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A Bias-Corrected RMSD Item Fit Statistic: An Evaluation and Comparison to Alternatives

Author

Listed:
  • Carmen Köhler

    (DIPF | Leibniz Institute for Research and Information in Education)

  • Alexander Robitzsch

    (Leibniz Institute for Science and Mathematics Education (IPN)
    Centre for International Student Assessment (ZIB))

  • Johannes Hartig

    (DIPF | Leibniz Institute for Research and Information in Education)

Abstract

Testing whether items fit the assumptions of an item response theory model is an important step in evaluating a test. In the literature, numerous item fit statistics exist, many of which show severe limitations. The current study investigates the root mean squared deviation (RMSD) item fit statistic, which is used for evaluating item fit in various large-scale assessment studies. The three research questions of this study are (1) whether the empirical RMSD is an unbiased estimator of the population RMSD; (2) if this is not the case, whether this bias can be corrected; and (3) whether the test statistic provides an adequate significance test to detect misfitting items. Using simulation studies, it was found that the empirical RMSD is not an unbiased estimator of the population RMSD, and nonparametric bootstrapping falls short of entirely eliminating this bias. Using parametric bootstrapping, however, the RMSD can be used as a test statistic that outperforms the other approaches—infit and outfit, S − X 2 —with respect to both Type I error rate and power. The empirical application showed that parametric bootstrapping of the RMSD results in rather conservative item fit decisions, which suggests more lenient cut-off criteria.

Suggested Citation

  • Carmen Köhler & Alexander Robitzsch & Johannes Hartig, 2020. "A Bias-Corrected RMSD Item Fit Statistic: An Evaluation and Comparison to Alternatives," Journal of Educational and Behavioral Statistics, , vol. 45(3), pages 251-273, June.
    • Handle: RePEc:sae:jedbes:v:45:y:2020:i:3:p:251-273
    DOI: 10.3102/1076998619890566
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    References listed on IDEAS

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    Cited by:

    1. Scott Monroe, 2021. "Testing Latent Variable Distribution Fit in IRT Using Posterior Residuals," Journal of Educational and Behavioral Statistics, , vol. 46(3), pages 374-398, June.

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