The skew-t factor analysis model

Abstract

Factor analysis is a classical data reduction technique that seeks a potentially lower number of unobserved variables that can account for the correlations among the observed variables. This paper presents an extension of the factor analysis model by assuming jointly a restricted version of multivariate skew t distribution for the latent factors and unobservable errors, called the skew-t factor analysis model. The proposed model shows robustness to violations of normality assumptions of the underlying latent factors and provides flexibility in capturing extra skewness as well as heavier tails of the observed data. A computationally feasible ECM algorithm is developed for computing maximum likelihood estimates of the parameters. The usefulness of the proposed methodology is illustrated by a real-life example and results also demonstrates its better performance over various existing methods.