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.

翻译：贝叶斯结构方程建模（BSEM）具有诸多优势，例如原则性的不确定性量化、小样本正则化以及灵活的模型设定。然而，其所依赖的马尔可夫链蒙特卡洛（MCMC）方法，对于心理测量学严谨实践所需的“设定-批评-优化”迭代循环而言，计算成本过高。我们提出INLAvaan，这是一个基于集成嵌套拉普拉斯近似（INLA）框架的R语言包，用于实现快速、近似的贝叶斯结构方程模型，该框架由Jamil与Rue（2026, arXiv:2603.25690 [stat.ME]）为结构方程模型开发。本文作为配套手稿，描述了该软件包背后的架构决策与计算策略。两个实质性应用——一个256参数的双因子环形模型和一个具有全信息缺失数据处理功能的多水平中介模型——展示了该方法在MCMC需要数小时运行时间及仔细收敛检验的设定下的表现。相比之下，INLAvaan能够在数秒内提供校准后的后验汇总结果。