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Development and Application of an Exploratory Reduced Reparameterized Unified Model

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  • Steven Andrew Culpepper

    (University of Illinois at Urbana-Champaign)

  • Yinghan Chen

    (University of Nevada, Reno)

Abstract

Exploratory cognitive diagnosis models (CDMs) estimate the Q matrix, which is a binary matrix that indicates the attributes needed for affirmative responses to each item. Estimation of Q is an important next step for improving classifications and broadening application of CDMs. Prior research primarily focused on an exploratory version of the restrictive deterministic-input, noisy-and-gate model, and research is needed to develop exploratory methods for more flexible CDMs. We consider Bayesian methods for estimating an exploratory version of the more flexible reduced reparameterized unified model (rRUM). We show that estimating the rRUM Q matrix is complicated by a confound between elements of Q and the rRUM item parameters. A Bayesian framework is presented that accurately recovers Q using a spike–slab prior for item parameters to select the required attributes for each item. We present Monte Carlo simulation studies, demonstrating the developed algorithm improves upon prior Bayesian methods for estimating the rRUM Q matrix. We apply the developed method to the Examination for the Certificate of Proficiency in English data set. The results provide evidence of five attributes with a partially ordered attribute hierarchy.

Suggested Citation

  • Steven Andrew Culpepper & Yinghan Chen, 2019. "Development and Application of an Exploratory Reduced Reparameterized Unified Model," Journal of Educational and Behavioral Statistics, , vol. 44(1), pages 3-24, February.
    • Handle: RePEc:sae:jedbes:v:44:y:2019:i:1:p:3-24
    DOI: 10.3102/1076998618791306
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    References listed on IDEAS

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    1. Steven Andrew Culpepper, 2016. "Revisiting the 4-Parameter Item Response Model: Bayesian Estimation and Application," Psychometrika, Springer;The Psychometric Society, vol. 81(4), pages 1142-1163, December.
    2. Jonathan Templin & Laine Bradshaw, 2014. "Hierarchical Diagnostic Classification Models: A Family of Models for Estimating and Testing Attribute Hierarchies," Psychometrika, Springer;The Psychometric Society, vol. 79(2), pages 317-339, April.
    3. Chia-Yi Chiu & Jeffrey Douglas & Xiaodong Li, 2009. "Cluster Analysis for Cognitive Diagnosis: Theory and Applications," Psychometrika, Springer;The Psychometric Society, vol. 74(4), pages 633-665, December.
    4. Eddelbuettel, Dirk & Francois, Romain, 2011. "Rcpp: Seamless R and C++ Integration," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 40(i08).
    5. 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.
    6. E. Maris, 1999. "Estimating multiple classification latent class models," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 187-212, June.
    7. 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.
    8. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    9. 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.
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