Nonignorable missing outcomes are common in real world datasets and often require strong parametric assumptions to achieve identification. These assumptions can be implausible or untestable, and so we may forgo them in favour of partially identified models that narrow the set of a priori possible values to an identification region. Here we propose a new nonparametric Bayes method that allows for the incorporation of multiple clinically relevant restrictions of the parameter space simultaneously. We focus on two common restrictions, instrumental variables and the direction of missing data bias, and investigate how these restrictions narrow the identification region for parameters of interest. Additionally, we propose a rejection sampling algorithm that allows us to quantify the evidence for these assumptions in the data. We compare our method to a standard Heckman selection model in both simulation studies and in an applied problem examining the effectiveness of cash-transfers for people experiencing homelessness.

翻译：非随机缺失结果在现实数据集中普遍存在，通常需要严格的参数假设才能实现识别。这些假设可能不合理或无法验证，因此我们可以放弃这些假设，转而采用部分识别模型，将先验可能值的集合缩小至识别区域。本文提出一种新的非参数贝叶斯方法，能够同时纳入参数空间的多种临床相关约束。我们重点关注两种常见约束：工具变量和缺失数据偏差方向，并研究这些约束如何缩小感兴趣参数的识别区域。此外，我们提出一种拒绝采样算法，可以量化数据中这些假设的证据。通过模拟研究以及一项针对无家可归者现金转移有效性的应用问题，我们将所提方法与标准赫克曼选择模型进行了比较。