In this paper, we analyze a specific class of missing not at random (MNAR) assumptions called tree graphs, extending upon the work of pattern graphs. We build off previous work by introducing the idea of a conjugate odds family in which certain parametric models on the selection odds can preserve the data distribution family across all missing data patterns. Under a conjugate odds family and a tree graph assumption, we are able to model the full data distribution elegantly in the sense that for the observed data, we obtain a model that is conjugate from the complete-data, and for the missing entries, we create a simple imputation model. In addition, we investigate the problem of graph selection, sensitivity analysis, and statistical inference. Using both simulations and real data, we illustrate the applicability of our method.

翻译：本文分析了一类特定的非随机缺失（MNAR）假设，称为树图，该假设扩展了模式图的研究框架。我们在前人研究基础上引入了共轭概率族的概念，在该族中，选择概率的特定参数化模型能够保持数据分布族在所有缺失数据模式中的一致性。在共轭概率族与树图假设下，我们能够优雅地建模完整数据分布：对于观测数据，我们获得了一个与完整数据共轭的模型；对于缺失条目，我们构建了简单的插补模型。此外，我们研究了图选择、敏感性分析和统计推断问题。通过模拟实验与真实数据，我们验证了该方法的适用性。