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We propose a parsimonious extension of the classical latent class model tocluster categorical data by relaxing the class conditional independenceassumption. Under this new mixture model, named Conditional Modes Model,variables are grouped into conditionally independent blocks. The correspondingblock distribution is a parsimonious multinomial distribution where the fewfree parameters correspond to the most likely modality crossings, while theremaining probability mass is uniformly spread over the other modalitycrossings. Thus, the proposed model allows to bring out the intra-classdependency between variables and to summarize each class by a fewcharacteristic modality crossings. The model selection is performed via aMetropolis-within-Gibbs sampler to overcome the computational intractability ofthe block structure search. As this approach involves the computation of theintegrated complete-data likelihood, we propose a new method (exact for thecontinuous parameters and approximated for the discrete ones) which avoids thebiases of the \textsc{bic} criterion pointed out by our experiments. Finally,the parameters are only estimated for the best model via an \textsc{em}algorithm. The characteristics of the new model are illustrated on simulateddata and on two biological data sets. These results strengthen the idea thatthis simple model allows to reduce biases involved by the conditionalindependence assumption and gives meaningful parameters. Both applications wereperformed with the R package \texttt{CoModes}

Finite mixture model of conditional dependencies modes to cluster categorical data