A fresh look at ignorability for likelihood inference
arXiv:1811.05560
Abstract
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.
arXiv comment8 pages, no figures