Model-based clustering, classification, and discriminant analysis of data with mixed type

We propose a mixture of latent variables model for the model-based clustering, classification, and discriminant analysis of data comprising variables with mixed type. This approach is a generalization of latent variable analysis, and model fitting is carried out within the expectation-maximization framework. Our approach is outlined and a simulation study conducted to illustrate the effect of sample size and noise on the standard errors and the recovery probabilities for the number of groups. Our modelling methodology is then applied to two real data sets and their clustering and classification performance is discussed. We conclude with discussion and suggestions for future work.