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.

翻译：我们引入一个简单的诊断测试,评估线性因果模型整体或部分是否适合,误差独立于共变体。我们特别考虑隐蔽混淆可能存在的情况。我们开发了一种方法,并讨论其区分与潜在变量的反应相混淆的共变体和与非潜在变量的反应相混淆的共变体的能力。因此,我们提供了一个测试和方法,以部分适中为主。测试的基础是将新颖的较高级最低平方体原则与普通最低平方体进行比较。尽管其简单性,提议的方法极为笼统,而且被证明对高维环境也有效。