Don't Tie Yourself to an Onion: Don’t Tie Yourself to Assumptions of Normality

Maarten Marsman, Gunter Maris, Timo Bechger

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

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A structural measurement model (Adams, Wilson, & Wu, 1997) consists of an item response theory model for responses conditional on ability and a structural model that describes the distribution of ability in the population. As a rule, ability is assumed to be normally distributed in the population. However, there are situations where there is reason to assume that the distribution of ability is nonnormal. In this paper, we show that nonnormal ability distributions are easily modeled in a Bayesian framework
Original languageEnglish
Title of host publicationPsychometrics in Practice at RCEC
EditorsTheo J.H.M. Eggen, Bernard P. Veldkamp
ISBN (Print)978-90-365-3374-4
Publication statusPublished - 2012


  • Item response theory (IRT)
  • One-parameter logistic model
  • Finite mixture
  • Markov chain Monte Carlo
  • Plausible values
  • Bayes estimates
  • Gibbs sampler


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