Fitting Structural Equation Models via Variational Approximations

TL;DR

This paper introduces a fast variational Bayes method for fitting structural equation models, offering a computationally efficient alternative to traditional MCMC techniques with reliable inference.

Contribution

It develops a mean field variational Bayes approach for structural equation models and enhances approximation quality using bootstrap methods.

Findings

Variational method is significantly faster than MCMC.

Bootstrap improves the accuracy of variational approximations.

Method provides reliable inference for complex models.

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.