Missing values present challenges in the analysis of data across many areas of research. Handling incomplete data incorrectly can lead to bias, over-confident intervals, and inaccurate inferences. One principled method of handling incomplete data is multiple imputation. This article considers incomplete data in which values are missing for three or more qualitatively different reasons and applies a modified multiple imputation framework in the analysis of that data. Included are a proof of the methodology used for three-stage multiple imputation with its limiting distribution, an extension to more than three types of missing values, an extension to the ignorability assumption with proof, and simulations demonstrating that the estimator is unbiased and efficient under the ignorability assumption.

中文翻译：

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三个或更多阶段的多重插补

缺失值给许多研究领域的数据分析带来了挑战。不正确地处理不完整的数据会导致偏差、过度自信的区间和不准确的推论。处理不完整数据的一种原则方法是多重插补。本文考虑了由于三个或更多定性不同原因而缺失值的不完整数据，并在分析该数据时应用了修改后的多重插补框架。包括用于三阶段多重插补及其极限分布的方法的证明、对三种以上缺失值的扩展、对具有证明的可忽略性假设的扩展以及证明估计量在以下情况下无偏且有效的模拟可忽略性假设。