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The Restricted DINA Model: A Comprehensive Cognitive Diagnostic Model for Classroom-Level Assessments

Author

Listed:
  • Pablo Nájera
  • Francisco J. Abad

    (Universidad Autónoma de Madrid)

  • Chia-Yi Chiu

    (University of Minnesota Twin Cities)

  • Miguel A. Sorrel

    (Universidad Autónoma de Madrid)

Abstract

The nonparametric classification (NPC) method has been proven to be a suitable procedure for cognitive diagnostic assessments at a classroom level. However, its nonparametric nature impedes the obtention of a model likelihood, hindering the exploration of crucial psychometric aspects, such as model fit or reliability. Reporting the reliability and validity of scores is imperative in any applied context. The present study proposes the restricted deterministic input, noisy “and†gate (R-DINA) model, a parametric cognitive diagnosis model based on the NPC method that provides the same attribute profile classifications as the nonparametric method while allowing to derive a model likelihood and, subsequently, to compute fit and reliability indices. The suitability of the new proposal is examined by means of an exhaustive simulation study and a real data illustration. The results show that the R-DINA model properly recovers the posterior probabilities of attribute mastery, thus becoming a suitable alternative for comprehensive small-scale diagnostic assessments.

Suggested Citation

  • 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.
    • Handle: RePEc:sae:jedbes:v:48:y:2023:i:6:p:719-749
    DOI: 10.3102/10769986231158829
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    References listed on IDEAS

    as
    1. 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.
    2. Matthew S. Johnson & Sandip Sinharay, 2020. "The Reliability of the Posterior Probability of Skill Attainment in Diagnostic Classification Models," Journal of Educational and Behavioral Statistics, , vol. 45(1), pages 5-31, February.
    3. 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.
    4. Yinghan Chen & Ying Liu & Steven Andrew Culpepper & Yuguo Chen, 2021. "Inferring the Number of Attributes for the Exploratory DINA Model," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 30-64, March.
    5. Xuliang Gao & Wenchao Ma & Daxun Wang & Yan Cai & Dongbo Tu, 2021. "A Class of Cognitive Diagnosis Models for Polytomous Data," Journal of Educational and Behavioral Statistics, , vol. 46(3), pages 297-322, June.
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    8. Shiyu Wang & Jeff Douglas, 2015. "Consistency of Nonparametric Classification in Cognitive Diagnosis," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 85-100, March.
    9. Chen-Wei Liu & Björn Andersson & Anders Skrondal, 2020. "A Constrained Metropolis–Hastings Robbins–Monro Algorithm for Q Matrix Estimation in DINA Models," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 322-357, June.
    10. 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.
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