Semiparametric mixed effects models for unsupervised classification of Italian schools

The main purpose of the paper is to improve research on school effectiveness by applying a new strategy for uncovering subpopulations of schools that differ in terms of distribution of student outcomes. We propose a semiparametric mixed effects model with an expectation–maximization algorithm to estimate its parameters and we apply it to the Italian Institute for the Educational Evaluation of Instruction and Training data of 2013–2014 as a tool for the identification of latent subpopulations of schools. The semiparametric assumption provides the random effects of the mixed effects model to be distributed according to a discrete distribution with an (a priori) unknown number of support points. This modelling induces an automatic clustering of schools (the higher level of hierarchy), where schools within the same cluster share the same random effects. The latent subpopulations of schools identified may then be exploited through the use of multinomial models that include school level features. The novelties introduced by this paper are twofold: first, the semiparametric expectation–maximization algorithm is an innovative method that could be used in many classification problems; second, its application to education data represents a new approach to study school effectiveness.