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A Class of Multidimensional IRT Models for Testing Unidimensionality and Clustering Items

Published online by Cambridge University Press:  01 January 2025

Francesco Bartolucci
Francesco Bartolucci*
Affiliation:
Università di Perugia
*
Requests for reprints should be sent to Francesco Bartolucci, Dipartimento di Economia, Finanza e Statistica, Università di Perugia, Via Pascoli 20, 06123 Perugia, Italy. E-mail: bart@stat.unipg.it
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Abstract

We illustrate a class of multidimensional item response theory models in which the items are allowed to have different discriminating power and the latent traits are represented through a vector having a discrete distribution. We also show how the hypothesis of unidimensionality may be tested against a specific bidimensional alternative by using a likelihood ratio statistic between two nested models in this class. For this aim, we also derive an asymptotically equivalent Wald test statistic which is faster to compute. Moreover, we propose a hierarchical clustering algorithm which can be used, when the dimensionality of the latent structure is completely unknown, for dividing items into groups referred to different latent traits. The approach is illustrated through a simulation study and an application to a dataset collected within the National Assessment of Educational Progress, 1996.

Keywords

2PL modelEM algorithmlatent class modelNAEP dataRasch model
Type
Original Paper
Information
Psychometrika , Volume 72 , Issue 2 , June 2007 , pp. 141 - 157
Copyright
Copyright © 2007 The Psychometric Society

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Footnotes

The author would like to thank the Editor, an Associate Editor and three anonymous referees for stimulating comments. I also thank L. Scaccia, F. Pennoni and M. Lupparelli for having done part of the simulations.

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