Conditions of completeness of the Q-matrix of tests for cognitive diagnosis

Hans Friedrich Koehn, Chia Yi Chiu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish (US)
Title of host publicationQuantitative Psychology Research - The 80th Annual Meeting of the Psychometric Society
EditorsWen-Chung Wang, Jeffrey A. Douglas, Marie Wiberg, L. Andries van der Ark, Daniel M. Bolt
PublisherSpringer New York LLC
Pages255-264
Number of pages10
ISBN (Print)9783319387574
DOIs
StatePublished - Jan 1 2016
Event80th annual meeting of the Psychometric Society, 2015 - Beijing, China
Duration: Jul 12 2015Jul 16 2015

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume167
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

Other80th annual meeting of the Psychometric Society, 2015
CountryChina
CityBeijing
Period7/12/157/16/15

Fingerprint

Q-matrix
Completeness
Diagnostic Tests
Complications
Diagnostics
Requirements

Keywords

  • Cognitive diagnosis
  • Diagnostic classification models
  • Identifiability
  • Q-Matrix completeness

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Koehn, H. F., & Chiu, C. Y. (2016). Conditions of completeness of the Q-matrix of tests for cognitive diagnosis. In W-C. Wang, J. A. Douglas, M. Wiberg, L. A. van der Ark, & D. M. Bolt (Eds.), Quantitative Psychology Research - The 80th Annual Meeting of the Psychometric Society (pp. 255-264). (Springer Proceedings in Mathematics and Statistics; Vol. 167). Springer New York LLC. https://doi.org/10.1007/978-3-319-38759-8_19

Conditions of completeness of the Q-matrix of tests for cognitive diagnosis. / Koehn, Hans Friedrich; Chiu, Chia Yi.

Quantitative Psychology Research - The 80th Annual Meeting of the Psychometric Society. ed. / Wen-Chung Wang; Jeffrey A. Douglas; Marie Wiberg; L. Andries van der Ark; Daniel M. Bolt. Springer New York LLC, 2016. p. 255-264 (Springer Proceedings in Mathematics and Statistics; Vol. 167).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Koehn, HF & Chiu, CY 2016, Conditions of completeness of the Q-matrix of tests for cognitive diagnosis. in W-C Wang, JA Douglas, M Wiberg, LA van der Ark & DM Bolt (eds), Quantitative Psychology Research - The 80th Annual Meeting of the Psychometric Society. Springer Proceedings in Mathematics and Statistics, vol. 167, Springer New York LLC, pp. 255-264, 80th annual meeting of the Psychometric Society, 2015, Beijing, China, 7/12/15. https://doi.org/10.1007/978-3-319-38759-8_19
Koehn HF, Chiu CY. Conditions of completeness of the Q-matrix of tests for cognitive diagnosis. In Wang W-C, Douglas JA, Wiberg M, van der Ark LA, Bolt DM, editors, Quantitative Psychology Research - The 80th Annual Meeting of the Psychometric Society. Springer New York LLC. 2016. p. 255-264. (Springer Proceedings in Mathematics and Statistics). https://doi.org/10.1007/978-3-319-38759-8_19
Koehn, Hans Friedrich ; Chiu, Chia Yi. / Conditions of completeness of the Q-matrix of tests for cognitive diagnosis. Quantitative Psychology Research - The 80th Annual Meeting of the Psychometric Society. editor / Wen-Chung Wang ; Jeffrey A. Douglas ; Marie Wiberg ; L. Andries van der Ark ; Daniel M. Bolt. Springer New York LLC, 2016. pp. 255-264 (Springer Proceedings in Mathematics and Statistics).
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