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Bayesian Estimation of a Multilevel IRT Model Using Gibbs Sampling

Published online by Cambridge University Press:  01 January 2025

Jean-Paul Fox  and
Cees A. W. Glas
Jean-Paul Fox*
Affiliation:
University of Twente
Cees A. W. Glas
Affiliation:
University of Twente
*
Requests for reprints should be sent to Jean-Paul Fox, Department of Educational Measurement and Data Analysis, University of Twente, RO. Box 217, 7500 AE Enschede, THE NETHERLANDS. E-mail: [email protected]
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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.

Keywords

Bayes estimatesGibbs sampleritem response theory (IRT)Markov chain Monte Carlomultilevel modeltwo-parameter normal ogive model
Type
Articles
Information
Psychometrika , Volume 66 , Issue 2 , June 2001 , pp. 271 - 288
Copyright
Copyright © 2001 The Psychometric Society

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