The Reduced RUM as a Logit Model: Parameterization and Constraints

Chia Yi Chiu, Hans Friedrich Köhn

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)350-370
Number of pages21
Issue number2
StatePublished - Jun 1 2016


  • EM
  • LCDM
  • MCMC
  • Mplus
  • Reduced RUM
  • cognitive diagnosis
  • general cognitive diagnostic models

ASJC Scopus subject areas

  • Psychology(all)
  • Applied Mathematics

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