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

Hans-Friedrich Köhn () and Chia-Yi Chiu ()
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Hans-Friedrich Köhn: University of Illinois at Urbana-Champaign
Chia-Yi Chiu: Rutgers, The State University of New Jersey

Psychometrika, 2017, vol. 82, issue 1, No 6, 112-132

Abstract: 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-matrix; completeness; cognitive diagnosis; general cognitive diagnostic models; G-DINA; LCDM (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s11336-016-9536-7

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