Within the educational context, a key goal is to assess students acquiredskills and to cluster students according to their ability level. In thisregard, a relevant element to be accounted for is the possible effect of theschool students come from. For this aim, we provide a methodological tool whichtakes into account the multilevel structure of the data (i.e., students inschools) in a suitable way. This approach allows us to cluster both studentsand schools into homogeneous classes of ability and effectiveness, and toassess the effect of certain students and school characteristics on theprobability to belong to such classes. The approach relies on an extended classof multidimensional latent class IRT models characterized by: (i) latent traitsdefined at student level and at school level, (ii) latent traits representedthrough random vectors with a discrete distribution, (iii) the inclusion ofcovariates at student level and at school level, and (iv) a two-parameterlogistic parametrization for the conditional probability of a correct responsegiven the ability. The approach is applied for the analysis of data collectedby two national tests administered in Italy to middle school students in June2009: the INVALSI Italian Test and Mathematics Test. Results allow us to studythe relationships between observed characteristics and latent trait standingwithin each latent class at the different levels of the hierarchy. They showthat examinees and school expected observed scores, at a given latent traitlevel, are dependent on both unobserved (latent class) group membership andobserved first and second level covariates.
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