Higher-Order Least Squares: Assessing Partial Goodness of Fit of Linear Causal Models
提出一种简单诊断检验，用于评估线性因果模型的整体或部分拟合优度，尤其适用于可能存在隐藏混杂变量的情况，通过比较高阶最小二乘与普通最小二乘来区分哪些协变量与响应变量存在混杂。
We introduce a simple diagnostic test for assessing the overall or partial goodness of fit of a linear causal model with errors being independent of the covariates. In particular, we consider situations where hidden confounding is potentially present. We develop a method and discuss its capability to distinguish between covariates that are confounded with the response by latent variables and those that are not. Thus, we provide a test and methodology for partial goodness of fit. The test is based on comparing a novel higher-order least squares principle with ordinary least squares. In spite of its simplicity, the proposed method is extremely general and is also proven to be valid for high-dimensional settings. Supplementary materials for this article are available online.