A Bayesian approach to person-fit analysis in item response theory models

Cornelis A.W. Glas, R.R. Meijer

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Abstract

A Bayesian approach to the evaluation of person fit in item response theory (IRT) models is presented. In a posterior predictive check, the observed value on a discrepancy variable is positioned in its posterior distribution. In a Bayesian framework, a Markov Chain Monte Carlo procedure can be used to generate samples of the posterior distribution of the parameters of interest. These draws can also be used to compute the posterior predictive distribution of the discrepancy variable. The procedure is worked out in detail for the three-parameter normal ogive model, but it is also shown that the procedure can be directly generalized to many other IRT models. Type I error rate and the power against some specific model violations are evaluated using a number of simulation studies.
Original languageEnglish
Place of PublicationEnschede
PublisherUniversity of Twente, Faculty Educational Science and Technology
Number of pages38
Publication statusPublished - 2001

Publication series

NameOMD Research Report
PublisherUniversity of Twente, Faculty of Educational Science and Technology
No.01-09

Keywords

  • Markov Processes
  • Bayesian Statistics
  • Item Response Theory
  • Monte Carlo Methods
  • Simulation
  • IR-103756
  • METIS-205694
  • Models

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