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A Procedure for Assessing the Completeness of the Q-Matrices of Cognitively Diagnostic Tests

Published online by Cambridge University Press:  01 January 2025

Hans-Friedrich Köhn  and
Chia-Yi Chiu
Hans-Friedrich Köhn
Affiliation:
University of Illinois at Urbana-Champaign
Chia-Yi Chiu*
Affiliation:
Rutgers, The State University of New Jersey
*
Correspondence should be made to Chia-Yi Chiu, Rutgers, The State University of New Jersey, New Brunswick, NJ USA. Email: chia-yi.chiu@gse.rutgers.edu
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Abstract

The Q-matrix of a cognitively diagnostic test is said to be complete if it allows for the identification of all possible proficiency classes among examinees. Completeness of the Q-matrix is therefore a key requirement for any cognitively diagnostic test. However, completeness of the Q-matrix is often difficult to establish, especially, for tests with a large number of items involving multiple attributes. As an additional complication, completeness is not an intrinsic property of the Q-matrix, but can only be assessed in reference to a specific cognitive diagnosis model (CDM) supposed to underly the data—that is, the Q-matrix of a given test can be complete for one model but incomplete for another. In this article, a method is presented for assessing whether a given Q-matrix is complete for a given CDM. The proposed procedure relies on the theoretical framework of general CDMs and is therefore legitimate for CDMs that can be reparameterized as a general CDM.

Keywords

Q-matrixcompletenesscognitive diagnosisgeneral cognitive diagnostic modelsG-DINALCDM
Type
Original Paper
Information
Psychometrika , Volume 82 , Issue 1 , March 2017 , pp. 112 - 132
Copyright
Copyright © 2016 The Psychometric Society

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