  The mixture of factor analyzers (MFA) model provides a powerful tool for
analyzing high-dimensional data as it can reduce the number of free parameters
through its factor-analytic representation of the component covariance
matrices. This paper extends the MFA model to incorporate a restricted version
of the multivariate skew-normal distribution to model the distribution of the
latent component factors, called mixtures of skew-normal factor analyzers
(MSNFA). The proposed MSNFA model allows us to relax the need for the normality
assumption for the latent factors in order to accommodate skewness in the
observed data. The MSNFA model thus provides an approach to model-based density
estimation and clustering of high-dimensional data exhibiting asymmetric
characteristics. A computationally feasible ECM algorithm is developed for
computing the maximum likelihood estimates of the parameters. Model selection
can be made on the basis of three commonly used information-based criteria. The
potential of the proposed methodology is exemplified through applications to
two real examples, and the results are compared with those obtained from
fitting the MFA model.

Methodology