Bayesian Estimation of the DINA Q matrix

Research output: Contribution to journalArticlepeer-review


Cognitive diagnosis models are partially ordered latent class models and are used to classify students into skill mastery profiles. The deterministic inputs, noisy “and” gate model (DINA) is a popular psychometric model for cognitive diagnosis. Application of the DINA model requires content expert knowledge of a Q matrix, which maps the attributes or skills needed to master a collection of items. Misspecification of Q has been shown to yield biased diagnostic classifications. We propose a Bayesian framework for estimating the DINA Q matrix. The developed algorithm builds upon prior research (Chen, Liu, Xu, & Ying, in J Am Stat Assoc 110(510):850–866, 2015) and ensures the estimated Q matrix is identified. Monte Carlo evidence is presented to support the accuracy of parameter recovery. The developed methodology is applied to Tatsuoka’s fraction-subtraction dataset.

Original languageEnglish (US)
Pages (from-to)89-108
Number of pages20
Issue number1
StatePublished - Mar 1 2018


  • Bayesian statistics
  • Q matrix
  • cognitive diagnosis models
  • deterministic inputs
  • fraction-subtraction data
  • noisy “and” gate (DINA) model

ASJC Scopus subject areas

  • General Psychology
  • Applied Mathematics


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