基于加权的缺失数据图模型中的识别与估计
Weighting-Based Identification and Estimation in Graphical Models of Missing Data
AI总结：
本文提出基于树的识别算法和递归逆概率加权方法，用于缺失数据图模型中的识别与估计，解决了选择偏差问题并提供了有效的估计方程。
摘要：
我们提出了一种构造性算法，用于识别缺失数据图模型中的完整数据分布。完整数据分布是无限制的，而缺失机制被假设根据一个条件有向无环图进行因子分解。我们的方法采用一种干预主义视角，将缺失性指标视为可以干预的变量。在这个设定中，对缺失性指标进行干预序列可能会诱导并传播选择偏差，因此即使倾向分数对可用干预是不变的，识别也可能失败。为了解决这一挑战，我们引入了一个基于树的识别算法，该算法明确跟踪选择偏差的产生和传播，并确定是否可以通过可接受的干预策略避免。所得到的树既提供了在给定缺失机制下的可识别性诊断，也提供了构造性表征。基于这些结果，我们开发了递归的逆概率加权程序，这些程序反映了识别算法的干预逻辑，从而为缺失机制和完整数据分布的功能性提供有效的估计方程。模拟研究和实际数据应用展示了所提出方法的实用性。一个配套的R包flexMissing实现了所有提出的过程。
英文摘要：
We propose a constructive algorithm for identifying complete data distributions in graphical models of missing data. The complete data distribution is unrestricted, while the missingness mechanism is assumed to factorize according to a conditional directed acyclic graph. Our approach follows an interventionist perspective in which missingness indicators are treated as variables that can be intervened on. A central challenge in this setting is that sequences of interventions on missingness indicators may induce and propagate selection bias, so that identification can fail even when a propensity score is invariant to available interventions. To address this challenge, we introduce a tree-based identification algorithm that explicitly tracks the creation and propagation of selection bias and determines whether it can be avoided through admissible intervention strategies. The resulting tree provides both a diagnostic and a constructive characterization of identifiability under a given missingness mechanism. Building on these results, we develop recursive inverse probability weighting procedures that mirror the intervention logic of the identification algorithm, yielding valid estimating equations for both the missingness mechanism and functionals of the complete data distribution. Simulation studies and a real-data application illustrate the practical performance of the proposed methods. An accompanying R package, flexMissing, implements all proposed procedures.
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