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Bayesian Estimation of the DINA Q matrix

Author

Listed:
  • Yinghan Chen

    (University of Nevada, Reno)

  • Steven Andrew Culpepper

    (University of Illinois at Urbana-Champaign)

  • Yuguo Chen

    (University of Illinois at Urbana-Champaign)

  • Jeffrey Douglas

    (University of Illinois at Urbana-Champaign)

Abstract

Cognitive diagnosis models are partially ordered latent class models and are used to classify students into skill mastery profiles. The deterministic inputs, noisy “and” gate model (DINA) is a popular psychometric model for cognitive diagnosis. Application of the DINA model requires content expert knowledge of a Q matrix, which maps the attributes or skills needed to master a collection of items. Misspecification of Q has been shown to yield biased diagnostic classifications. We propose a Bayesian framework for estimating the DINA Q matrix. The developed algorithm builds upon prior research (Chen, Liu, Xu, & Ying, in J Am Stat Assoc 110(510):850–866, 2015) and ensures the estimated Q matrix is identified. Monte Carlo evidence is presented to support the accuracy of parameter recovery. The developed methodology is applied to Tatsuoka’s fraction-subtraction dataset.

Suggested Citation

  • Yinghan Chen & Steven Andrew Culpepper & Yuguo Chen & Jeffrey Douglas, 2018. "Bayesian Estimation of the DINA Q matrix," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 89-108, March.
    • Handle: RePEc:spr:psycho:v:83:y:2018:i:1:d:10.1007_s11336-017-9579-4
    DOI: 10.1007/s11336-017-9579-4
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    References listed on IDEAS

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    1. Chen, Yunxiao & Liu, Jingchen & Xu, Gongjun & Ying, Zhiliang, 2015. "Statistical analysis of Q-matrix based diagnostic classification models," LSE Research Online Documents on Economics 103183, London School of Economics and Political Science, LSE Library.
    2. Jingchen Liu, 2017. "On the Consistency of Q-Matrix Estimation: A Commentary," Psychometrika, Springer;The Psychometric Society, vol. 82(2), pages 523-527, June.
    3. Curtis Tatsuoka, 2002. "Data analytic methods for latent partially ordered classification models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 51(3), pages 337-350, July.
    4. Robert Mislevy & Mark Wilson, 1996. "Marginal maximum likelihood estimation for a psychometric model of discontinuous development," Psychometrika, Springer;The Psychometric Society, vol. 61(1), pages 41-71, March.
    5. 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.
    6. 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.
    7. Yunxiao Chen & Jingchen Liu & Gongjun Xu & Zhiliang Ying, 2015. "Statistical Analysis of Q -Matrix Based Diagnostic Classification Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 850-866, June.
    8. Steven Andrew Culpepper, 2015. "Bayesian Estimation of the DINA Model With Gibbs Sampling," Journal of Educational and Behavioral Statistics, , vol. 40(5), pages 454-476, October.
    9. 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.
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