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Bayesian Modeling of Measurement Error in Predictor Variables Using Item Response Theory

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 send to Jean-Paul Fox, Department of Educational Measurement and Data Analysis, University of Twente, P.O. Box 217, 7500 AE Enschede, THE NETHERLANDS. E-Mail: Fox@edte.utwente.nl
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Abstract

It is shown that measurement error in predictor variables can be modeled using item response theory (IRT). The predictor variables, that may be defined at any level of an hierarchical regression model, are treated as latent variables. The normal ogive model is used to describe the relation between the latent variables and dichotomous observed variables, which may be responses to tests or questionnaires. It will be shown that the multilevel model with measurement error in the observed predictor variables can be estimated in a Bayesian framework using Gibbs sampling. In this article, handling measurement error via the normal ogive model is compared with alternative approaches using the classical true score model. Examples using real data are given.

Keywords

classical test theoryGibbs sampleritem response theoryhierarchical linear modelsMarkov Chain Monte Carlomeasurement errormultilevel modelmultilevel IRTtwo-parameter normal ogive model
Type
Articles
Information
Psychometrika , Volume 68 , Issue 2 , June 2003 , pp. 169 - 191
Copyright
Copyright © 2003 The Psychometric Society

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Footnotes

This paper is part of the dissertation by Fox (2001) that won the 2002 Psychometric Society Dissertation Award.

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