Bivariate semi-parametric mixed-effects models for classifying the effects of Italian classes on multiple student achievements

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 can be ap- plied in many multivariate classification p roblems a nd e nables t he i dentification of subpopulations within the higher level of the hierarchy. In the case study, we ap- ply the BSPEM algorithm to data about Italian middle schools, considering students nested within classes, and we identify subpopulations of classes that have different class effects on reading and mathematics student achievements.