Robust Factor Analysis Using the Multivariate t-Distribution

Factor analysis is a standard method for multivariate analysis. The sampling model in the most popular factor analysis is Gaussian and has thus often been criticized for its lack of robustness. A simple robust extension of the Gaussian factor analysis model is obtained by replacing the multivariate Gaussian distribution with a multivariate t-distribution. We develop computational methods for both maximum likelihood estimation and Bayesian estimation of the factor analysis model. The proposed methods include the ECME and PX-EM algorithms for maximum likelihood estimation and Gibbs sampling methods for Bayesian inference. Numerical examples show that use of multivariate t-distribution improves the robustness for the parameter estimation in factor analysis.