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.
翻译:最近,一些作者认为,在一种共同的混乱环境中,如果多种治疗是独立的,如果存在共同的潜在困惑者,那么这一问题是可以克服的。已经表明,根据一个直线高斯治疗模式,如果没有对结果模型的参数假设,因果效果是无法辨认的。在本文中,我们表明,如果我们假设结果结果的一般二进制选择模式与非概率联系,则因果关系确实可以确定。 我们的识别方法基于治疗和潜在混淆者之间的不一致,以及潜在结果变量的非库西性。我们进一步制定基于两步的可能性估算程序。