Variational Bayes for Mixture of Gaussian Structural Equation Models

TL;DR

This paper develops mean-field variational Bayes algorithms for complex Gaussian mixture SEMs that handle non-Gaussian data features, covariates, and missing data, with practical model selection tools.

Contribution

It introduces novel variational inference methods for mixture Gaussian SEMs, extending Bayesian SEM analysis to more flexible and realistic data scenarios.

Findings

Algorithms perform well in simulations

Effective model selection criteria are proposed

Real data application demonstrates practical utility

Abstract

Structural equation models (SEMs) are commonly used to study the structural relationship between observed variables and latent constructs. Recently, Bayesian fitting procedures for SEMs have received more attention thanks to their potential to facilitate the adoption of more flexible model structures, and variational approximations have been shown to provide fast and accurate inference for Bayesian analysis of SEMs. However, the application of variational approximations is currently limited to very simple, elemental SEMs. We develop mean-field variational Bayes algorithms for two SEM formulations for data that present non-Gaussian features such as skewness and multimodality. The proposed models exploit the use of mixtures of Gaussians, include covariates for the analysis of latent traits and consider missing data. We also examine two variational information criteria for model selection that are straightforward to compute in our variational inference framework. The performance of the MFVB algorithms and information criteria is investigated in a simulated data study and a real data application.