, Volume 58, Issue 1, pp 37–52 | Cite as

The asymptotic posterior normality of the latent trait in an IRT model

  • Hua-Hua Chang
  • William Stout


It has long been part of the item response theory (IRT) folklore that under the usual empirical Bayes unidimensional IRT modeling approach, the posterior distribution of examinee ability given test response is approximately normal for a long test. Under very general and nonrestrictive nonparametric assumptions, we make this claim rigorous for a broad class of latent models.

Key words

item response theory empirical Bayes posterior distribution ability estimation confidence interval manifest probably Dutch Identity 


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Copyright information

© The Psychometric Society 1993

Authors and Affiliations

  • Hua-Hua Chang
    • 1
  • William Stout
    • 2
  1. 1.Educational Testing ServicePrinceton
  2. 2.Department of StatisticsUniversity of IllinoisChampaign

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