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Attribute Hierarchy Models in Cognitive Diagnosis: Identifiability of the Latent Attribute Space and Conditions for Completeness of the Q-Matrix

Attribute Hierarchy Models in Cognitive Diagnosis: Identifiability of the Latent Attribute Space... Educational researchers have argued that a realistic view of the role of attributes in cognitively diagnostic modeling should account for the possibility that attributes are not isolated entities, but interdependent in their effect on test performance. Different approaches have been discussed in the literature; among them the proposition to impose a hierarchical structure so that mastery of one or more attributes is a prerequisite of mastering one or more other attributes. A hierarchical organization of attributes constrains the latent attribute space such that several proficiency classes, as they exist if attributes are not hierarchically organized, are no longer defined because the corresponding attribute combinations cannot occur with the given attribute hierarchy. Hence, the identification of the latent attribute space is often difficult—especially, if the number of attributes is large. As an additional complication, constructing a complete Q-matrix may not at all be straightforward if the attributes underlying the test items are supposed to have a hierarchical structure. In this article, the conditions of identifiability of the latent space if attributes are hierarchically organized and the conditions of completeness of the Q-matrix are studied. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Classification Springer Journals

Attribute Hierarchy Models in Cognitive Diagnosis: Identifiability of the Latent Attribute Space and Conditions for Completeness of the Q-Matrix

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References (32)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Classification Society of North America
Subject
Statistics; Statistical Theory and Methods; Pattern Recognition; Bioinformatics; Signal,Image and Speech Processing; Psychometrics; Marketing
ISSN
0176-4268
eISSN
1432-1343
DOI
10.1007/s00357-018-9278-6
Publisher site
See Article on Publisher Site

Abstract

Educational researchers have argued that a realistic view of the role of attributes in cognitively diagnostic modeling should account for the possibility that attributes are not isolated entities, but interdependent in their effect on test performance. Different approaches have been discussed in the literature; among them the proposition to impose a hierarchical structure so that mastery of one or more attributes is a prerequisite of mastering one or more other attributes. A hierarchical organization of attributes constrains the latent attribute space such that several proficiency classes, as they exist if attributes are not hierarchically organized, are no longer defined because the corresponding attribute combinations cannot occur with the given attribute hierarchy. Hence, the identification of the latent attribute space is often difficult—especially, if the number of attributes is large. As an additional complication, constructing a complete Q-matrix may not at all be straightforward if the attributes underlying the test items are supposed to have a hierarchical structure. In this article, the conditions of identifiability of the latent space if attributes are hierarchically organized and the conditions of completeness of the Q-matrix are studied.

Journal

Journal of Classification – Springer Journals

Published: Nov 16, 2018

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