A two-level multivariate response model for data with latent structures

A novel approach is proposed for analysing multilevel multivariate response data. The approach is based on identifying a one-dimensional latent variable spanning the space of responses, which then induces correlation between upper-level units. The latent variable, which can be thought of as a random effect, is estimated along with the other model parameters using an EM algorithm, which can be seen in the tradition of the 'nonparametric maximum likelihood' estimator for two-level linear (univariate response) models. Simulations and real data examples from different fields are provided to illustrate the proposed methods in the context of regression and clustering applications.