TY - GEN
T1 - Conditions of completeness of the Q-matrix of tests for cognitive diagnosis
AU - Köhn, Hans Friedrich
AU - Chiu, Chia Yi
N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2016.
PY - 2016
Y1 - 2016
N2 - The associations between the items of a test based on the cognitive diagnosis framework and the skills required to solve them are documented in the Q-matrix. If the items have skill profiles that allow for the identification of all possible proficiency classes among examinees, then the Q-matrix of the test is said to be complete. An incomplete Q-matrix causes examinees to be assigned to proficiency classes to which they do not belong. Thus, completeness of the Q-matrix is an integral requirement of 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 diagnostic classification model (DCM) supposed to underlie 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 DCMs, conditions of Q-completeness are studied. Rules are derived to determine the completeness of a given Q-matrix.
AB - The associations between the items of a test based on the cognitive diagnosis framework and the skills required to solve them are documented in the Q-matrix. If the items have skill profiles that allow for the identification of all possible proficiency classes among examinees, then the Q-matrix of the test is said to be complete. An incomplete Q-matrix causes examinees to be assigned to proficiency classes to which they do not belong. Thus, completeness of the Q-matrix is an integral requirement of 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 diagnostic classification model (DCM) supposed to underlie 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 DCMs, conditions of Q-completeness are studied. Rules are derived to determine the completeness of a given Q-matrix.
KW - Cognitive diagnosis
KW - Diagnostic classification models
KW - Identifiability
KW - Q-Matrix completeness
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U2 - 10.1007/978-3-319-38759-8_19
DO - 10.1007/978-3-319-38759-8_19
M3 - Conference contribution
AN - SCOPUS:84981306133
SN - 9783319387574
T3 - Springer Proceedings in Mathematics and Statistics
SP - 255
EP - 264
BT - Quantitative Psychology Research - The 80th Annual Meeting of the Psychometric Society
A2 - Wang, Wen-Chung
A2 - Douglas, Jeffrey A.
A2 - Wiberg, Marie
A2 - van der Ark, L. Andries
A2 - Bolt, Daniel M.
PB - Springer
T2 - 80th annual meeting of the Psychometric Society, 2015
Y2 - 12 July 2015 through 16 July 2015
ER -