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Mutual Information Item Selection Method in Cognitive Diagnostic Computerized Adaptive Testing With Short Test Length

Mutual Information Item Selection Method in Cognitive Diagnostic Computerized Adaptive Testing... Cognitive diagnostic computerized adaptive testing (CD-CAT) purports to combine the strengths of both CAT and cognitive diagnosis. Cognitive diagnosis models aim at classifying examinees into the correct mastery profile group so as to pinpoint the strengths and weakness of each examinee whereas CAT algorithms choose items to determine those strengths and weakness as efficiently as possible. Most of the existing CD-CAT item selection algorithms are evaluated when test length is relatively long whereas several applications of CD-CAT, such as in interim assessment, require an item selection algorithm that is able to accurately recover examinees’ mastery profile with short test length. In this article, we introduce the mutual information item selection method in the context of CD-CAT and then provide a computationally easier formula to make the method more amenable in real time. Mutual information is then evaluated against common item selection methods, such as Kullback–Leibler information, posterior weighted Kullback–Leibler information, and Shannon entropy. Based on our simulations, mutual information consistently results in nearly the highest attribute and pattern recovery rate in more than half of the conditions. We conclude by discussing how the number of attributes, Q-matrix structure, correlations among the attributes, and item quality affect estimation accuracy. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Educational and Psychological Measurement SAGE

Mutual Information Item Selection Method in Cognitive Diagnostic Computerized Adaptive Testing With Short Test Length

Educational and Psychological Measurement , Volume 73 (6): 19 – Dec 1, 2013

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References (47)

Publisher
SAGE
Copyright
© The Author(s) 2013
ISSN
0013-1644
eISSN
1552-3888
DOI
10.1177/0013164413498256
Publisher site
See Article on Publisher Site

Abstract

Cognitive diagnostic computerized adaptive testing (CD-CAT) purports to combine the strengths of both CAT and cognitive diagnosis. Cognitive diagnosis models aim at classifying examinees into the correct mastery profile group so as to pinpoint the strengths and weakness of each examinee whereas CAT algorithms choose items to determine those strengths and weakness as efficiently as possible. Most of the existing CD-CAT item selection algorithms are evaluated when test length is relatively long whereas several applications of CD-CAT, such as in interim assessment, require an item selection algorithm that is able to accurately recover examinees’ mastery profile with short test length. In this article, we introduce the mutual information item selection method in the context of CD-CAT and then provide a computationally easier formula to make the method more amenable in real time. Mutual information is then evaluated against common item selection methods, such as Kullback–Leibler information, posterior weighted Kullback–Leibler information, and Shannon entropy. Based on our simulations, mutual information consistently results in nearly the highest attribute and pattern recovery rate in more than half of the conditions. We conclude by discussing how the number of attributes, Q-matrix structure, correlations among the attributes, and item quality affect estimation accuracy.

Journal

Educational and Psychological MeasurementSAGE

Published: Dec 1, 2013

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