A Bayesian Regularized Approach to Exploratory Factor Analysis in One Step

Abstract

This research proposes a one-step Bayesian regularized approach to exploratory factor analysis (EFA) with an unknown number of factors. The proposed Bayesian regularized exploratory factor analysis (BREFA) model builds on the idea of bi-level Bayesian sparse group selection and can produce exact zero estimates at both the factor and loading levels. It can distinguish true factors from spurious factors and provide estimations of model and tuning parameters simultaneously. In addition to achieving model simplicity at both the factor and item levels, the approach provides interval estimates that can be used for significance testing, making it capable of addressing both uncorrelated and correlated factors. The Bayesian hierarchical formulation is implemented using Markov chain Monte Carlo estimation with the multivariate spike and slab priors and posterior median estimator. Based on simulated and real data analysis, BREFA demonstrates clear advantages or flexibility compared with traditional and Bayesian EFA, in terms of factor extraction, parameter estimation, and model interpretation.