  Mixtures of Gaussian factors are powerful tools for modeling an unobserved
heterogeneous population, offering - at the same time - dimension reduction and
model-based clustering. Unfortunately, the high prevalence of spurious
solutions and the disturbing effects of outlying observations, along maximum
likelihood estimation, open serious issues. In this paper we consider
restrictions for the component covariances, to avoid spurious solutions, and
trimming, to provide robustness against violations of normality assumptions of
the underlying latent factors. A detailed AECM algorithm for this new approach
is presented. Simulation results and an application to the AIS dataset show the
aim and effectiveness of the proposed methodology.
