The FC1 Rule of Identification for Confirmatory Factor Analysis

Abstract

Establishing the identification of a confirmatory factor analysis (CFA) model continues to be one of the most difficult tasks in structural equation modeling. Proving the identification of such models algebraically is both error prone and time consuming. Unfortunately, very few general rules of identification exist for CFA models and they are limited to simple models that do not allow for correlated errors. This article presents a new, highly general, sufficient condition of identification for CFA models with a factor complexity of one. This rule places no limits on the number of latent variables or number of indicator variables and allows for extremely complex error structures. The ease and generality of this test is demonstrated by identifying a number of substantive and hypothetical models.