Identifiability of causal effects with multiple causes and a binary outcome. (12th March 2021)

• Record Type: Journal Article
• Authors: Kong, Dehan; Yang, Shu; Wang, Linbo
• Is Part Of: Biometrika. Volume 109:Number 1(2022)
• Page Start: 265
• Page End: 272
• Publication Date: 2021-03-12
• Subjects: Binary choice model -- Latent ignorability -- Unmeasured confounding; Biometry -- Periodicals; 570.1519505
• DOI: 10.1093/biomet/asab016
• Languages: English
• ISSNs: 0006-3444

Abstract

Summary: 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.