Development and Application of an Exploratory Reduced Reparameterized Unified Model

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)3-24
Number of pages22
JournalJournal of Educational and Behavioral Statistics
Volume44
Issue number1
DOIs
StatePublished - Feb 1 2019

Keywords

  • Bayesian
  • exploratory cognitive diagnosis modeling
  • reduced reparameterized unified model
  • spike–slab priors

ASJC Scopus subject areas

  • Education
  • Social Sciences (miscellaneous)

Fingerprint Dive into the research topics of 'Development and Application of an Exploratory Reduced Reparameterized Unified Model'. Together they form a unique fingerprint.

  • Cite this