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Hans-Friedrich Koehn

University of Illinois at Urbana-Champaign



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Chia-Yi Chiu

Rutgers University



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152 – Recent Advances in Diagnostic Classification Models

Assessing the Completeness of the Q-Matrix in Cognitively Diagnostic Modeling

Sponsor: Mental Health Statistics Section
Keywords: Q-matrix, Completeness, Cognitive Diagnosis, General Cognitive Diagnostic Models

Hans-Friedrich Koehn

University of Illinois at Urbana-Champaign

Chia-Yi Chiu

Rutgers University

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 skills. 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. For different types of CDMs, conditions of Q-completeness are studied. Rules are derived to determine the completeness of a given Q-matrix.

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