A multivariate latent variable model for the analysis of health status over time

latent variable model for the analysis of multivariate mixed longitudinal data is proposed. It extends a previous factor mixture model to longi-tudinal data. The model is based on the introduction of two hidden variables: a continuous latent variable for modeling the association among theobserved variables at each time point and a latent discrete variable that follows a first-order Markov chain with the aim of taking into account theunobserved heterogeneity. The aim of the proposed model is twofold: it allows us to perform dimension reduction when data are of mixed type andit performs model based clustering in the latent space. We derive an EM algorithm for the maximum likelihood estimation of the model parameters.The method is illustrated by an application to a longitudinal dataset on health status.