Full Law Identification under Missing Data in the Categorical Colluder Model

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.