Multiple imputation provides an effective way to handle missing data. When several possible models are under consideration for the data, multiple imputation is typically performed under a single-best model selected from the candidate models. This single-model selection approach ignores the uncertainty associated with the model selection and so leads to underestimation of the variance of multiple imputation estimator. In this article, we propose a new multiple imputation procedure incorporating model uncertainty in the final inference. The proposed method incorporates possible candidate models for the data into the imputation procedure using the idea of Bayesian model averaging. The proposed method is directly applicable to handling item nonresponse in survey sampling. Asymptotic properties of the proposed method are investigated. A limited simulation study confirms that our model averaging approach provides better estimation performance than the single-model selection approach.

中文翻译：

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考虑复杂抽样下多重插补中的模型不确定性

多重插补提供了一种处理缺失数据的有效方法。当考虑数据的多个可能模型时，通常在从候选模型中选择的单个最佳模型下执行多重插补。这种单模型选择方法忽略了与模型选择相关的不确定性，因此导致低估了多重插补估计量的方差。在本文中，我们提出了一种新的多重插补程序，将模型不确定性纳入最终推理。所提出的方法使用贝叶斯模型平均的思想将数据的可能候选模型合并到插补过程中。所提出的方法直接适用于处理抽样调查中的项目不答复。研究了所提出方法的渐近特性。