Bayesian estimation of the DINA \(Q\) matrix. (English) Zbl 1402.62302

Summary: 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 [Y. Chen et al., J. Am. Stat. Assoc. 110, No. 510, 850–866 (2015; Zbl 1373.62565)] 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.


62P15 Applications of statistics to psychology
62H30 Classification and discrimination; cluster analysis (statistical aspects)
91E10 Cognitive psychology


Zbl 1373.62565
Full Text: DOI


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