Model-based time-varying clustering of multivariate longitudinal data with covariates and outliers

A class of multivariate linear models under the longitudinal setting, in which unobserved heterogeneity may evolve over time, is introduced. A latent structure is considered to model heterogeneity, having a discrete support and following a first-order Markov chain. Heavy-tailed multivariate distributions are introduced to deal with outliers. Maximum likelihood estimation is performed to estimate parameters by using expectation–maximization and expectation–conditional-maximization algorithms. Notes on model identifiability and robustness are provided, along with all computational details needed to implement the proposal. Three applications on artificial and real data are illustrated. These focus on the potential effects of outliers on clustering and their identification.