, Volume 68, Issue 2, pp 169–191

Bayesian modeling of measurement error in predictor variables using item response theory


DOI: 10.1007/BF02294796

Cite this article as:
Fox, JP. & Glas, C.A.W. Psychometrika (2003) 68: 169. doi:10.1007/BF02294796


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.

Key words

classical test theory Gibbs sampler item response theory hierarchical linear models Markov Chain Monte Carlo measurement error multilevel model multilevel IRT two-parameter normal ogive model 

Copyright information

© The Psychometric Society 2003

Authors and Affiliations

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

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