On joint identification and latent variable estimation in factor analysis models

A factor analysis model is a representation y=Ax+e, of m observable variables y=[y₁....y₂]^T, assumed zero-mean and with finite variance, as linear combinations of n common factors x=[x₁...x₂]^T, plus uncorrelated “noise” or “error” terms e=[e₁ ...e₂]^T. It is imposed that the m components of the error e be mutually uncorrelated random variables. The aim of the model is provide an “explanation” of the mutual interrelation between the observable variables y in terms of small number of common factors