Non-identifiability and testability of missing mechanisms in incomplete two-way contingency tables

Abstract

We showed that any missing mechanism is reproduced by EMAR or MNAR with equal fit for observed likelihood if there are non-negative solutions of maximum likelihood equations. This is a generalization of Molen-berghs et al. (2008) and Jeon et al. (2019). Nonetheless, as MCAR becomes a nested model of MNAR, a natural question is whether or not MNAR and MCAR are testable by using the well-known three statistics, LR (Likelihood ratio), Wald, and Score test statistics. Through simulation studies, we compared these three statistics. We investigated to what extent the boundary solution affect tesing MCAR against MNAR, which is the only testable pair of missing mechanisms based on observed likelihood. We showed that all three statistics are useful as long as the boundary proximity is far from 1.