title: A Procedure for Assessing the Completeness of the Q-Matrices of Cognitively Diagnostic Tests.
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.
authors.affiliation: University of Illinois at Urbana-Champaign, Champaign, IL, USA.
authors.forename: Hans-Friedrich
authors.initials: HF
authors.lastname: Köhn
authors.affiliation: Rutgers, The State University of New Jersey, New Brunswick, NJ, USA. chia-yi.chiu@gse.rutgers.edu.
authors.forename: Chia-Yi
authors.initials: CY
authors.lastname: Chiu
mesh_terms: D000465:Algorithms; D003071:Cognition; D004521:Educational Measurement; D006801:Humans; D011594:Psychometrics; D013223:Statistics as Topic
keywords: G-DINA; LCDM; Q-matrix; cognitive diagnosis; completeness; general cognitive diagnostic models