the item parameters) are reported. The results indicate that the T11 test is comparatively most powerful against violations of the assumption of parallel item characteristic curves, which includes the presence of unequal item discriminations and a non-zero lower asymptote. Against the remaining model violations, which can be summarized as local dependence, M2 is found to be most powerful. T10 and LR are found to be sensitive against violations of the assumption of parallel item characteristic curves, but are insensitive against local dependence. |
| first_indexed | 2024-12-11T07:22:03Z |
| format | Article |
| id | doaj.art-4be69cff860d4e0680a8eafec35bd7c6 |
| institution | Directory Open Access Journal |
| issn | 1664-1078 |
| language | English |
| last_indexed | 2024-12-11T07:22:03Z |
| publishDate | 2019-01-01 |
| publisher | Frontiers Media S.A. |
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| series | Frontiers in Psychology |
| spelling | doaj.art-4be69cff860d4e0680a8eafec35bd7c62022-12-22T01:16:04ZengFrontiers Media S.A.Frontiers in Psychology1664-10782019-01-01910.3389/fpsyg.2018.02710424123An Evaluation of Overall Goodness-of-Fit Tests for the Rasch ModelRudolf DebelakFor assessing the fit of item response theory models, it has been suggested to apply overall goodness-of-fit tests as well as tests for individual items and item pairs. Although numerous goodness-of-fit tests have been proposed in the literature for the Rasch model, their relative power against several model violations has not been investigated so far. This study compares four of these tests, which are all available in R software: T10, T11, M2, and the LR test. Results on the Type I error rate and the sensitivity to violations of different assumptions of the Rasch model (unidimensionality, local independence on the level of item pairs, equal item discrimination, zero as a lower asymptote for the item characteristic curves, invariance of the item parameters) are reported. The results indicate that the T11 test is comparatively most powerful against violations of the assumption of parallel item characteristic curves, which includes the presence of unequal item discriminations and a non-zero lower asymptote. Against the remaining model violations, which can be summarized as local dependence, M2 is found to be most powerful. T10 and LR are found to be sensitive against violations of the assumption of parallel item characteristic curves, but are insensitive against local dependence.https://www.frontiersin.org/article/10.3389/fpsyg.2018.02710/fullitem response theoryRasch modelitem fittype I errorpower |
| spellingShingle | Rudolf Debelak An Evaluation of Overall Goodness-of-Fit Tests for the Rasch Model Frontiers in Psychology item response theory Rasch model item fit type I error power |
| title | An Evaluation of Overall Goodness-of-Fit Tests for the Rasch Model |
| title_full | An Evaluation of Overall Goodness-of-Fit Tests for the Rasch Model |
| title_fullStr | An Evaluation of Overall Goodness-of-Fit Tests for the Rasch Model |
| title_full_unstemmed | An Evaluation of Overall Goodness-of-Fit Tests for the Rasch Model |
| title_short | An Evaluation of Overall Goodness-of-Fit Tests for the Rasch Model |
| title_sort | evaluation of overall goodness of fit tests for the rasch model |
| topic | item response theory Rasch model item fit type I error power |
| url | https://www.frontiersin.org/article/10.3389/fpsyg.2018.02710/full |
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