COMPOSITE LIKELIHOOD INFERENCE FOR SIMULTANEOUS CLUSTERING AND DIMENSIONALITY REDUCTION OF MIXED-TYPE LONGITUDINAL DATA

We introduce a multivariate hidden Markov model (HMM) for mixedtype (continuous and ordinal) variables. As some of the considered variables may not contribute to the clustering structure, we built a hidden Markov-based model such that we are able to recognize discriminative and noise dimensions. The variables are considered to be linear combinations of two independent sets of latent factors where one contains the information about the cluster structure, following an HMM, and the other one contains noise dimensions distributed as a multivariate normal (and it does not change over time). The resulting model is parsimonious, but its computational burden may be cumbersome. To overcome any computational issue, a composite likelihood approach is introduced to estimate model parameters.