Psychometrika

, Volume 66, Issue 2, pp 271–288 | Cite as

Bayesian estimation of a multilevel IRT model using gibbs sampling

Articles

Abstract

In this article, 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 it 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 using results from different tests in one analysis where the parameters of the IRT model and the multilevel model can be concurrently estimated. The two-parameter normal ogive model is used for the IRT measurement model. It will be shown that the parameters of the two-parameter normal ogive model and the multilevel model can be estimated in a Bayesian framework using Gibbs sampling. Examples using simulated and real data are given.

Key words

Bayes estimates Gibbs sampler item response theory (IRT) Markov chain Monte Carlo multilevel model two-parameter normal ogive model 

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Copyright information

© The Psychometric Society 2001

Authors and Affiliations

  1. 1.Department of Educational Measurement and Data AnalysisUniversity of TwenteEnschedeThe Netherlands

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