利用辅助边际分布通过热卡插补和序贯插补对调查中不可忽略缺失数据进行插补
Imputation of Nonignorable Missing Data in Surveys Using Auxiliary Margins Via Hot Deck and Sequential Imputation
AI总结：
本文针对调查数据中不可忽略的单元和项目无应答问题，提出两种对MD-AM框架的改进：用随机热卡插补替代联合模型设定，并用链式方程多重插补处理项目无应答，模拟和实证表明该方法比不利用辅助边际信息的模型估计更准确。
摘要：
调查数据收集经常受到单元无应答和项目无应答的困扰。为了减少对缺失机制强假设的依赖，统计学家可以利用已知的总体边际分布信息，例如来自人口普查或行政数据库的信息。一种实现这一目标的方法是带辅助边际的缺失数据（Missing Data with Auxiliary Margins，MD-AM）框架，该框架对单元无应答和项目无应答同时使用多重插补，使调查加权估计与已知边际分布一致。然而，该框架依赖于对调查数据和无应答指标联合分布的设定与估计，在包含大量混合类型变量的数据中，这在计算和实践上可能极具挑战性。我们提出对MD-AM框架的两项改进以简化插补任务。第一，不再为单元受访者数据设定联合模型，而是使用随机热卡插补，同时仍然利用已知的边际分布。第二，对于项目无应答造成的缺失数据，不再从联合模型隐含的条件分布中抽样，而是在单元无应答插补之前，对项目无应答采用链式方程多重插补（multiple imputation by chained equations）。通过使用不可忽略缺失机制的模拟研究，我们证明所提出的方法能够比不利用辅助信息的模型提供更准确的点估计和区间估计。我们使用美国当前人口调查（U.S. Current Population Survey）中选民投票率数据对该方法进行了说明。
英文摘要：
Survey data collection often is plagued by unit and item nonresponse. To reduce reliance on strong assumptions about the missingness mechanisms, statisticians can use information about population marginal distributions known, for example, from censuses or administrative databases. One approach that does so is the Missing Data with Auxiliary Margins, or MD-AM, framework, which uses multiple imputation for both unit and item nonresponse so that survey-weighted estimates accord with the known marginal distributions. However, this framework relies on specifying and estimating a joint distribution for the survey data and nonresponse indicators, which can be computationally and practically daunting in data with many variables of mixed types. We propose two adaptations to the MD-AM framework to simplify the imputation task. First, rather than specifying a joint model for unit respondents' data, we use random hot deck imputation while still leveraging the known marginal distributions. Second, instead of sampling from conditional distributions implied by the joint model for the missing data due to item nonresponse, we apply multiple imputation by chained equations for item nonresponse before imputation for unit nonresponse. Using simulation studies with nonignorable missingness mechanisms, we demonstrate that the proposed approach can provide more accurate point and interval estimates than models that do not leverage the auxiliary information. We illustrate the approach using data on voter turnout from the U.S. Current Population Survey.
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