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Variational Bayes Inference Algorithm for the Saturated Diagnostic Classification Model

Author

Listed:
  • Kazuhiro Yamaguchi

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

  • Kensuke Okada

    (University of Tokyo)

Abstract

Saturated diagnostic classification models (DCM) can flexibly accommodate various relationships among attributes to diagnose individual attribute mastery, and include various important DCMs as sub-models. However, the existing formulations of the saturated DCM are not better suited for deriving conditionally conjugate priors of model parameters. Because their derivation is the key in developing a variational Bayes (VB) inference algorithm, in the present study, we proposed a novel mixture formulation of saturated DCM. Based on it, we developed a VB inference algorithm of the saturated DCM that enables us to perform scalable and computationally efficient Bayesian estimation. The simulation study indicated that the proposed algorithm could recover the parameters in various conditions. It has also been demonstrated that the proposed approach is particularly suited to the case when new data become sequentially available over time, such as in computerized diagnostic testing. In addition, a real educational dataset was comparatively analyzed with the proposed VB and Markov chain Monte Carlo (MCMC) algorithms. The result demonstrated that very similar estimates were obtained between the two methods and that the proposed VB inference was much faster than MCMC. The proposed method can be a practical solution to the problem of computational load.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:psycho:v:85:y:2020:i:4:d:10.1007_s11336-020-09739-w
    DOI: 10.1007/s11336-020-09739-w
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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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    6. Jonathan Templin & Laine Bradshaw, 2013. "Measuring the Reliability of Diagnostic Classification Model Examinee Estimates," Journal of Classification, Springer;The Classification Society, vol. 30(2), pages 251-275, July.
    7. 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.
    8. 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.
    9. Jimmy de la Torre, 2011. "The Generalized DINA Model Framework," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 179-199, April.
    10. Grimmer, Justin, 2011. "An Introduction to Bayesian Inference via Variational Approximations," Political Analysis, Cambridge University Press, vol. 19(1), pages 32-47, January.
    11. 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.
    12. 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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    Cited by:

    1. 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.
    2. Chengyu Cui & Chun Wang & Gongjun Xu, 2024. "Variational Estimation for Multidimensional Generalized Partial Credit Model," Psychometrika, Springer;The Psychometric Society, vol. 89(3), pages 929-957, September.

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