Identification Problem for The Analysis of Binary Data with Non-ignorable Missing

TL;DR

This paper introduces a new necessary and sufficient condition to determine the identifiability of models analyzing binary data with non-ignorable missingness, addressing a key challenge in statistical inference.

Contribution

It provides a simple method to verify model identifiability in binary data with non-ignorable missingness, which was previously difficult to assess.

Findings

Established a new condition for model identifiability

Enabled easy verification of model identifiability

Addressed a gap in binary data missingness analysis

Abstract

When a missing-data mechanism is NMAR or non-ignorable, missingness is itself vital information and it must be taken into the likelihood, which, however, needs to introduce additional parameters to be estimated. The incompleteness of the data and introduction of more parameters can cause the identification problem. When a response variable is binary, it becomes a more serious problem because of less information of bi- nary data, however, there are no methods to briefly verify whether a mode is identified or not. Therefore, we provide a new necessary and sufficient condition to easily check model identifiability when analyzing binary data with non-ignorable missing by condi- tional models. This condition can give us what condition is needed for a model to have identifiability as well as make easily check the identifiability of a model.