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

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 current methods do not allow modeling latent variances as a function of other latent variables. In this paper, we develop a Bayesian framework for Gaussian distributional SEM which overcomes this limitation. We validate our framework using extensive simulations, which demonstrate that the new models produce reliable statistical inference and can be computed 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.