A robust factor analysis model based on the canonical fundamental skew-t distribution

The traditional factor analysis rested on the assumption of multivariate normality has been extended by considering the restricted multivariate skew-t (rMST) distribution for the unobserved factors and errors jointly. However, the rMST distribution has limited use for characterising skewness that concentrates in a single direction. This paper is devoted to introducing a more flexible robust factor analysis model based on the broader canonical fundamental skew-t (CFUST) distribution, called the CFUSTFA model. The proposed new model can account for more complex features of skewness toward multiple directions. An efficient alternating expectation conditional maximization algorithm fabricated under several reduced complete-data spaces is developed to estimate parameters under the maximum likelihood (ML) perspective. To assess the variability of parameter estimates, we present an information-based approach to approximating the asymptotic covariance matrix of the ML estimators. The effectiveness and applicability of the proposed techniques are demonstrated through the analysis of simulated and real datasets.