Metaphor Taken as Math: Indeterminancy in the Factor Analysis Model

The issue of indeterminacy in the factor analysis model has been the source of a lengthy and on-going debate. This debate can be seen as featuring two relevant interpretations of indeterminacy. The alternative solution position considers the latent common factor to be a random variate whose properties are determined by functional constraints inherent in the model. When the model fits the data, an infinity of random variates are criterially latent common factors to the set of manifest variates analyzed. The posterior moment position considers the latent common factor to be a single random entity with a non-point posterior distribution, given the manifest variables. It is argued here that: (a) The issue of indeterminacy centres on the criterion for the claim "X is a latent common factor to Y"; (b) the alternative solution position is correct, the posterior moment position representing a conflation of the criterion, which is provided by the equations of the model, with metaphors, analogies, and senses of "factor" that are external to the model. A number of implications for applied work involving factor analysis are discussed.