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Keywords: Bayesian inference, structural equation modeling, mean field Variational Bayes
Structural equation modeling (SEM) is a commonly used technique to capture the structural relationship between sets of observed and unobservable variables. In Bayesian settings, inference and fitting for SEMS are typically performed via Markov chain Monte Carlo (MCMC) methods. However, these methods can be computationally intensive, especially for models with a large number of manifest variables or complicated structures. Variational inference is a fast alternative to MCMC but it has not been adequately explored for SEMs. In this paper, we develop a mean field Variational Bayes (MFVB) algorithm for fitting basic SEMs. We show that MFVB provides reliable inference while being significantly faster than MCMC in different scenarios. Classical MFVB tends to underestimate the posterior variance, we therefore propose to use bootstrap to overcome this issue. We consider a few bootstrap strategies and demonstrate how it can improve the accuracy of MFVB considerably through simulated examples and an application with real data.