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Variational Bayes Inference for the DINA Model

Author

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  • Kazuhiro Yamaguchi

    (216185University of Iowa Japan Society for the Promotion of Science)

  • Kensuke Okada

    (13143University of Tokyo)

Abstract

In this article, we propose a variational Bayes (VB) inference method for the deterministic input noisy AND gate model of cognitive diagnostic assessment. The proposed method, which applies the iterative algorithm for optimization, is derived based on the optimal variational posteriors of the model parameters. The proposed VB inference enables much faster computation than the existing Markov chain Monte Carlo (MCMC) method, while still offering the benefits of a full Bayesian framework. A simulation study revealed that the proposed VB estimation adequately recovered the parameter values. Moreover, an example using real data revealed that the proposed VB inference method provided similar estimates to MCMC estimation with much faster computation.

Suggested Citation

  • 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.
    • Handle: RePEc:sae:jedbes:v:45:y:2020:i:5:p:569-597
    DOI: 10.3102/1076998620911934
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    References listed on IDEAS

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    1. Michel Philipp & Carolin Strobl & Jimmy de la Torre & Achim Zeileis, 2018. "On the Estimation of Standard Errors in Cognitive Diagnosis Models," Journal of Educational and Behavioral Statistics, , vol. 43(1), pages 88-115, February.
    2. K. Humphreys & D. Titterington, 2003. "Variational approximations for categorical causal modeling with latent variables," Psychometrika, Springer;The Psychometric Society, vol. 68(3), pages 391-412, September.
    3. 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.
    4. White, Arthur & Murphy, Thomas Brendan, 2014. "BayesLCA: An R Package for Bayesian Latent Class Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 61(i13).
    5. 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.
    6. Frank Rijmen & Minjeong Jeon, 2013. "Fitting an item response theory model with random item effects across groups by a variational approximation method," Annals of Operations Research, Springer, vol. 206(1), pages 647-662, July.
    7. E. Maris, 1999. "Estimating multiple classification latent class models," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 187-212, June.
    8. Minjeong Jeon & Frank Rijmen & Sophia Rabe-Hesketh, 2017. "A Variational Maximization–Maximization Algorithm for Generalized Linear Mixed Models with Crossed Random Effects," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 693-716, September.
    9. David M. Blei & Alp Kucukelbir & Jon D. McAuliffe, 2017. "Variational Inference: A Review for Statisticians," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 859-877, April.
    10. Frank Rijmen & Minjeong Jeon, 2013. "Erratum to: Fitting an item response theory model with random item effects across groups by a variational approximation," Annals of Operations Research, Springer, vol. 206(1), pages 663-663, July.
    11. Steven Andrew Culpepper, 2019. "Estimating the Cognitive Diagnosis $$\varvec{Q}$$ Q Matrix with Expert Knowledge: Application to the Fraction-Subtraction Dataset," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 333-357, June.
    12. Jimmy de la Torre, 2011. "The Generalized DINA Model Framework," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 179-199, April.
    13. 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.
    14. Ormerod, J. T. & Wand, M. P., 2010. "Explaining Variational Approximations," The American Statistician, American Statistical Association, vol. 64(2), pages 140-153.
    15. Grimmer, Justin, 2011. "An Introduction to Bayesian Inference via Variational Approximations," Political Analysis, Cambridge University Press, vol. 19(1), pages 32-47, January.
    16. 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.
    17. Jimmy Torre, 2011. "Erratum to: The Generalized DINA Model Framework," Psychometrika, Springer;The Psychometric Society, vol. 76(3), pages 510-510, July.
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    Citations

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    Cited by:

    1. Yuqi Gu, 2023. "Generic Identifiability of the DINA Model and Blessing of Latent Dependence," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 117-131, March.
    2. Kazuhiro Yamaguchi, 2023. "Bayesian Analysis Methods for Two-Level Diagnosis Classification Models," Journal of Educational and Behavioral Statistics, , vol. 48(6), pages 773-809, December.
    3. Kazuhiro Yamaguchi & Kensuke Okada, 2020. "Variational Bayes Inference Algorithm for the Saturated Diagnostic Classification Model," Psychometrika, Springer;The Psychometric Society, vol. 85(4), pages 973-995, December.
    4. Motonori Oka & Kensuke Okada, 2023. "Scalable Bayesian Approach for the Dina Q-Matrix Estimation Combining Stochastic Optimization and Variational Inference," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 302-331, March.
    5. Kazuhiro Yamaguchi & Jonathan Templin, 2022. "Direct Estimation of Diagnostic Classification Model Attribute Mastery Profiles via a Collapsed Gibbs Sampling Algorithm," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1390-1421, December.

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