Classification of Italian classes via bivariate semiparametric multilevel models

In this work, we propose a bivariate semi-parametric mixed-effects model where the random effects are assumed to follow a discrete distribution with an unknown number of support points, together with an Expectation-Maximization algorithm to estimate its parameters - the BSPEM algorithm. This model for hierarchical data enables the identification of subpopulations within the higher level of hierarchy. The bivariate setting allows to estimate the distributions of the model coefficients related to each response variable as well as their joint distribution. In the case study, we apply the BSPEM algorithm to data about Italian middle schools, considering students nested within classes, and we identify subpopulations of classes that have different effects on reading and mathematics student achievements. The strength of the proposed bivariate semi-parametric mixed-effects model is twofold: first, it is an innovative model that can be applied in many classification problems dealing with multiple outcomes; second, when applied in the educational context, given the strong connections among student learning processes in different school subjects, it results to be extremely informative in modeling the correlation between multiple class effects. The identified subpopulations of classes are then explained in terms of teacher characteristics, teaching practices and class body composition.