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A Proof of the Duality of the DINA Model and the DINO Model

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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 Deterministic Input Noisy Output “AND” gate (DINA) model and the Deterministic Input Noisy Output “OR” gate (DINO) model are two popular cognitive diagnosis models (CDMs) for educational assessment. They represent different views on how the mastery of cognitive skills and the probability of a correct item response are related. Recently, however, Liu, Xu, and Ying demonstrated that the DINO model and the DINA model share a “dual” relation. This means that one model can be expressed in terms of the other, and which of the two models is fitted to a given data set is essentially irrelevant because the results are identical. In this article, a proof of the duality of the DINA model and the DINO model is presented that is tailored to the form and parameterization of general CDMs that have become the new theoretical standard in cognitively diagnostic modeling.

Suggested Citation

  • Hans-Friedrich Köhn & Chia-Yi Chiu, 2016. "A Proof of the Duality of the DINA Model and the DINO Model," Journal of Classification, Springer;The Classification Society, vol. 33(2), pages 171-184, July.
    • Handle: RePEc:spr:jclass:v:33:y:2016:i:2:d:10.1007_s00357-016-9202-x
    DOI: 10.1007/s00357-016-9202-x
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. E. Maris, 1999. "Estimating multiple classification latent class models," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 187-212, June.
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    Cited by:

    1. 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.
    2. Steven Andrew Culpepper, 2023. "A Note on Weaker Conditions for Identifying Restricted Latent Class Models for Binary Responses," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 158-174, March.
    3. Pablo Nájera & Francisco J. Abad & Chia-Yi Chiu & Miguel A. Sorrel, 2023. "The Restricted DINA Model: A Comprehensive Cognitive Diagnostic Model for Classroom-Level Assessments," Journal of Educational and Behavioral Statistics, , vol. 48(6), pages 719-749, December.
    4. Peida Zhan & Hong Jiao & Kaiwen Man & Lijun Wang, 2019. "Using JAGS for Bayesian Cognitive Diagnosis Modeling: A Tutorial," Journal of Educational and Behavioral Statistics, , vol. 44(4), pages 473-503, August.
    5. Kazuhiro Yamaguchi & Kensuke Okada, 2020. "Variational Bayes Inference for the DINA Model," Journal of Educational and Behavioral Statistics, , vol. 45(5), pages 569-597, October.

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