A flexible factor analysis based on the class of mean-mixture of normal distributions

Factor analysis is a statistical technique for data reduction and structure detection that traditionally relies on the normality assumption for factors. However, due to the presence of non-normal features such as asymmetry and heavy tails in many practical situations, the first two moments cannot adequately explain the factors. An extension of the factor analysis model is introduced by assuming a generalization of the multivariate restricted skew-normal distribution for the vector of unobserved factors. An efficient and computationally tractable EM-type algorithm is adopted for computing the maximum likelihood estimates by presenting a hierarchical representation of the proposed model. Finally, the efficiency and advantages of the proposed novel methodology are demonstrated through both simulated and real benchmark datasets.