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An Evaluation of Overall Goodness-of-Fit Tests for the Rasch Model


Debelak, Rudolf (2019). An Evaluation of Overall Goodness-of-Fit Tests for the Rasch Model. Frontiers in Psychology, 9:2710 -2710.

Abstract

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.

Abstract

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:06 Faculty of Arts > Institute of Psychology
Dewey Decimal Classification:150 Psychology
Scopus Subject Areas:Social Sciences & Humanities > General Psychology
Uncontrolled Keywords:Rasch model, Item Response Theory, Model fit
Language:English
Date:10 January 2019
Deposited On:20 Feb 2019 13:50
Last Modified:01 Jul 2021 14:20
Publisher:Frontiers Research Foundation
ISSN:1664-1078
OA Status:Gold
Free access at:PubMed ID. An embargo period may apply.
Publisher DOI:https://doi.org/10.3389/fpsyg.2018.02710
PubMed ID:30687170
Project Information:
  • : FunderSNSF
  • : Grant ID100019_152548
  • : Project TitleDetecting Heterogeneity in Complex IRT Models for Measuring Latent Traits

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