Pattern graphs: A graphical approach to nonmonotone missing data

We introduce the concept of pattern graphs–directed acyclic graphs representing how response patterns are associated. A graph represents an identifying restriction that is nonparametrically identified/saturated and often a missing not at random restriction. selection model mixture formulations using show they equivalent. leads to inverse probability weighting estimator as well imputation-based estimator. also study semiparametric efficiency theory derive multiply-robust graphs.