This paper is dealing with estimation and model selection in the Latent Block Model (LBM) for categorical data. First, after providing sufficient conditions ensuring the identifiability of this model, it generalises estimation procedures and model selection criteria derived for binary data. Secondly, it develops Bayesian inference through Gibbs sampling. And, with a well calibrated non informative prior distribution, Bayesian estimation is proved to avoid the traps encountered by the LBM with the maximum likelihood methodology. Then model selection criteria are presented. In particular an exact expression of the ICL criterion requiring no asymptotic approximation is derived. Finally numerical experiments on both simulated and real data sets highlight the interest of the proposed estimation and model selection procedures.
