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.

翻译：理解心理理论的复杂性需要能够预测潜变量（如人格因素、创造力或智力）均值和方差变化的方法。结构方程模型（SEM）是分析潜变量间复杂关系的首选框架，但现有方法不允许将潜变量方差建模为其他潜变量的函数。本文提出了一种克服这一局限性的高斯分布性SEM的贝叶斯框架。通过大量仿真实验验证，新模型能够生成可靠的统计推断，且计算效率足以支持日常实践应用。我们通过一项来自人格心理学的实质性假设案例研究，展示了该框架的实际适用性。