Determination of the number of factors in the presence of correlated error terms

Abstract

The problem of the determination of the number of latent factors is analysed within a generalized factor model, where nonzero elements out of the diagonal of the variance-covariance matrix of error terms are admitted. In this framework, it is proved that classical methods for the selection of the factor model such as likelihood ratio test and information criteria are biased and systematically overestimate the number of factors. A Monte Carlo experiment shows the different behavior of classical methods and of two alternative criteria which have been developed for the generalized model.