Bayesian SEM: A more flexible representation of substantive theory

This paper proposes a new approach to factor analysis and structural equation modeling using Bayesian analysis. The new approach replaces parameter specifications of exact zeros and exact equalities with approximate zeros and equalities based on informative, smallvariance priors. It is argued that this produces an analysis that better reflects substantive theories. The proposed Bayesian approach is beneficial in applications where parameters are added to a conventional model such that a non-identified model is obtained if maximumlikelihood estimation is applied. This approach is useful for measurement aspects of latent variable modeling such as with CFA and the measurement part of SEM. Three application areas are studied: Cross-loadings in CFA, residual correlations in CFA, and measurement non-invariance in MIMIC modeling. The approach encompasses three elements: Model testing, model estimation, and model modification. Monte Carlo simulations and real data are analyzed using Mplus.