Common Factor Model Stochastic Model, Data Analysis Technique or What?

Abstract

Factor analysis is a very frequently used methodology. Users not only in the social sciences but also in geography, medicine, chemistry, biology and economics like it. There are mainly two interpretations of the common factor analysis model as a data analytic procedure or as a stochastic model:

• The common factor analysis as a data analytic procedure. In this case the common factors and the parameters have no substantial meaning. They just serve to represent the observable variables, as it is, for instance, done by the principal components.

• The common factor analysis model as a causal model. In this case the unobservable common factors are considered as “true” indipendent variables linked by a linear relation with the observable variables. The common factors and the factor loadings are “true” as the regressors and the parameters in the regression model. As in the regression model, the true parameters are to be estimated with the observations on the variables. Furthermore the determination of the common factor scores is of great importance, because the parameters have only a substantial meaning knowing the underlying factors.