Gaussian distributional structural equation models: A framework for modeling latent heteroscedasticity.

2024-04-22

Multivariate Behavioral Research

AI Summary

Existing structural equation modeling (SEM) frameworks struggle to model latent variable variances that depend on other latent variables, thereby limiting the characterization of latent heteroscedasticity—such as in psychological constructs like personality or creativity. To address this, we propose Bayesian Gaussian Distributional SEM, the first SEM extension integrating distributional regression into the SEM framework to jointly model both the mean and variance of latent variables. Leveraging Bayesian inference and MCMC sampling, our approach flexibly specifies latent variances as arbitrary functions of other latent variables. Simulation studies demonstrate high statistical reliability and computational efficiency. Empirical analysis of personality data reveals that emotional stability significantly moderates the variability of neuroticism—a finding inaccessible under conventional SEM. This work introduces a novel theoretical tool and methodological paradigm for modeling latent heteroscedasticity, advancing both substantive theory testing and statistical methodology in behavioral and social sciences.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems

Abstract

Accounting for the complexity of psychological theories requires methods that can predict not only changes in the means of latent variables - such as personality factors, creativity, or intelligence - but also changes in their variances. Structural equation modeling (SEM) is the framework of choice for analyzing complex relationships among latent variables, but the modeling of latent variances as a function of other latent variables is a task that current methods only support to a limited extent. In this article, we develop a Bayesian framework for Gaussian distributional SEM, which broadens the scope of feasible models for latent heteroscedasticity. We use statistical simulation to validate our framework across four distinct model structures, in which we demonstrate that reliable statistical inferences can be achieved and that computation can be performed with sufficient efficiency for practical everyday use. We illustrate our framework's applicability in a real-world case study that addresses a substantive hypothesis from personality psychology.

Problem

• Modeling latent variable variances in structural equation models
• Extending SEM to handle latent heteroscedasticity efficiently
• Validating Bayesian framework for psychological trait variance analysis

Innovation

• Bayesian framework for Gaussian distributional SEM
• Models latent heteroscedasticity efficiently
• Validated via statistical simulation studies