We explain how to obtain a generalized maximum likelihood chi-square statistic, X2 ML and a full-model Akaike Information Criterion (AIC) statistic for piecewise structural equation modeling (SEM); i.e. structural equations without latent variables whose causal topology can be represented as a directed acyclic graph (DAG). The full piecewise SEM is decomposed into submodels as a Markov network, each of which can have different distributional assumptions or functional links and that can be modeled by any method that produces maximum likelihood parameter estimates. The generalized X2 ML is a function of the difference in the maximum likelihoods of the model and its saturated equivalent and the full-model AIC is calculated by summing the AIC statistics of each of the submodels.

中文翻译：

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与有向无环图一致的路径模型的广义 AIC 和卡方统计

我们解释了如何为分段结构方程建模 (SEM) 获得广义最大似然卡方统计量 X2 ML 和全模型 Akaike 信息准则 (AIC) 统计量；即没有潜在变量的结构方程，其因果拓扑可以表示为有向无环图（DAG）。完整的分段 SEM 被分解为马尔可夫网络的子模型，每个子模型可以具有不同的分布假设或功能链接，并且可以通过任何产生最大似然参数估计的方法进行建模。广义 X2 ML 是模型的最大似然与其饱和等效值之差的函数，并且全模型 AIC 是通过对每个子模型的 AIC 统计量求和来计算的。