Adjusting Person Fit Index for Skewness in Cognitive Diagnosis Modeling

Kevin Carl P. Santos (), Jimmy Torre and Matthias Davier
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Kevin Carl P. Santos: University of the Philippines-Diliman
Jimmy Torre: The University of Hong Kong,
Matthias Davier: National Board of Medical Examiners

Journal of Classification, 2020, vol. 37, issue 2, No 9, 399-420

Abstract: 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.

Keywords: Cognitive diagnosis models; Person fit; Aberrant response patterns; χ2-approximation; Cornish-Fisher expansion; Edgeworth expansion (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00357-019-09325-5

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