Multi-level IRT with measurement error in the predictor variables

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A two-level regression model is imposed on the ability parameters in an item response theory (IRT) model. The advantage of using latent rather than observed scores as dependent variables of a multilevel model is that this offers the possibility of separating the influence of item difficulty and ability level and modeling response variation and measurement error. Another advantage is that, contrary to observed scores, latent scores are test-independent, which offers the possibility of entering results from different tests in one analysis. Further, it will be shown through simulation that problems of measurement error in covariates in multilevel models can also be solved in the framework of IRT-multilevel modeling. The two-parameter normal ogive model is used for the IRT measurement model in this study, and it is shown that the parameters of the two-parameter normal ogive model and the multilevel model can be estimated simultaneously in a Bayesian framework using Gibbs sampling. Various examples using simulated data are given.
Original languageEnglish
Place of PublicationEnschede
PublisherUniversiteit Twente TO/OMD
Publication statusPublished - 1998

Publication series

NameOMD research report
PublisherUniversity of Twente, Faculty of Educational Science and Technology


  • Simulation
  • Error of Measurement
  • Item Response Theory
  • Regression (Statistics)
  • Responses
  • IR-103768
  • Bayesian Statistics
  • Ability
  • Difficulty Level
  • METIS-136529
  • Predictor Variables


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