Implementation and Workflows for INLA-Based Approximate Bayesian Structural Equation Modelling

TL;DR

This paper introduces INLAvaan, an R package that enables fast approximate Bayesian structural equation modeling using INLA, significantly reducing computation time compared to traditional MCMC methods.

Contribution

It presents a new computational approach and software implementation for Bayesian SEM that is faster and more efficient than existing MCMC-based methods.

Findings

INLAvaan delivers calibrated posterior summaries in seconds.

Demonstrated on complex models where MCMC takes hours.

Provides a practical tool for psychometric Bayesian SEM.

Abstract

Bayesian structural equation modelling (BSEM) offers many advantages such as principled uncertainty quantification, small-sample regularisation, and flexible model specification. However, the Markov chain Monte Carlo (MCMC) methods on which it relies are computationally prohibitive for the iterative cycle of specification, criticism, and refinement that careful psychometric practice demands. We present INLAvaan, an R package for fast, approximate Bayesian SEM built around the Integrated Nested Laplace Approximation (INLA) framework for structural equation models developed by Jamil & Rue (2026, arXiv:2603.25690 [stat.ME]). This paper serves as a companion manuscript that describes the architectural decisions and computational strategies underlying the package. Two substantive applications -- a 256-parameter bifactor circumplex model and a multilevel mediation model with full-information missing-data handling -- demonstrate the approach on specifications where MCMC would require hours of run time and careful convergence work. In constrast, INLAvaan delivers calibrated posterior summaries in seconds.