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A Multidimensional Item Response Model: Constrained Latent Class Analysis Using the Gibbs Sampler and Posterior Predictive Checks

Published online by Cambridge University Press:  01 January 2025

Herbert Hoijtink  and
Ivo W. Molenaar
Herbert Hoijtink*
Affiliation:
Department of Statistics and Measurement Theory, University of Groningen
Ivo W. Molenaar
Affiliation:
Department of Statistics and Measurement Theory, University of Groningen
*
Requests for reprints should be send to Herbert Hoijtink, Grote Kruisstraat 2/1, 9712 TS Groningen, THE NETHERLANDS.
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Abstract

In this paper it will be shown that a certain class of constrained latent class models may be interpreted as a special case of nonparametric multidimensional item response models. The parameters of this latent class model will be estimated using an application of the Gibbs sampler. It will be illustrated that the Gibbs sampler is an excellent tool if inequality constraints have to be taken into consideration when making inferences. Model fit will be investigated using posterior predictive checks. Checks for manifest monotonicity, the agreement between the observed and expected conditional association structure, marginal local homogeneity, and the number of latent classes will be presented.

Keywords

Gibbs samplerposterior predictive checksnonparametric item response theorymultidimensionalmanifest monotonicitylocal homogeneityconditional association
Type
Original Paper
Information
Psychometrika , Volume 62 , Issue 2 , June 1997 , pp. 171 - 189
Copyright
Copyright © 1997 The Psychometric Society

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Footnotes

This paper is supported by grant S40-645 of the Dutch Organization for Scientific Research (NWO).

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