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MCMC Estimation and Some Model-Fit Analysis of Multidimensional IRT Models

Published online by Cambridge University Press:  01 January 2025

A. A. Béguin  and
C. A. W. Glas
A. A. Béguin*
Affiliation:
University of Twente
C. A. W. Glas
Affiliation:
University of Twente
*
Requests for reprints should be sent to Anton Béguin, CITO group, P.O. Box 1034, 6801 MG Arnhem, THE NETHERLANDS.
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Abstract

A Bayesian procedure to estimate the three-parameter normal ogive model and a generalization of the procedure to a model with multidimensional ability parameters are presented. The procedure is a generalization of a procedure by Albert (1992) for estimating the two-parameter normal ogive model. The procedure supports analyzing data from multiple populations and incomplete designs. It is shown that restrictions can be imposed on the factor matrix for testing specific hypotheses about the ability structure. The technique is illustrated using simulated and real data.

Keywords

Bayes estimatesfull-information factor analysisGibbs sampleritem response theoryMarkov chain Monte Carlomultidimensional item response theorynormal ogive model
Type
Articles
Information
Psychometrika , Volume 66 , Issue 4 , December 2001 , pp. 541 - 561
Copyright
Copyright © 2001 The Psychometric Society

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Footnotes

The authors would like to thank Norman Verhelst for his valuable comments and ACT, CITO group and SweSAT for the use of their data.

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