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

Research output: Contribution to journalArticlepeer-review


The specification of the 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 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 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.

Original languageEnglish (US)
Pages (from-to)613-635
Number of pages23
Issue number2
StatePublished - Jun 2023


  • Bayesian analysis
  • Indian buffet process
  • cognitive diagnosis model
  • latent class model
  • spike-and-slab prior

ASJC Scopus subject areas

  • Applied Mathematics
  • General Psychology


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