Principal stratification is a general framework for studying causal mechanisms involving post-treatment variables. When estimating principal causal effects, the principal ignorability assumption is commonly invoked, which we study in detail in this manuscript. Our first key contribution is studying a commonly used strategy of using parametric models to jointly model the outcome and principal strata without requiring the principal ignorability assumption. We show that even if the joint distribution of principal strata is known, this strategy necessarily leads to only partial identification of causal effects, even under very simple and correctly specified outcome models. While principal ignorability can lead to point identification in this setting, we discuss alternative, weaker assumptions and show how they lead to more informative partial identification regions. An additional contribution is that we provide theoretical support to strategies used in the literature for identifying association parameters that govern the joint distribution of principal strata. We prove that this is possible, but only if the principal ignorability assumption is violated. Additionally, due to partial identifiability of causal effects even when these association parameters are known, we show that these association parameters are only identifiable under strong parametric constraints. Lastly, we extend these results to more flexible semiparametric and nonparametric Bayesian models.

翻译：主分层是研究涉及处理后变量的因果机制的一般框架。在估计主因果效应时，通常需要主可忽略性假设，本文对此进行了详细研究。我们的第一个关键贡献是研究了一种常用策略：在不要求主可忽略性假设的情况下，使用参数模型联合建模结果变量和主层。我们证明，即使主层的联合分布已知，该策略也必然导致因果效应只能被部分识别，即使在非常简单且正确设定的结果模型下也是如此。虽然主可忽略性在此情境下可导致点识别，但我们讨论了替代性的、更弱的假设，并展示了它们如何导致信息量更大的部分识别区域。另一项贡献是，我们为文献中用于识别主导主层联合分布的关联参数的策略提供了理论支持。我们证明这是可能的，但仅当主可忽略性假设被违反时才成立。此外，由于即使在这些关联参数已知的情况下因果效应也只能被部分识别，我们表明这些关联参数仅在强参数约束下才可识别。最后，我们将这些结果扩展到更灵活的半参数和非参数贝叶斯模型。