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Adjusting Person Fit Index for Skewness in Cognitive Diagnosis Modeling

Author

Listed:
  • Kevin Carl P. Santos

    (University of the Philippines-Diliman)

  • Jimmy Torre

    (The University of Hong Kong,)

  • Matthias Davier

    (National Board of Medical Examiners)

Abstract

Because the validity of diagnostic information generated by cognitive diagnosis models (CDMs) depends on the appropriateness of the estimated attribute profiles, it is imperative to ensure the accurate measurement of students’ test performance by conducting person fit (PF) evaluation to avoid flawed remediation measures. The standardized log-likelihood statistic lZ has been extended to the CDM framework. However, its null distribution is found to be negatively skewed. To address this issue, this study applies different methods of adjusting the skewness of lZ that have been proposed in the item response theory context, namely, χ2-approximation, Cornish-Fisher expansion, and Edgeworth expansion to bring its null distribution closer to the standard normal distribution. The skewness-corrected PF statistics are investigated by calculating their type I error and detection rates using a simulation study. Fraction-subtraction data are also used to illustrate the application of these PF statistics.

Suggested Citation

  • Kevin Carl P. Santos & Jimmy Torre & Matthias Davier, 2020. "Adjusting Person Fit Index for Skewness in Cognitive Diagnosis Modeling," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 399-420, July.
    • Handle: RePEc:spr:jclass:v:37:y:2020:i:2:d:10.1007_s00357-019-09325-5
    DOI: 10.1007/s00357-019-09325-5
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    References listed on IDEAS

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    1. Tom Snijders, 2001. "Asymptotic null distribution of person fit statistics with estimated person parameter," Psychometrika, Springer;The Psychometric Society, vol. 66(3), pages 331-342, September.
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    3. Matthias Davier & Ivo Molenaar, 2003. "A person-fit index for polytomous rasch models, latent class models, and their mixture generalizations," Psychometrika, Springer;The Psychometric Society, vol. 68(2), pages 213-228, June.
    4. C. Glas & Anna Dagohoy, 2007. "A Person Fit Test For Irt Models For Polytomous Items," Psychometrika, Springer;The Psychometric Society, vol. 72(2), pages 159-180, June.
    5. Jimmy de la Torre, 2011. "The Generalized DINA Model Framework," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 179-199, April.
    6. Jimmy Torre, 2011. "Erratum to: The Generalized DINA Model Framework," Psychometrika, Springer;The Psychometric Society, vol. 76(3), pages 510-510, July.
    7. Kikumi Tatsuoka, 1984. "Caution indices based on item response theory," Psychometrika, Springer;The Psychometric Society, vol. 49(1), pages 95-110, March.
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