A computationally efficient and robust method to estimate exploratory factor analysis models with correlated residuals.

A critical assumption in exploratory factor analysis (EFA) is that manifest variables are no longer correlated after the influences of the common factors are controlled. The assumption may not be valid in some EFA applications; for example, questionnaire items share other characteristics in addition to their relations to common factors. We present a computationally efficient and robust method to estimate EFA with correlated residuals. We provide details on the implementation of the method with both ordinary least squares estimation and maximum likelihood estimation. We demonstrate the method using empirical data and conduct a simulation study to explore its statistical properties. The results are (a) that the new method encountered much fewer convergence problems than the existing method; (b) that the EFA model with correlated residuals produced a more satisfactory model fit than the conventional EFA model; and (c) that the EFA model with correlated residuals and the conventional EFA model produced very similar estimates for factor loadings. (PsycInfo Database Record (c) 2024 APA, all rights reserved).