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arXiv · 2109.14544

Higher-order least squares: assessing partial goodness of fit of linear causal models

Christoph Schultheiss·Peter Bühlmann·Ming Yuan
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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.

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Christoph Schultheiss, Peter Bühlmann, Ming Yuan. 2022-11-18. Higher-order least squares: assessing partial goodness of fit of linear causal models. https://doi.org/10.1080/01621459.2022.2157728

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