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

Yinghan Chen (), Steven Andrew Culpepper () and Yuguo Chen ()
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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

Psychometrika, 2023, vol. 88, issue 2, No 10, 613-635

Abstract: 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.

Keywords: Bayesian analysis; cognitive diagnosis model; Indian buffet process; latent class model; spike-and-slab prior (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11336-022-09900-7

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