Fitting Structural Equation Models via Variational Approximations

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.

Accommodating and Extending Various Models for Special Effects Within the Generalized Partially Confirmatory Factor Analysis Framework

“…The variational inference (e.g., Anderson & Peterson, 1987; Hinton & Van Camp, 1993) based on the Bayesian approach is promising, which can inherit many of MCMC’s benefits and balance computational efficiency and accuracy at the same time. Recently, this algorithm had been introduced under the FA and structural equation modeling context (Dang & Maestrini, 2022; Khan et al, 2010), which can provide a basis for its implementation under the revised GPCFA framework. From the structure perspective, extensions of the GPCFA to accommodate more variants such as the three-parameter testlet effect model are worth exploring.…”

Bayesian modelling of effects of prenatal alcohol exposure on child cognition based on data from multiple cohorts

“…Fast approximate inference, such as variational Bayes methods (Attias 1999) could potentially be used instead. However, variational inference is currently only available for very simple SEMs (Dang & Maestrini 2022) and the black‐box algorithm in STAN is not accurate for even the simple models. Second, the model does not fit non‐normal outcomes very well.…”

Variational Bayes inference for hidden Markov diagnostic classification models

“…In addition, Simulation 2 indicated underestimation of posterior SDs and the coverage of 95% CI of the VB method. A bootstrap procedure in conjunction with the VB method (Dang & Maestrini, 2022) can be used to address this problem. This procedure randomly selects a bootstrap sample and applies the VB method to obtain multiple VB estimates.…”