Joint Assessment of the Differential Item Functioning and Latent Trait Dimensionality of Students' National Tests

TLDR: This paper investigates if assumptions of unidimensionality and absence of Di erential Item Functioning hold for two national tests administered in Italy to middle school students in June 2009: the Italian Test and the Mathematics Test.

Abstract: Within the educational context, students’ assessment tests are routinely vali-dated through Item Response Theory (IRT) models which assume unidimensionalityand absence of Di erential Item Functioning (DIF). In this paper, we investigate ifsuch assumptions hold for two national tests administered in Italy to middle schoolstudents in June 2009: the Italian Test and the Mathematics Test. To this aim, werely on an extended class of multidimensional latent class IRT models characterisedby: (i) a two-parameter logistic parameterisation for the conditional probability ofa correct response, (ii) latent traits represented through a random vector with a dis-crete distribution, and (iii) the inclusion of (uniform) DIF to account for students’gender and geographical area. A classi cation of the items into unidimensionalgroups is also proposed and represented by a dendrogram, which is obtained froma hierarchical clustering algorithm. The results provide evidence for DIF e ects forboth Tests. Besides, the assumption of unidimensionality is strongly rejected forthe Italian Test, whereas it is reasonable for the Mathematics Test.Keywords: EM algorithm; Hierarchical clustering; Item Response Theory; Multi-dimensional latent variable models; Two-parameter logistic parameterisation.