A class of multidimensional IRT models for testing unidimensionality and clustering items |
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Authors: | Francesco Bartolucci |
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Institution: | (1) Dipartimento di Economia, Finanza e Statistica, Università di Perugia, Via Pascoli 20, 06123 Perugia, Italy |
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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.
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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Keywords: | 2PL model EM algorithm latent class model NAEP data Rasch model |
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