Development and Application of an Exploratory Reduced Reparameterized Unified Model. (February 2019)

• Record Type: Journal Article
• Authors: Culpepper, Steven Andrew; Chen, Yinghan
• Is Part Of: Journal of educational and behavioral statistics. Volume 44:Number 1(2019)
• Page Start: 3
• Page End: 24
• Publication Date: 2019-02
• Subjects: exploratory cognitive diagnosis modeling -- reduced reparameterized unified model -- Bayesian -- spike–slab priors; Educational statistics -- Periodicals; Social sciences -- Statistical methods -- Periodicals; 370.2
• DOI: 10.3102/1076998618791306
• Languages: English
• ISSNs: 1076-9986

Abstract

Exploratory cognitive diagnosis models (CDMs) estimate theQ matrix, which is a binary matrix that indicates the attributes needed for affirmative responses to each item. Estimation ofQ 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 rRUMQ matrix is complicated by a confound between elements ofQ and the rRUM item parameters. A Bayesian framework is presented that accurately recoversQ 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 rRUMQ 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.