Model-based co-clustering for ordinal data

A model-based co-clustering algorithm for ordinal data is presented. This algorithm relies on the latent block model embedding a probability distribution specific to ordinal data (the so-called BOS or Binary Ordinal Search distribution). Model inference relies on a Stochastic EM algorithm coupled with a Gibbs sampler, and the ICL-BIC criterion is used for selecting the number of co-clusters (or blocks). The main advantage of this ordinal dedicated co-clustering model is its parsimony, the interpretability of the co-cluster parameters (mode, precision) and the possibility to take into account missing data. Numerical experiments on simulated data show the efficiency of the inference strategy, and real data analyses illustrate the interest of the proposed procedure.