ROBUST FACTOR ANALYSIS USING THE MULTIVARIATE t-DISTRIBUTION

Abstract

Factor analysis is a standard method for multivariate analysis. The sam- pling 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 maxi- mum 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. Numer- ical examples show that use of multivariate t-distribution improves the robustness for the parameter estimation in factor analysis.