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

Hans Friedrich Köhn, Chia Yi Chiu

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)112-132
Number of pages21
JournalPsychometrika
Volume82
Issue number1
DOIs
StatePublished - Mar 1 2017

Keywords

  • G-DINA
  • LCDM
  • Q-matrix
  • cognitive diagnosis
  • completeness
  • general cognitive diagnostic models

ASJC Scopus subject areas

  • Psychology(all)
  • Applied Mathematics

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