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

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 paper, 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.

Update incorporating reviewer feedback, content matches published version

References in corpus (14)

• The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo
• Rank-normalization, folding, and localization: An improved $\hat{R}$ for assessing convergence of MCMC
• The prior can generally only be understood in the context of the likelihood
• A General Framework for the Parametrization of Hierarchical Models
• Validating Bayesian Inference Algorithms with Simulation-Based Calibration
• Bayesian comparison of latent variable models: Conditional vs marginal likelihoods
• Efficient Bayesian Structural Equation Modeling in Stan
• Simulation-Based Calibration Checking for Bayesian Computation: The Choice of Test Quantities Shapes Sensitivity
• Intuitive Joint Priors for Bayesian Linear Multilevel Models: The R2D2M2 prior
• Some models are useful, but how do we know which ones? Towards a unified Bayesian model taxonomy
• Fitting Structural Equation Models via Variational Approximations
• Opaque prior distributions in Bayesian latent variable models
• Simulation-Based Prior Knowledge Elicitation for Parametric Bayesian Models
• Primed Priors for Simulation-Based Validation of Bayesian Models