ABSTRACT
In certain mathematical statistical circles, there appear to linger doubts about the soundness of latent variables, in particular common factors in factor models. In what follows we will show, to the best of our knowledge for the first time, that a common latent factor in a factor model can be conceived of as a genuine scientific construct obeying the usual formal criteria for such constructs. Following the discussion in Simon (1977, ch. 6.6) it will be shown that a common factor in a factor model can be transformed into a network of regression relationships between the manifest (observed) variables. Because this transformation is invertible, we end up with two strictly equivalent models; the factor model and a model without the factor. This shows that the latent factor in a factor model serves as a placeholder for a system of relationships between the manifest variables and thus obeys the most stringent criterion for valid scientific constructs (cf. Simon, 1977).
