Efficient Bayesian Structural Equation Modeling in Stan

Abstract

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 MCMC samples. 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 & 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.

arXiv comment21 pages, 5 figures

References in corpus (4)

• Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory
• Validating Bayesian Inference Algorithms with Simulation-Based Calibration
• Bayesian comparison of latent variable models: Conditional vs marginal likelihoods
• Efficient Bayesian Structural Equation Modeling in Stan

Cited by in corpus (4)

• Efficient Bayesian Structural Equation Modeling in Stan
• Fitting Structural Equation Models via Variational Approximations
• Opaque prior distributions in Bayesian latent variable models
• Gaussian distributional structural equation models: A framework for modeling latent heteroscedasticity