{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T02:24:03Z","timestamp":1790562243857,"version":"4.1.0"},"reference-count":28,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2021,3,12]],"date-time":"2021-03-12T00:00:00Z","timestamp":1615507200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,2,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>Unobserved confounding presents a major threat to causal inference in observational studies. Recently, several authors have suggested that this problem could be overcome in a shared confounding setting where multiple treatments are independent given a common latent confounder. It has been shown that under a linear Gaussian model for the treatments, the causal effect is not identifiable without parametric assumptions on the outcome model. In this note, we show that the causal effect is indeed identifiable if we assume a general binary choice model for the outcome with a non-probit link. Our identification approach is based on the incongruence between Gaussianity of the treatments and latent confounder and non-Gaussianity of a latent outcome variable. We further develop a two-step likelihood-based estimation procedure.<\/jats:p>","DOI":"10.1093\/biomet\/asab016","type":"journal-article","created":{"date-parts":[[2021,3,10]],"date-time":"2021-03-10T20:12:02Z","timestamp":1615407122000},"page":"265-272","source":"Crossref","is-referenced-by-count":13,"title":["Identifiability of causal effects with multiple causes and a binary outcome"],"prefix":"10.1093","volume":"109","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3480-4915","authenticated-orcid":false,"given":"Dehan","family":"Kong","sequence":"first","affiliation":[{"name":"Department of Statistical Sciences, University of Toronto, 700 University Avenue, Toronto, Ontario M5G 1X6, Canada kongdehan@utstat.toronto.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7703-707X","authenticated-orcid":false,"given":"Shu","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Statistical Sciences, University of Toronto, 700 University Avenue, Toronto, Ontario M5G 1X6, Canada syang24@ncsu.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Linbo","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Statistical Sciences, University of Toronto, 700 University Avenue, Toronto, Ontario M5G 1X6, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2021,3,12]]},"reference":[{"key":"2022022618083684700_B1","first-page":"111","article-title":"Statistical inference in factor analysis","volume-title":"Proc. 3rd Berkeley Sympos. 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