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Bayesian Inference for an Unknown Number of Attributes in Restricted Latent Class Models

Author

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  • Yinghan Chen

    (University of Nevada, Reno)

  • Steven Andrew Culpepper

    (University of Illinois at Urbana-Champaign)

  • Yuguo Chen

    (University of Illinois at Urbana-Champaign)

Abstract

The specification of the $${\varvec{Q}}$$ Q matrix in cognitive diagnosis models is important for correct classification of attribute profiles. Researchers have proposed many methods for estimation and validation of the data-driven $${\varvec{Q}}$$ Q matrices. However, inference of the number of attributes in the general restricted latent class model remains an open question. We propose a Bayesian framework for general restricted latent class models and use the spike-and-slab prior to avoid the computation issues caused by the varying dimensions of model parameters associated with the number of attributes, K. We develop an efficient Metropolis-within-Gibbs algorithm to estimate K and the corresponding $${\varvec{Q}}$$ Q matrix simultaneously. The proposed algorithm uses the stick-breaking construction to mimic an Indian buffet process and employs a novel Metropolis–Hastings transition step to encourage exploring the sample space associated with different values of K. We evaluate the performance of the proposed method through a simulation study under different model specifications and apply the method to a real data set related to a fluid intelligence matrix reasoning test.

Suggested Citation

  • Yinghan Chen & Steven Andrew Culpepper & Yuguo Chen, 2023. "Bayesian Inference for an Unknown Number of Attributes in Restricted Latent Class Models," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 613-635, June.
    • Handle: RePEc:spr:psycho:v:88:y:2023:i:2:d:10.1007_s11336-022-09900-7
    DOI: 10.1007/s11336-022-09900-7
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    References listed on IDEAS

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