Missing data: A unified taxonomy guided by conditional independence

Recent work attempts to clarify the not always well-understood difference between realised and everywhere definitions of missing at random (MAR) and missing completely at random. Another branch of the literature exploits always-observed covariates to give variable-based definitions of MAR and missing completely at random. We develop a unified taxonomy encompassing all approaches. In this taxonomy, the new concept of complementary MAR is introduced, and its relationship with the concept of data observed at random is discussed. All relationships among these definitions are analysed and represented graphically. Conditional independence, both at the random variable and at the event level, is the formal language we adopt to connect all these definitions. Both the univariate and the multivariate case are covered. Attention is paid to monotone missingnessandtotheconceptofsequentialMAR.Specifically, formonotonemissingness, weproposeasequentialMARdefinitionthatmightbe more appropriate than both everywhere and variable-based MAR to model dropout in certain contexts.