  We consider unsupervised classification by means of a latent multinomial
variable which categorizes a scalar response into one of L components of a
mixture model. This process can be thought as a hierarchical model with first
level modelling a scalar response according to a mixture of parametric
distributions, the second level models the mixture probabilities by means of a
generalised linear model with functional and scalar covariates. The traditional
approach of treating functional covariates as vectors not only suffers from the
curse of dimensionality since functional covariates can be measured at very
small intervals leading to a highly parametrised model but also does not take
into account the nature of the data. We use basis expansion to reduce the
dimensionality and a Bayesian approach to estimate the parameters while
providing predictions of the latent classification vector. By means of a
simulation study we investigate the behaviour of our approach considering
normal mixture model and zero inflated mixture of Poisson distributions. We
also compare the performance of the classical Gibbs sampling approach with
Variational Bayes Inference.
