TY - JOUR
T1 - Development and Application of an Exploratory Reduced Reparameterized Unified Model
AU - Culpepper, Steven Andrew
AU - Chen, Yinghan
N1 - Funding Information:
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by the Spencer Foundation Grant #201700062 and by a grant from the National Science Foundation Methodology, Measurement, and Statistics program grant #1632023. Opinions reflect those of the authors and do not necessarily reflect those of the granting agency.
Publisher Copyright:
© 2018 AERA.
PY - 2019/2/1
Y1 - 2019/2/1
N2 - 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.
AB - 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.
KW - Bayesian
KW - exploratory cognitive diagnosis modeling
KW - reduced reparameterized unified model
KW - spike–slab priors
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U2 - 10.3102/1076998618791306
DO - 10.3102/1076998618791306
M3 - Article
AN - SCOPUS:85052584238
SN - 1076-9986
VL - 44
SP - 3
EP - 24
JO - Journal of Educational and Behavioral Statistics
JF - Journal of Educational and Behavioral Statistics
IS - 1
ER -