Bayesian Structural Equation Modeling With Cross-Loadings and Residual Covariances

A recent article in the Journal of Management gives a critique of a Bayesian approach to factor analysis proposed in Psychological Methods. This commentary responds to the authors’ critique by clarifying key issues, especially the use of priors for residual covariances. A discussion is also presented of cross-loadings and model selection tools. Simulated data are used to illustrate the ideas. A reanalysis of the example used by the authors reveals a superior model overlooked by the authors.