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Unobserved confounding presents a major threat to causal inference from observational studies. Recently, several authors suggest that this problem may 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 paper, 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.
Unobserved confounding is a major hurdle for causal inference from observational data. Confounders---the variables that affect both the causes and the outcome---induce spurious non-causal correlations between the two. Wang & Blei (2018) lower this hu
Although the exposure can be randomly assigned in studies of mediation effects, any form of direct intervention on the mediator is often infeasible. As a result, unmeasured mediator-outcome confounding can seldom be ruled out. We propose semiparametr
(This comment has been updated to respond to Wang and Bleis rejoinder [arXiv:1910.07320].) The premise of the deconfounder method proposed in Blessings of Multiple Causes by Wang and Blei [arXiv:1805.06826], namely that a variable that renders mult
Causal inference has been increasingly reliant on observational studies with rich covariate information. To build tractable causal models, including the propensity score models, it is imperative to first extract important features from high dimension
Instrumental variable methods are widely used for inferring the causal effect of an exposure on an outcome when the observed relationship is potentially affected by unmeasured confounders. Existing instrumental variable methods for nonlinear outcome