A fresh look at ignorability for likelihood inference

When data are incomplete, a random vector Y for the data process together with a binary random vector R for the process that causes missing data, are modelled jointly. We review conditions under which R can be ignored for drawing likelihood inferences about the distribution for Y. The standard approach of Rubin (1976) and Seaman et. al. (2013) Statist. Sci., 28:2 pp. 257--268 emulates complete-data methods exactly, and directs an investigator to choose a full model in which missing at random (MAR) and distinct of parameters holds if the goal is not to use a full model. Another interpretation of ignorability lurking in the literature considers ignorable likelihood estimation independently of any model for the conditional distribution R given Y. We discuss shortcomings of the standard approach, and argue that the alternative gives the `right' conditions for ignorability because it treats the problem on its merits, rather than emulating methodology developed for when the investigator is in possession of all of the data.