Assessing the Completeness of the Q-Matrices of Cognitively Diagnostic Modeling

• Activity Number: 152
• Type: Invited
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Mental Health Statistics Section
• Author(s): Chia-Yi Chiu* and Hans-Friedrich Koehn
• Companies: Rutgers University and University of Illinois at Urbana-Champaign
• Keywords: Q-matrix ; Completeness ; Cognitive Diagnosis ; General Cognitive Diagnostic Models

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 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.