Testing Unidimensionality and Clustering Items: An Application to the INVALSI Students’ Assessment Data

We aim at studying if the assumption of unidimensionality is met for the data collected on middle school students by the National Institute for the Evalu- ation of the Education System (INVALSI). The applied methodology relies on a class of multidimensional latent class Item Response Theory models based on: (i) a two-parameter logistic parameterization for the conditional probability of a correct response, (ii) latent traits represented through a random vector with a discrete distribution, and (iii) the inclusion of differential item functioning (DIF) effects due to students’ gender and geographical status. On the basis of this model, a hierarchical clustering algorithm is also proposed for dividing items into unidimensional groups referred to different abilities. The resulting classification of the items is represented by a dendrogram.