Handling data with nonignorable missing responses is difficult because of the identifiability issue caused by nonignorable nonresponse. An effective approach in the literature is to impose a parametric model on the nonresponse propensity (while the conditional distribution of the response given covariates is totally unspecified), and to utilize a nonresponse instrument, a useful covariate vector that can be excluded from the propensity given the response and other covariates. However, how to find a nonresponse instrument from a given set of covariates is not well addressed. Further, one may also want to select a parametric propensity model from a set of candidate models. We propose a simultaneous propensity model and instrument selection criterion. In the presence of nonignorable nonresponse, the proposed method can consistently select the most compact correct parametric propensity model and instrument from a group of candidate models, if one of these candidate models is correct and an instrument exists. Simulation results show that our proposed method works quite well. A real data example is presented for illustration. Statistica Sinica: Newly accepted Paper (accepted author-version subject to English editing)

中文翻译：

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具有不可忽略不响应和工具变量的倾向模型选择

由于不可忽略的不响应引起的可识别性问题，处理具有不可忽略的缺失响应的数据是困难的。文献中的一种有效方法是对无响应倾向施加参数模型（而给定协变量的响应的条件分布完全未指定），并利用无响应工具，一个有用的协变量向量，可以从给定的倾向中排除响应和其他协变量。然而，如何从一组给定的协变量中找到无响应工具并没有得到很好的解决。此外，人们可能还想从一组候选模型中选择一个参数化倾向模型。我们提出了一个同时的倾向模型和工具选择标准。在出现不可忽视的无反应时，如果这些候选模型中的一个是正确的并且存在工具，则所提出的方法可以从一组候选模型中一致地选择最紧凑的正确参数倾向模型和工具。仿真结果表明，我们提出的方法效果很好。提供了一个真实的数据示例以供说明。Statistica Sinica：新接受的论文（接受的作者版本需英文编辑）