Multilevel cross-classified latent class models

We propose an extension of latent class models to deal with multilevel cross- classified data structures, where each observation is considered simultaneously nested within two groups, such as for instance, children within both schools and neighborhoods. We show how such a situation can be dealt with by having a separate set of mixture components for each of the crossed classifications. Unfortunately, given the intractability of the derived loglikelihood, the EM algorithm can no longer be used in the estimation process. We therefore propose an approximate estimation of this model using a stochastic version of the EM algorithm similar to Gibbs sampling.