Approximate Bayesian Inference for Structural Equation Models using Integrated Nested Laplace Approximations

2026-03-26

AI Summary

This work proposes an efficient approximate Bayesian inference framework for Bayesian structural equation modeling (SEM) that overcomes the high computational cost of traditional Markov chain Monte Carlo (MCMC) methods. By integrating simplified Laplace approximations, variational Bayes corrections, skew-normal marginal estimation, and Gaussian copula sampling within an integrated nested Laplace approximation (INLA) framework, the approach achieves substantial gains in computational efficiency. In normal-theory SEM, the method attains computational speed comparable to maximum likelihood estimation while preserving the accuracy and uncertainty quantification inherent to full Bayesian inference, thereby offering a balanced trade-off between statistical reliability and computational tractability.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems

Abstract

Markov chain Monte Carlo (MCMC) methods remain the mainstay of Bayesian estimation of structural equation models (SEM); however they often incur a high computational cost. We present a bespoke approximate Bayesian approach to SEM, drawing on ideas from the integrated nested Laplace approximation (INLA; Rue et al., 2009, J. R. Stat. Soc. Series B Stat. Methodol.) framework. We implement a simplified Laplace approximation that efficiently profiles the posterior density in each parameter direction while correcting for asymmetry, allowing for parametric skew-normal estimation of the marginals. Furthermore, we apply a variational Bayes correction to shift the marginal locations, thereby better capturing the posterior mass. Essential quantities, including factor scores and model-fit indices, are obtained via an adjusted Gaussian copula sampling scheme. For normal-theory SEM, this approach offers a highly accurate alternative to sampling-based inference, achieving near-'maximum likelihood' speeds while retaining the precision of full Bayesian inference.

Problem

• Structural Equation Models
• Bayesian Inference
• Computational Efficiency
• Markov Chain Monte Carlo
• Approximate Inference

Innovation

• Integrated Nested Laplace Approximation
• Structural Equation Models
• Approximate Bayesian Inference
• Variational Bayes Correction
• Skew-Normal Marginals