The key problems in missing data models involve the identifiability of two distributions: the target law and the full law. The target law refers to the joint distribution of the data variables, while the full law refers to the joint distribution of both the data variables and the response indicators. It has not been clearly stated how identifiability of the target law and the full law relate to multiple imputation. We show that imputations can be drawn from the correct conditional distributions if only if the full law is identifiable. This result means that direct application of multiple imputation may not be the method of choice in cases where the target law is identifiable but the full law is not. In such cases, alternative imputation approaches sometimes enable estimation of the target law. For this purpose, we introduce decomposable multiple imputation.

翻译：缺失数据模型中的关键问题涉及两个分布的可识别性：目标律与全律。目标律指数据变量的联合分布，而全律指数据变量与响应指标的联合分布。目标律与全律的可识别性如何与多重插补相关联，此前尚未得到明确阐述。我们证明：当且仅当全律可识别时，才能从正确的条件分布中抽取插补值。这一结果表明，在目标律可识别而全律不可识别的情形下，直接应用多重插补可能并非最优选择。在此类情形中，替代性插补方法有时能够实现对目标律的估计。为此，我们提出了可分解多重插补方法。