The Reduced RUM as a Logit Model: Parameterization and Constraints

Chia Yi Chiu, Hans Friedrich Koehn

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)350-370
Number of pages21
JournalPsychometrika
Volume81
Issue number2
DOIs
StatePublished - Jun 1 2016

Fingerprint

Markov Chains
Logit Model
Parameterization
Logistic Models
Educational Measurement
Latent Class Analysis
Attribute
Markov Chain Monte Carlo
Model
Markov processes
Latent Class Model
Expectation Maximization
Datasets
Expectation-maximization Algorithm
Synthetic Data
Unknown

Keywords

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

ASJC Scopus subject areas

  • Psychology(all)
  • Applied Mathematics

Cite this

The Reduced RUM as a Logit Model : Parameterization and Constraints. / Chiu, Chia Yi; Koehn, Hans Friedrich.

In: Psychometrika, Vol. 81, No. 2, 01.06.2016, p. 350-370.

Research output: Contribution to journalArticle

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