On identifiability in models for incomplete binary data

Abstract

In recent work by various authors, models for categorical response data subject to non-ignorable non-response have been considered. While the emphasis of those papers has been largely on the computational aspects of fitting those models, it has also been observed that such models present certain analytical difficulties. In particular, it can happen that the parameters of the model are not identifiable. In this note, the issue of identifiability is examined. A simple non-ignorable non-response model is considered and necessary and sufficient conditions for identifiability are given. An example exhibiting a type of non-identifiability not previously discussed is presented.