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When Cognitive Diagnosis Meets Computerized Adaptive Testing: CD-CAT

Published online by Cambridge University Press:  01 January 2025

Ying Cheng
Ying Cheng*
Affiliation:
University of Notre Dame
*
Requests for reprints should be sent to Ying Cheng, 118 Haggar Hall, Notre Dame, IN, 46556, USA. E-mail: ycheng4@nd.edu
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Abstract

Computerized adaptive testing (CAT) is a mode of testing which enables more efficient and accurate recovery of one or more latent traits. Traditionally, CAT is built upon Item Response Theory (IRT) models that assume unidimensionality. However, the problem of how to build CAT upon latent class models (LCM) has not been investigated until recently, when Tatsuoka (J. R. Stat. Soc., Ser. C, Appl. Stat. 51:337–350, 2002) and Tatsuoka and Ferguson (J. R. Stat., Ser. B 65:143–157, 2003) established a general theorem on the asymptotically optimal sequential selection of experiments to classify finite, partially ordered sets. Xu, Chang, and Douglas (Paper presented at the annual meeting of National Council on Measurement in Education, Montreal, Canada, 2003) then tested two heuristics in a simulation study based on Tatsuoka’s theoretical work in the context of computerized adaptive testing. One of the heuristics was developed based on Kullback–Leibler information, and the other based on Shannon entropy. In this paper, we showcase the application of the optimal sequential selection methodology in item selection of CAT that is built upon cognitive diagnostic models. Two new heuristics are proposed, and are compared against the randomized item selection method and the two heuristics investigated in Xu et al. (Paper presented at the annual meeting of National Council on Measurement in Education, Montreal, Canada, 2003). Finally, we show the connection between the Kullback–Leibler-information-based approaches and the Shannon-entropy-based approach, as well as the connection between algorithms built upon LCM and those built upon IRT models.

Keywords

optimal sequential selectionlatent class modelcomputerized adaptive testingcognitive diagnosisitem response theory
Type
Theory and Methods
Information
Psychometrika , Volume 74 , Issue 4 , December 2009 , pp. 619 - 632
Copyright
Copyright © 2009 The Psychometric Society

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Footnotes

The author would like to thank the editors, anonymous reviewers, and Drs. Hua-Hua Chang and Jeff Douglas for their constructive suggestions.

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