A robust factor analysis model using the restricted skew- $$t$$ t distribution

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, called the skew- $$t$$ t factor analysis model, constructed by assuming a restricted version of the multivariate skew- $$t$$ t distribution for the latent factors and a symmetric $$t$$ t -distribution for the unobservable errors jointly. 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 expectation conditional maximization algorithm is developed for computing maximum likelihood estimates of model parameters. The usefulness of the proposed methodology is illustrated using both simulated and real data. Copyright Sociedad de Estadística e Investigación Operativa 2015