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How to Build a Complete Q-Matrix for a Cognitively Diagnostic Test

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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 guarantees the identifiability of all possible proficiency classes among examinees. An incomplete Q-matrix causes examinees to be assigned to proficiency classes to which they do not belong. Completeness of the Q-matrix is therefore a key requirement of any cognitively diagnostic test. The importance of the completeness property of the Q-matrix of a test as a fundamental condition to guarantee a reliable estimate of an examinee’s attribute profile has only recently been realized by researchers. In fact, inspection of extant assessments based on the cognitive diagnosis framework often revealed that, in hindsight, the Q-matrices used with these tests were not complete. Thus, the availability of rules for building a complete Q-matrix at the early stages of test development is perhaps at least as desirable as rules for identifying the completeness of a given Q-matrix. This article presents procedures for constructing Q-matrices that are complete. The famous Fraction-Subtraction test problems by K. K. Tatsuoka (1984) are used throughout for illustration.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jclass:v:35:y:2018:i:2:d:10.1007_s00357-018-9255-0
    DOI: 10.1007/s00357-018-9255-0
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    References listed on IDEAS

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    1. 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.
    2. George B. Macready & C. Mitchell Dayton, 1977. "The Use of Probabilistic Models in the Assessment of Mastery," Journal of Educational and Behavioral Statistics, , vol. 2(2), pages 99-120, June.
    3. Chia-Yi Chiu & Jeffrey Douglas & Xiaodong Li, 2009. "Cluster Analysis for Cognitive Diagnosis: Theory and Applications," Psychometrika, Springer;The Psychometric Society, vol. 74(4), pages 633-665, December.
    4. Jimmy de la Torre, 2009. "DINA Model and Parameter Estimation: A Didactic," Journal of Educational and Behavioral Statistics, , vol. 34(1), pages 115-130, March.
    5. Kikumi K. Tatsuoka, 1985. "A Probabilistic Model for Diagnosing Misconceptions By The Pattern Classification Approach," Journal of Educational and Behavioral Statistics, , vol. 10(1), pages 55-73, March.
    6. Jimmy Torre & Jeffrey Douglas, 2004. "Higher-order latent trait models for cognitive diagnosis," Psychometrika, Springer;The Psychometric Society, vol. 69(3), pages 333-353, September.
    7. Jimmy de la Torre & Jeffrey Douglas, 2008. "Model Evaluation and Multiple Strategies in Cognitive Diagnosis: An Analysis of Fraction Subtraction Data," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 595-624, December.
    8. Chia-Yi Chiu & Jeff Douglas, 2013. "A Nonparametric Approach to Cognitive Diagnosis by Proximity to Ideal Response Patterns," Journal of Classification, Springer;The Classification Society, vol. 30(2), pages 225-250, July.
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    Cited by:

    1. Douglas L. Steinley, 2019. "Editorial: Journal of Classification Vol. 36-3," Journal of Classification, Springer;The Classification Society, vol. 36(3), pages 393-396, October.
    2. Douglas L. Steinley, 2018. "Editorial," Journal of Classification, Springer;The Classification Society, vol. 35(3), pages 391-393, October.

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