The foundations of factor analysis

Abstract

A new approach to factor analysis and related latent variable methods is proposed which is based on data reduction using the idea of Bayesian sufficiency. Considerations of symmetry, invariance and independence are used to determine an appropriate family of models. The results are expressed in terms of linear functions of the manifest variables after the manner of principal components analysis. The approach justifies some of the practices based on the normal theory factor model and lays a foundation for the treatment of nonnormal, including categorical, variables.