Abstract

Structural equation models are commonly used to capture the relationship between sets of observed and unobservable variables. Traditionally these models are fitted using frequentist approaches, but recently researchers and practitioners have developed increasing interest in Bayesian inference. In Bayesian settings, inference for these models is typically performed via Markov chain Monte Carlo methods, which may be computationally intensive for models with a large number of manifest variables or complex structures. Variational approximations can be a fast alternative; however, they have not been adequately explored for this class of models. We develop a mean field variational Bayes approach for fitting elemental structural equation models and demonstrate how bootstrap can considerably improve the variational approximation quality. We show that this variational approximation method can provide reliable inference while being significantly faster than Markov chain Monte Carlo methods.

摘要

结构方程模型通常用于捕获观察变量集和不可观察变量集之间的关系。传统上，这些模型使用频率论方法进行拟合，但最近研究人员和实践者对贝叶斯推理产生了越来越大的兴趣。在贝叶斯设置中，这些模型的推理通常是通过马尔可夫链蒙特卡罗方法执行的，这对于具有大量显变量或复杂结构的模型来说可能是计算密集型的。变分近似可以是一种快速的替代方法；然而，对于这类模型，它们还没有得到充分的探索。我们开发了一种用于拟合元素结构方程模型的平均场变分贝叶斯方法，并展示了引导程序如何显着提高变分近似质量。