Missing data may be disastrous for the identifiability of causal and statistical estimands. In graphical missing data models, colluders are dependence structures that have a special importance for identification considerations. It has been shown that the presence of a colluder makes the full law, i.e., the joint distribution of variables and response indicators, non-parametrically non-identifiable. However, with additional mild assumptions regarding the variables involved with the colluder structure, identifiability is regained. We present a necessary and sufficient condition for the identification of the full law in the presence of a colluder structure with arbitrary categorical variables.

翻译：缺失数据可能对因果和统计估计量的可识别性造成灾难性影响。在图形化缺失数据模型中，共谋者是一种依赖结构，对识别问题具有特殊重要性。已有研究表明，共谋者的存在会导致全分布律（即变量与响应指标的联合分布）无法通过非参数方法识别。然而，通过对共谋结构所涉及的变量附加温和假设，可重新获得可识别性。本文提出了在任意分类变量构成的共谋结构存在时，全分布律可识别的充分必要条件。