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Bayesian Estimation of the DINA Model With Gibbs Sampling

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  • Steven Andrew Culpepper

    (University of Illinois at Urbana-Champaign)

Abstract

A Bayesian model formulation of the deterministic inputs, noisy “and†gate (DINA) model is presented. Gibbs sampling is employed to simulate from the joint posterior distribution of item guessing and slipping parameters, subject attribute parameters, and latent class probabilities. The procedure extends concepts in Béguin and Glas, Culpepper, and Sahu for estimating the guessing and slipping parameters in the three- and four-parameter normal-ogive models. The ability of the model to recover parameters is demonstrated in a simulation study. The technique is applied to a mental rotation test. The algorithm and vignettes are freely available to researchers as the “dina†R package.

Suggested Citation

  • Steven Andrew Culpepper, 2015. "Bayesian Estimation of the DINA Model With Gibbs Sampling," Journal of Educational and Behavioral Statistics, , vol. 40(5), pages 454-476, October.
    • Handle: RePEc:sae:jedbes:v:40:y:2015:i:5:p:454-476
    DOI: 10.3102/1076998615595403
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    References listed on IDEAS

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    1. Yunxiao Chen & Jingchen Liu & Gongjun Xu & Zhiliang Ying, 2015. "Statistical Analysis of Q -Matrix Based Diagnostic Classification Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 850-866, June.
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    3. Chen, Yunxiao & Liu, Jingchen & Xu, Gongjun & Ying, Zhiliang, 2015. "Statistical analysis of Q-matrix based diagnostic classification models," LSE Research Online Documents on Economics 103183, London School of Economics and Political Science, LSE Library.
    4. A. Béguin & C. Glas, 2001. "MCMC estimation and some model-fit analysis of multidimensional IRT models," Psychometrika, Springer;The Psychometric Society, vol. 66(4), pages 541-561, December.
    5. E. Maris, 1999. "Estimating multiple classification latent class models," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 187-212, June.
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    Cited by:

    1. Michel Philipp & Carolin Strobl & Jimmy de la Torre & Achim Zeileis, 2018. "On the Estimation of Standard Errors in Cognitive Diagnosis Models," Journal of Educational and Behavioral Statistics, , vol. 43(1), pages 88-115, February.
    2. Steven Andrew Culpepper, 2019. "An Exploratory Diagnostic Model for Ordinal Responses with Binary Attributes: Identifiability and Estimation," Psychometrika, Springer;The Psychometric Society, vol. 84(4), pages 921-940, December.
    3. Steven Andrew Culpepper, 2019. "Estimating the Cognitive Diagnosis $$\varvec{Q}$$ Q Matrix with Expert Knowledge: Application to the Fraction-Subtraction Dataset," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 333-357, June.
    4. Yinghan Chen & Steven Andrew Culpepper & Yuguo Chen & Jeffrey Douglas, 2018. "Bayesian Estimation of the DINA Q matrix," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 89-108, March.

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