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Consistency of Cluster Analysis for Cognitive Diagnosis: The Reduced Reparameterized Unified Model and the General Diagnostic Model

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  • Chia-Yi Chiu

    (Rutgers, The State University of New Jersey)

  • Hans-Friedrich Köhn

    (University of Illinois at Urbana-Champaign)

Abstract

The asymptotic classification theory of cognitive diagnosis (ACTCD) provided the theoretical foundation for using clustering methods that do not rely on a parametric statistical model for assigning examinees to proficiency classes. Like general diagnostic classification models, clustering methods can be useful in situations where the true diagnostic classification model (DCM) underlying the data is unknown and possibly misspecified, or the items of a test conform to a mix of multiple DCMs. Clustering methods can also be an option when fitting advanced and complex DCMs encounters computational difficulties. These can range from the use of excessive CPU times to plain computational infeasibility. However, the propositions of the ACTCD have only been proven for the Deterministic Input Noisy Output “AND” gate (DINA) model and the Deterministic Input Noisy Output “OR” gate (DINO) model. For other DCMs, there does not exist a theoretical justification to use clustering for assigning examinees to proficiency classes. But if clustering is to be used legitimately, then the ACTCD must cover a larger number of DCMs than just the DINA model and the DINO model. Thus, the purpose of this article is to prove the theoretical propositions of the ACTCD for two other important DCMs, the Reduced Reparameterized Unified Model and the General Diagnostic Model.

Suggested Citation

  • Chia-Yi Chiu & Hans-Friedrich Köhn, 2016. "Consistency of Cluster Analysis for Cognitive Diagnosis: The Reduced Reparameterized Unified Model and the General Diagnostic Model," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 585-610, September.
    • Handle: RePEc:spr:psycho:v:81:y:2016:i:3:d:10.1007_s11336-016-9499-8
    DOI: 10.1007/s11336-016-9499-8
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    References listed on IDEAS

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    1. Jonathan Templin & Laine Bradshaw, 2014. "Hierarchical Diagnostic Classification Models: A Family of Models for Estimating and Testing Attribute Hierarchies," Psychometrika, Springer;The Psychometric Society, vol. 79(2), pages 317-339, April.
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    3. Jimmy de la Torre, 2011. "The Generalized DINA Model Framework," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 179-199, April.
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    5. Stephen Johnson, 1967. "Hierarchical clustering schemes," Psychometrika, Springer;The Psychometric Society, vol. 32(3), pages 241-254, September.
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