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Bayesian Estimation of the DINA Q matrix

Published online by Cambridge University Press:  01 January 2025

Yinghan Chen ,
Steven Andrew Culpepper ,
Yuguo Chen  and
Jeffrey Douglas
Yinghan Chen
Affiliation:
University of Nevada, Reno
Steven Andrew Culpepper*
Affiliation:
University of Illinois at Urbana-Champaign
Yuguo Chen
Affiliation:
University of Illinois at Urbana-Champaign
Jeffrey Douglas
Affiliation:
University of Illinois at Urbana-Champaign
*
Correspondence should be made to Steven Andrew Culpepper, Department of Statistics, University of Illinois at Urbana-Champaign, 725 South Wright Street, Champaign, IL 61820, USA. Email: sculpepp@illinois.edu
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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 modelsdeterministic inputsnoisy “and” gate (DINA) modelQ matrixBayesian statisticsfraction-subtraction data
Type
Original Paper
Information
Psychometrika , Volume 83 , Issue 1 , March 2018 , pp. 89 - 108
Copyright
Copyright © 2017 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (doi:10.1007/s11336-017-9579-4) contains supplementary material, which is available to authorized users.

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