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A Procedure for Assessing the Completeness of the Q-Matrices of Cognitively Diagnostic Tests

Author

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  • Hans-Friedrich Köhn

    (University of Illinois at Urbana-Champaign)

  • Chia-Yi Chiu

    (Rutgers, The State University of New Jersey)

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.

Suggested Citation

  • Hans-Friedrich Köhn & Chia-Yi Chiu, 2017. "A Procedure for Assessing the Completeness of the Q-Matrices of Cognitively Diagnostic Tests," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 112-132, March.
    • Handle: RePEc:spr:psycho:v:82:y:2017:i:1:d:10.1007_s11336-016-9536-7
    DOI: 10.1007/s11336-016-9536-7
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    References listed on IDEAS

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    Cited by:

    1. Yu Wang & Chia-Yi Chiu & Hans Friedrich Köhn, 2023. "Nonparametric Classification Method for Multiple-Choice Items in Cognitive Diagnosis," Journal of Educational and Behavioral Statistics, , vol. 48(2), pages 189-219, April.
    2. Chia-Yi Chiu & Hans-Friedrich Köhn, 2019. "Consistency Theory for the General Nonparametric Classification Method," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 830-845, September.
    3. Douglas L. Steinley, 2018. "Editorial," Journal of Classification, Springer;The Classification Society, vol. 35(2), pages 195-197, July.
    4. Chia-Yi Chiu & Yan Sun & Yanhong Bian, 2018. "Cognitive Diagnosis for Small Educational Programs: The General Nonparametric Classification Method," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 355-375, June.
    5. Hans-Friedrich Köhn & Chia-Yi Chiu, 2018. "How to Build a Complete Q-Matrix for a Cognitively Diagnostic Test," Journal of Classification, Springer;The Classification Society, vol. 35(2), pages 273-299, July.
    6. Hans-Friedrich Köhn & Chia-Yi Chiu, 2019. "Attribute Hierarchy Models in Cognitive Diagnosis: Identifiability of the Latent Attribute Space and Conditions for Completeness of the Q-Matrix," Journal of Classification, Springer;The Classification Society, vol. 36(3), pages 541-565, October.

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