  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.
