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，可用于处理包含相依误差、非线性函数关系且采用非正态分层结构数据的路径模型。首先，我们将因果模型分解为若干小型独立子集，针对各子集内的数据类型适配相应方法，即可独立开展各子集的建模工作。其次，我们引入连接函数（Copula）对非正态分布变量间的相依误差进行建模。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结果完全一致；当存在非线性函数关系时，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。