Structural equation models (SEMs) are commonly used to study the structural relationship between observed variables and latent constructs. Recently, Bayesian fitting procedures for SEMs have received more attention thanks to their potential to facilitate the adoption of more flexible model structures, and variational approximations have been shown to provide fast and accurate inference for Bayesian analysis of SEMs. However, the application of variational approximations is currently limited to very simple, elemental SEMs. We develop mean-field variational Bayes algorithms for two SEM formulations for data that present non-Gaussian features such as skewness and multimodality. The proposed models exploit the use of mixtures of Gaussians, include covariates for the analysis of latent traits and consider missing data. We also examine two variational information criteria for model selection that are straightforward to compute in our variational inference framework. The performance of the MFVB algorithms and information criteria is investigated in a simulated data study and a real data application.

翻译：结构方程模型（SEMs）常用于研究观测变量与潜在构念之间的结构关系。近年来，SEMs的贝叶斯拟合方法因其能够促进更灵活模型结构的采用而受到更多关注，而变分近似已被证明可为SEMs的贝叶斯分析提供快速且准确的推断。然而，变分近似的应用目前仅限于非常简单的基元SEMs。针对呈现偏态和多峰性等非高斯特征的数据，我们为两种SEM公式开发了平均场变分贝叶斯算法。所提出的模型利用高斯混合分布，包含用于分析潜在特质的协变量，并考虑了缺失数据问题。我们还研究了两种可直接在变分推断框架中计算的变分信息准则用于模型选择。通过模拟数据研究和实际数据应用，对MFVB算法与信息准则的性能进行了验证。