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.

中文翻译：

---

具有多种原因和二元结果的因果关系的可识别性

总结 未观察到的混杂对观察性研究中的因果推断构成了重大威胁。最近，几位作者提出，这个问题可以在一个共同的混杂环境中克服，在这个环境中，多个治疗是独立的，给定一个共同的潜在混杂因素。已经表明，在治疗的线性高斯模型下，如果没有对结果模型的参数假设，因果效应是无法识别的。在本说明中，我们表明，如果我们假设具有非概率链接的结果的一般二元选择模型，则因果效应确实是可识别的。我们的识别方法基于治疗的高斯性与潜在混杂因素和潜在结果变量的非高斯性之间的不一致。我们进一步开发了一个基于似然性的两步估计程序。