A Bayesian approach for clustering and exact finite-sample model selection in longitudinal data mixtures

We consider mixtures of longitudinal trajectories, where one trajectory contains measurements over time of the variable of interest for one individual and each individual belongs to one cluster. The number of clusters as well as individual cluster memberships are unknown and must be inferred. We propose an original Bayesian clustering framework that allows us to obtain an exact finite-sample model selection criterion. Our approach is more flexible and parsimonious than asymptotic alternatives such as Bayesian Information Criterion (BIC) or Integrated Classification Likelihood (ICL) criterion in the choice of the number of clusters. Moreover, our approach has other desirable qualities: i) it keeps the computational effort of the clustering algorithm under control and ii) it generalizes to several families of regression mixture models, from linear to purely non-parametric.