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Ancestor regression in linear structural equation models

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  • C Schultheiss
  • P Bühlmann

Abstract

SummaryWe present a new method for causal discovery in linear structural equation models. We propose a simple technique based on statistical testing in linear models that can distinguish between ancestors and non-ancestors of any given variable. Naturally, this approach can then be extended to estimating the causal order among all variables. We provide explicit error control for false causal discovery, at least asymptotically. This holds true even under Gaussianity, where other methods fail due to non-identifiable structures. These Type I error guarantees come at the cost of reduced power. Additionally, we provide an asymptotically valid goodness-of-fit p-value for assessing whether multivariate data stem from a linear structural equation model.

Suggested Citation

  • C Schultheiss & P Bühlmann, 2023. "Ancestor regression in linear structural equation models," Biometrika, Biometrika Trust, vol. 110(4), pages 1117-1124.
    • Handle: RePEc:oup:biomet:v:110:y:2023:i:4:p:1117-1124.
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    References listed on IDEAS

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    1. Kalisch, Markus & Mächler, Martin & Colombo, Diego & Maathuis, Marloes H. & Bühlmann, Peter, 2012. "Causal Inference Using Graphical Models with the R Package pcalg," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 47(i11).
    2. J. Peters & P. Bühlmann, 2014. "Identifiability of Gaussian structural equation models with equal error variances," Biometrika, Biometrika Trust, vol. 101(1), pages 219-228.
    3. Peter Spirtes & Clark Glymour & Richard Scheines, 2001. "Causation, Prediction, and Search, 2nd Edition," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262194406, December.
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