Model selection procedure in multilevel cross-classified latent class models

The availability of proper selection criteria is of fundamental importance in the definition of latent class analysis models. When the data structure is multilevel the selection procedure must be applied to each level of the model. In the case of the multilevel cross-classified extension, we propose to apply a three step procedure that takes into account the mutually dependence between the two levels of the structure in the selection. The performances of the method are investigated through simulation studies in which different information criteria are considered. The definition of these criteria are based on approximations of the log-likelihood, which is intractable in such a cross-classified structure.