A note on identifiability conditions in confirmatory factor analysis

Recently, Chen, Li and Zhang have established simple conditions characterizing when latent factors are asymptotically identifiable within a certain model of confirmatory factor analysis. In this note, we prove a related characterization of when factor loadings are identifiable, under slightly weaker modeling assumptions and a slightly stronger definition of identifiability. We also check that the previously-established characterization for latent factors still holds in our modified model.