Missing at Random in Graphical Models

The notion of missing at random (MAR) plays a central role in the theory underlying current methods for handling missing data. However the standard definition of MAR is difficult to interpret in practice. In this paper, we assume the missing data model is represented as a directed acyclic graph that not only encodes the dependencies among the variables but also explicitly portrays the causal mechanisms responsible for the missingness process. We introduce an intuitively appealing notion of MAR in such graphical models, and establish its relation with the standard MAR and a few versions of MAR used in the literature. We address the question of whether MAR is testable, given that data are corrupted by missingness, by proposing a general method for identifying testable implications imposed by the graphical structure on the observed data.