Relaxing the confirmatory factor model in the Big Five: Exploratory, Bayesian, and machine learning approaches

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Confirmatory Factor Analysis (CFA) is a critical component of a psychologist’s assessment toolbox. CFA posits that the covariance between a large number of items can be explained with a smaller number of latent variables. The downside of CFA is that it makes often overly restrictive demands of the data with no cross-loadings. Three methods have been devised to relax this assumption: Exploratory Structural Equation Model (SEM), Bayesian SEM, and Regularized SEM. Each of these allow for the existence of cross-loadings, but a direct comparison of these methods is missing from the literature. The present compares results of these three methods using a sample of over 300 adults who completed the Big Five Inventory. The models were compared with regards to model fit, factor loadings, and factor correlations. All three of these methods provided substantially better fit to the data than the CFA model did, while producing lower factor correlations. However, these methods did not always demonstrate agreement in which items cross-loaded on which factors. Implications for the use of these methods to relax the overly restrictive assumptions in CFA is discussed.