Adjusting Person Fit Index for Skewness in Cognitive Diagnosis Modeling

• Published in: Journal of classification Vol. 37; no. 2; pp. 399 - 420
• Main Authors: Santos, Kevin Carl P., de la Torre, Jimmy, von Davier, Matthias
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.07.2020; Springer Nature B.V
• Subjects: Bioinformatics; Computer simulation; Diagnosis; Diagnostic systems; Error correction; Error detection; Item response theory; Marketing; Mathematics and Statistics; Normal distribution; Pattern Recognition; Psychometrics; Signal,Image and Speech Processing; Skewness; Statistical analysis; Statistical Theory and Methods; Statistics; Subtraction; approximation; Person fit; Edgeworth expansion; Aberrant response patterns; Cognitive diagnosis models; Cornish-Fisher expansion
• ISSN: 0176-4268; 1432-1343
• DOI: 10.1007/s00357-019-09325-5

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 l Z 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 l Z that have been proposed in the item response theory context, namely, χ 2 -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.