Abstract
In the standard formulation of factor analysis (FA), factor loadings and unique variances are treated as fixed parameters, while common and unique factors are regarded as latent random variables. A very different formulation of FA has recently been presented in which common and unique factors are also treated as parameters and all model parts are expressed as parameter matrices. This is referred to as matrix factor analysis (MFA), whose properties are discussed in this paper. It is shown that the MFA algorithm is clearly described with concepts in linear algebra and allows FA to be viewed as higher rank approximation of a data matrix in contrast to principal component analysis as lower rank approximation. We further give numerical illustrations for comparing MFA solutions with the standard FA ones and discuss a sparse FA procedure derived from MFA.
