Fitting Structural Equation Models via Variational Approximations

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.

Keywords:

• Approximate inference
• confirmatory factor analysis
• latent variables
• mean field variational Bayes
• nonparametric bootstrap

Additional information

Funding

The authors were supported by the Australian Research Council Center of Excellence for Mathematical and Statistical Frontiers (CE140100049). Luca Maestrini was also supported by the Australian Research Council Discovery Project DP180100597.