Bayesian Estimation of the DINA Q matrix

Yinghan Chen (), Steven Andrew Culpepper (), Yuguo Chen () and Jeffrey Douglas ()
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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
Jeffrey Douglas: University of Illinois at Urbana-Champaign

Psychometrika, 2018, vol. 83, issue 1, No 5, 89-108

Abstract: Abstract 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.

Keywords: cognitive diagnosis models; deterministic inputs; noisy “and” gate (DINA) model; Q matrix; Bayesian statistics; fraction-subtraction data (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s11336-017-9579-4

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