Heteroscedastic Factor Mixture Analysis

When data come from an unobserved heterogeneous population, common factor analysis is not appropriate to estimate the underlying constructs of interest. By replacing the traditional assumption of Gaussian distributed factors by a finite mixture of multivariate Gaussians, the unobserved heterogeneity can be modelled by latent classes. In so doing, we obtain a particular factor mixture analysis with heteroscedastic components. In this paper, the model is presented and a maximum likelihood estimation procedure via the expectation–maximization algorithm is developed. We also show that the approach well performs as a dimensionally reduced model-based clustering. Two real applications are illustrated and performances are compared to standard model-based clustering methods.