Testing Model Fit in Path Models with Dependent Errors Given Non-Normality, Non-Linearity and Hierarchical Data

We provide a generic method of testing path models that include dependent errors, nonlinear functional relationships and using nonnormal, hierarchically structured data. First, we provide a decomposition of the causal model into smaller, independent sets. These sets can be modeled independently of each other with methods that respect the type of data in these sets. Second, we introduce copulas to model the dependent errors between non-normally distributed variables. Our method yields identical results as classical covariance-based path modelling when meeting its assumptions of linearity and normality, outperforms classical SEM given nonlinear functional relationships, and can easily accommodate any parametric probability function and nonlinear functional relationships.本研究提出一种通用的路径模型检验方法，可用于构建并检验包含相依误差、非线性函数关系的路径模型，且适用于非正态、层次化结构的数据集。首先，我们将因果模型分解为若干小型独立子集，各子集可依据其自身数据类型适配对应的建模方法，实现独立建模；其次，我们引入Copula函数（Copula）以建模非正态分布变量间的相依误差。当满足线性性与正态性假设时，本方法的结果与经典基于协方差的路径建模完全一致；在存在非线性函数关系的场景下，本方法的性能优于经典结构方程模型（Structural Equation Model, SEM），且可灵活适配任意参数化概率函数与非线性函数关系。