Robust model estimation, through trimming and constraints, for mixtures of factor analyzers

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. We complement model estimation with restrictions for the component covariances and trimming, to provide robustness to violations of normality assumptions of the underlying latent factors. A detailed AECM algorithm, which enforces constraints on eigenvalues and tentatively discards outliers at each step, is also presented. Simulations and a real application are illustrated, and performances are compared to previous approaches showing aim and effectiveness of the proposed methodology. Moreover, the model estimation has been moved in a new setting where the mathematical and the statistical problem are well-posed