Semiparametric mixed effects models for unsupervised classification of Italian schools
This paper proposes an EM algorithm for non-parametric mixed-e ects models (NPEM algorithm) and applies it to the National Institute for the Educational Evaluation of Instruction and Training (INVALSI) data of 2013/2014 as a tool for unsupervised clustering of Italian schools. The main novelties introduced by NPEM algorithm, when applied to hierarchical data, are twofold: rst NPEM allows the covariates to be group speci c; second, it assumes the random e ects to be distributed according to a discrete distribution P ∗ with an (a priori) unknown number of support points. In doing so, it induces an automatic clustering of the grouping factor at higher level of hierarchy, enabling the identi cation of latent groups of schools that di er in their e ect on student achievements. The clustering may then be exploited through the use of school level features.