Markov chain Monte Carlo (MCMC) methods remain the mainstay of Bayesian estimation of structural equation models (SEM); however they often incur a high computational cost. We present a bespoke approximate Bayesian approach to SEM, drawing on ideas from the integrated nested Laplace approximation (INLA; Rue et al., 2009, J. R. Stat. Soc. Series B Stat. Methodol.) framework. We implement a simplified Laplace approximation that efficiently profiles the posterior density in each parameter direction while correcting for asymmetry, allowing for parametric skew-normal estimation of the marginals. Furthermore, we apply a variational Bayes correction to shift the marginal locations, thereby better capturing the posterior mass. Essential quantities, including factor scores and model-fit indices, are obtained via an adjusted Gaussian copula sampling scheme. For normal-theory SEM, this approach offers a highly accurate alternative to sampling-based inference, achieving near-'maximum likelihood' speeds while retaining the precision of full Bayesian inference.

翻译：马尔可夫链蒙特卡罗（MCMC）方法仍是结构方程模型（SEM）贝叶斯估计的主流工具，但其往往面临高昂的计算成本。我们提出一种针对SEM的定制化近似贝叶斯方法，借鉴集成嵌套拉普拉斯逼近（INLA; Rue等，2009,《英国皇家统计学会会刊B辑》统计方法）框架的思想。通过实现简化拉普拉斯逼近，我们可在各参数方向上高效映射后验密度并校正非对称性，从而对边缘分布实施参数化偏态正态估计。进一步地，我们采用变分贝叶斯校正对边缘位置进行偏移，以更精准地捕获后验质量。通过调整后的高斯连接函数采样方案，可获取因子得分和模型拟合指数等关键量。对于标准正态理论SEM，该方法为基于采样的推断提供了高精度替代方案，在保留完整贝叶斯推断精度的同时，实现了近乎"极大似然估计"的计算速度。