Adjusting Person Fit Index for Skewness in Cognitive Diagnosis Modeling

  • Kevin Carl P. SantosEmail author
  • Jimmy de la Torre
  • Matthias von Davier


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.


Cognitive diagnosis models Person fit Aberrant response patterns χ2-approximation Cornish-Fisher expansion Edgeworth expansion 


Funding information

This research was funded by the Philippine Commission on Higher Education, Philippine Social Science Council, and University of the Philippines-Diliman. Moreover, this research was carried out in part using the CoARE Facility of the DOST-Advance Science and Technology Institute and the Computing and Archiving Research Environment (CoARE) Project.


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Copyright information

© The Classification Society 2019

Authors and Affiliations

  1. 1.School of StatisticsUniversity of the Philippines-DilimanQuezon CityPhilippines
  2. 2.The University of Hong Kong, Pok Fu LamHong Kong
  3. 3.National Board of Medical ExaminersPhiladelphiaUSA

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