Efficient Bayesian Structural Equation Modeling in Stan

Structural equation models comprise a large class of popular statistical models, including factor analysis models, certain mixed models, and extensions thereof. Model estimation is complicated by the fact that we typically have multiple interdependent response variables and multiple latent variables (which may also be called random effects or hidden variables), often leading to slow and inefficient posterior sampling. In this paper, we describe and illustrate a general, efficient approach to Bayesian SEM estimation in Stan, contrasting it with previous implementations in R package blavaan (Merkle and Rosseel 2018). After describing the approaches in detail, we conduct a practical comparison under multiple scenarios. The comparisons show that the new approach is clearly better. We also discuss ways that the approach may be extended to other models that are of interest to psychometricians.