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The Reduced RUM as a Logit Model: Parameterization and Constraints

Published online by Cambridge University Press:  01 January 2025

Chia-Yi Chiu  and
Hans-Friedrich Köhn
Chia-Yi Chiu*
Affiliation:
Rutgers, The State University of New Jersey
Hans-Friedrich Köhn
Affiliation:
University of Illinois at Urbana-Champaign
*
Correspondence should be made to Chia-Yi Chiu, Rutgers, The State University of New Jersey, New Brunswick, NJ, USA. Email: chia-yi.chiu@gse.rutgers.edu
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Abstract

Cognitive diagnosis models (CDMs) for educational assessment are constrained latent class models. Examinees are assigned to classes of intellectual proficiency defined in terms of cognitive skills called attributes, which an examinee may or may not have mastered. The Reduced Reparameterized Unified Model (Reduced RUM) has received considerable attention among psychometricians. Markov Chain Monte Carlo (MCMC) or Expectation Maximization (EM) are typically used for estimating the Reduced RUM. Commercial implementations of the EM algorithm are available in the latent class analysis (LCA) routines of Latent GOLD and Mplus, for example. Fitting the Reduced RUM with an LCA routine requires that it be reparameterized as a logit model, with constraints imposed on the parameters. For models involving two attributes, these have been worked out. However, for models involving more than two attributes, the parameterization and the constraints are nontrivial and currently unknown. In this article, the general parameterization of the Reduced RUM as a logit model involving any number of attributes and the associated parameter constraints are derived. As a practical illustration, the LCA routine in Mplus is used for fitting the Reduced RUM to two synthetic data sets and to a real-world data set; for comparison, the results obtained by using the MCMC implementation in OpenBUGS are also provided.

Keywords

cognitive diagnosisgeneral cognitive diagnostic modelsLCDMReduced RUMEMMCMCMplus
Type
Article
Information
Psychometrika , Volume 81 , Issue 2 , June 2016 , pp. 350 - 370
Copyright
Copyright © 2015 The Psychometric Society

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