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A Gibbs Sampling Algorithm with Monotonicity Constraints for Diagnostic Classification Models

Author

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  • Kazuhiro Yamaguchi

    (University of Tsukuba, Institutes of Human Sciences)

  • Jonathan Templin

    (University of Iowa)

Abstract

Diagnostic classification models (DCMs) are restricted latent class models with a set of cross-class equality constraints and additional monotonicity constraints on their item parameters, both of which are needed to ensure the meaning of classes and model parameters. In this paper, we develop an efficient, Gibbs sampling-based Bayesian Markov chain Monte Carlo estimation method for general DCMs with monotonicity constraints. A simulation study was conducted to evaluate parameter recovery of the algorithm which showed accurate estimation of model parameters. Moreover, the proposed algorithm was compared to a previously developed Gibbs sampling algorithm which imposed constraints on only the main effect item parameters of the log-linear cognitive diagnosis model. The newly proposed algorithm showed less bias and faster convergence. An analysis of the 2000 Programme for International Student Assessment reading assessment data using this algorithm was also conducted.

Suggested Citation

  • Kazuhiro Yamaguchi & Jonathan Templin, 2022. "A Gibbs Sampling Algorithm with Monotonicity Constraints for Diagnostic Classification Models," Journal of Classification, Springer;The Classification Society, vol. 39(1), pages 24-54, March.
    • Handle: RePEc:spr:jclass:v:39:y:2022:i:1:d:10.1007_s00357-021-09392-7
    DOI: 10.1007/s00357-021-09392-7
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    References listed on IDEAS

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    Cited by:

    1. 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.
    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.

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