{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T02:04:37Z","timestamp":1775181877555,"version":"3.50.1"},"reference-count":36,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2025,6,26]],"date-time":"2025-06-26T00:00:00Z","timestamp":1750896000000},"content-version":"vor","delay-in-days":176,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,10,21]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>The field of causal discovery develops model selection methods to infer cause-effect relations among a set of random variables. For this purpose, different modelling assumptions have been proposed to render cause-effect relations identifiable. One prominent assumption is that the joint distribution of the observed variables follows a linear non-Gaussian structural equation model. In this paper, we develop novel goodness-of-fit tests that assess the validity of this assumption in the basic setting without latent confounders, as well as in extension to linear models that incorporate latent confounders. Our approach involves testing algebraic relations among second and higher moments that hold as a consequence of the linearity of the structural equations. Specifically, we show that the linearity implies rank constraints on matrices and tensors derived from moments. For a practical implementation of our tests, we consider a multiplier bootstrap method that uses incomplete $ U $-statistics to estimate subdeterminants, as well as asymptotic approximations to the null distribution of singular values. The methods are illustrated, in particular, for the T\u00fcbingen collection of benchmark datasets on cause-effect pairs.<\/jats:p>","DOI":"10.1093\/biomet\/asaf046","type":"journal-article","created":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T08:00:44Z","timestamp":1750838444000},"source":"Crossref","is-referenced-by-count":1,"title":["Goodness-of-fit tests for linear non-Gaussian structural equation models"],"prefix":"10.1093","volume":"112","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-8111-7021","authenticated-orcid":false,"given":"D","family":"Schkoda","sequence":"first","affiliation":[{"name":"TUM School of Computation, Information and Technology, Technical University of Munich , Boltzmannstra\u00dfe 3 , 85748 Garching bei M\u00fcnchen, \u00a0 daniela.schkoda@tum.de","place":["Germany"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5614-3025","authenticated-orcid":false,"given":"M","family":"Drton","sequence":"additional","affiliation":[{"name":"TUM School of Computation, Information and Technology, Technical University of Munich , Boltzmannstra\u00dfe 3 , 85748 Garching bei M\u00fcnchen,","place":["Germany"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2025,6,26]]},"reference":[{"key":"2026032607103008900_asaf046-B1","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.jeconom.2017.03.002","article-title":"A unifying theory of tests of rank","volume":"199","author":"Al-Sadoon","year":"2017","journal-title":"J. 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