  Missing data can be informative. Ignoring this information can lead to
misleading conclusions when the data model does not allow information to be
extracted from the missing data. We propose a co-clustering model, based on the
Latent Block Model, that aims to take advantage of this nonignorable
nonresponses, also known as Missing Not At Random data (MNAR). A variational
expectation-maximization algorithm is derived to perform inference and a model
selection criterion is presented. We assess the proposed approach on a
simulation study, before using our model on the voting records from the lower
house of the French Parliament, where our analysis brings out relevant groups
of MPs and texts, together with a sensible interpretation of the behavior of
non-voters.
