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Missing data can be informative. Ignoring this information can lead tomisleading conclusions when the data model does not allow information to beextracted from the missing data. We propose a co-clustering model, based on theLatent Block Model, that aims to take advantage of this nonignorablenonresponses, also known as Missing Not At Random data (MNAR). A variationalexpectation-maximization algorithm is derived to perform inference and a modelselection criterion is presented. We assess the proposed approach on asimulation study, before using our model on the voting records from the lowerhouse of the French Parliament, where our analysis brings out relevant groupsof MPs and texts, together with a sensible interpretation of the behavior ofnon-voters.

Learning from missing data with the Latent Block Model