Development and Application of an Exploratory Reduced Reparameterized Unified Model

Steven Andrew Culpepper and Yinghan Chen
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Steven Andrew Culpepper: University of Illinois at Urbana-Champaign
Yinghan Chen: University of Nevada, Reno

Journal of Educational and Behavioral Statistics, 2019, vol. 44, issue 1, 3-24

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.

Keywords: exploratory cognitive diagnosis modeling; reduced reparameterized unified model; Bayesian; spike–slab priors (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:44:y:2019:i:1:p:3-24

DOI: 10.3102/1076998618791306

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