  Missing data often result in undesirable bias and loss of efficiency. These
become substantial problems when the response mechanism is nonignorable, such
that the response model depends on unobserved variables. It is necessary to
estimate the joint distribution of unobserved variables and response indicators
to manage nonignorable nonresponse. However, model misspecification and
identification issues prevent robust estimates despite careful estimation of
the target joint distribution. In this study, we modelled the distribution of
the observed parts and derived sufficient conditions for model identifiability,
assuming a logistic regression model as the response mechanism and generalised
linear models as the main outcome model of interest. More importantly, the
derived sufficient conditions are testable with the observed data and do not
require any instrumental variables, which are often assumed to guarantee model
identifiability but cannot be practically determined beforehand. To analyse
missing data, we propose a new imputation method which incorporates verifiable
identifiability using only observed data. Furthermore, we present the
performance of the proposed estimators in numerical studies and apply the
proposed method to two sets of real data: exit polls for the 19th South Korean
election data and public data collected from the Korean Survey of Household
Finances and Living Conditions.
