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Abstract：
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.
摘要：
我们引入了一个简单的诊断测试，用于评估线性因果模型的整体或部分拟合优度，其中误差与协变量无关。特别是,我们考虑潜在存在隐藏的混杂因素的情况。我们开发了一种方法，并讨论了其区分与潜在变量的响应混淆的协变量与不混淆的协变量的能力。因此，我们提供了部分拟合优度的测试和方法。该测试基于将新颖的高阶最小二乘原理与普通最小二乘进行比较。尽管它很简单，所提出的方法是非常一般的，也被证明是有效的高维设置。本文的补充材料可在线获得。
