Monotone Missing Data: A Blessing and a Curse

Monotone missingness is commonly encountered in practice where a missing measurement compels another measurement to be missing. In graphical missing data models, monotonicity has implications for the identifiability of the full law, i.e., the joint distribution of actual variables and response indicators. In the general nonmonotone case, the full law is known to be nonparametrically identifiable if and only if neither colluders nor self-censoring edges are present in the graph. We show that monotonicity may enable the identification of the full law despite colluders and prevent the identification under mediated (pathwise) self-censoring. The results emphasize the importance of proper treatment of monotone missingness in the analysis of incomplete data.