Should I allow my confirmatory factors to correlate during factor score extraction? Implications for the applied researcher

With complex models becoming increasingly popular in the social sciences, many researchers have begun using latent variable modeling in multiple-steps, saving, estimating, or otherwise extracting factor scores from one confirmatory factor analysis (CFA) for use in a second inferential analysis. With two or more factors identified in a CFA, there exist few practical guidelines as to how researchers should proceed. In Study 1, we examine two common practices when CFAs have two or more factors: Fitting separate CFAs or allowing them to correlate in the model used for extraction. We provide a simulation study to demonstrate the bias introduced in each of the two approaches. In Study 2, we demonstrate that the between-factor correlation bias can be mitigated through the use of a different estimator; using ten Berge estimation shows near zero bias on the critical correlations between factors. Finally, we demonstrate this with an example dataset.