, 72:141 | Cite as

A class of multidimensional IRT models for testing unidimensionality and clustering items

  • Francesco BartolucciEmail author


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.

Key words

2PL model EM algorithm latent class model NAEP data Rasch model 


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Copyright information

© The Psychometric Society 2007

Authors and Affiliations

  1. 1.Dipartimento di Economia, Finanza e StatisticaUniversità di PerugiaPerugiaItaly

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