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Higher-Order Least Squares: Assessing Partial Goodness of Fit of Linear Causal Models

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  • Christoph Schultheiss
  • Peter Bühlmann
  • Ming Yuan

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.

Suggested Citation

  • Christoph Schultheiss & Peter Bühlmann & Ming Yuan, 2024. "Higher-Order Least Squares: Assessing Partial Goodness of Fit of Linear Causal Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(546), pages 1019-1031, April.
    • Handle: RePEc:taf:jnlasa:v:119:y:2024:i:546:p:1019-1031
    DOI: 10.1080/01621459.2022.2157728
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