On the Identifiability of Parameters in Thurstone's Multiple Factor Analysis

In econometric literature a parameter in a theoretical model has been called identifiable if it can be uniquely determined in terms of the joint probability distribution of the observed variables. In this paper the identifiability of parameters in four different factor analysis models is considered. The last of these four models corresponds to Thurstone's factor analysis. In Sections 7 and 11, the possibility of a statistical testing of the models is discussed. Section 10 deals with the problem of actually determining the parameter r (the number of common factors) in terms of the probability distribution of the observed variables.