  Mixture of factor analyzer (MFA) model is an efficient model for the analysis
of high dimensional data through which the factor-analyzer technique based on
the covariance matrices reducing the number of free parameters. The model also
provides an important methodology to determine latent groups in data. There are
several pieces of research to extend the model based on the asymmetrical and/or
with outlier datasets with some known computational limitations that have been
examined in frequentist cases. In this paper, an MFA model with a rich and
flexible class of skew normal (unrestricted) generalized hyperbolic (called
SUNGH) distributions along with a Bayesian structure with several computational
benefits have been introduced. The SUNGH family provides considerable
flexibility to model skewness in different directions as well as allowing for
heavy tailed data. There are several desirable properties in the structure of
the SUNGH family, including, an analytically flexible density which leads to
easing up the computation applied for the estimation of parameters. Considering
factor analysis models, the SUNGH family also allows for skewness and heavy
tails for both the error component and factor scores. In the present study, the
advantages of using this family of distributions have been discussed and the
suitable efficiency of the introduced MFA model using real data examples and
simulation has been demonstrated.
