Multilevel Model-Based Clustering: A New Proposal of Maximum-A-Posteriori Assignment

We deal with the problem of latent variable prediction in the context of multilevel latent class models for categorical responses provided by individuals nested in groups. In particular, we propose a posterior assignment rule that jointly predicts the individual- and group-level latent variables. This proposal is alternative to the common maximum- a-posteriori rule, which is based on first predicting the latent variables at cluster level and, then, those at individual level. To illustrate the proposal, we show the results of two simulation studies and two applications on data related to the national and the international assessment of student skills.