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A multilevel finite mixture item response model to cluster examinees and schools

  • Michela GnaldiEmail author
  • Silvia Bacci
  • Francesco Bartolucci
Regular Article

Abstract

Within the educational context, a key goal is to assess students’ acquired skills and to cluster students according to their ability level. In this regard, a relevant element to be accounted for is the possible effect of the school students come from. For this aim, we provide a methodological tool which takes into account the multilevel structure of the data (i.e., students in schools) and allows us to cluster both students and schools into homogeneous classes of ability and effectiveness, and to assess the effect of certain students’ and school characteristics on the probability to belong to such classes. The proposed approach relies on an extended class of multidimensional latent class IRT models characterised by: (i) latent traits defined at student and school level, (ii) latent traits represented through random vectors with a discrete distribution, (iii) the inclusion of covariates at student and school level, and (iv) a two-parameter logistic parametrisation for the conditional probability of a correct response given the ability. The approach is applied for the analysis of data collected by two national tests administered in Italy to middle school students in June 2009: the INVALSI Language Test and the Mathematics Test.

Keywords

EM algorithm INVALSI Tests Latent class model Multilevel multidimensional item response models Two-parameter logistic model 

Mathematics Subject Classification

62-07 62H30 62H12 62F99 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Michela Gnaldi
    • 1
    Email author
  • Silvia Bacci
    • 2
  • Francesco Bartolucci
    • 2
  1. 1.Department of Political SciencesUniversity of PerugiaPerugiaItaly
  2. 2.Department of EconomicsUniversity of PerugiaPerugiaItaly

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