Bayes Factors for Structural Equation Models with Blavaan and Bridge Sampling

Bayes factors offer a graded measure of statistical evidence that is increasingly popular in experimental psychology. In the field of structural equation modeling (SEM), however, computational and conceptual challenges have frustrated the broader adoption of Bayes factors. We present a practical Bayes factor workflow that uses bridge sampling to estimate marginal likelihoods for models specified in standard SEM syntax. The workflow starts from a unit-information (UI) prior derived from maximum-likelihood fits, providing a Bayesian analogue of the BIC. We then show how targeted prior variants for focal structural relations may alter and often sharpen the evidence, particularly when directional information is taken into account. A simulation study demonstrates that bridge-sampled UI Bayes factors closely track the BIC approximation and that correct directional prior information substantially increases support for the data-generating model. An empirical dataset is used to showcase two specific extensions, namely (a) robust mixture priors, and (b) Bayesian model averaging. The model averaging integrates across structurally different models and across different prior distributions for the model parameters. The proposed Bayes factor workflow is intended to make Bayesian model comparison in SEM feasible, transparent, and extensible.