Title: Multilevel latent class models for cross-classified data
Authors: Silvia Columbu - University of Cagliari (Italy) [presenting]
Jeroen Vermunt - Tilburg University (Netherlands)
Abstract: Latent class and mixture models have been extended to deal with multilevel datasets, for example, when children are nested within schools. One very useful version is an approach in which one has latent classes (or mixture components) at different levels (thus for both schools and children). These models can be estimated by maximum likelihood using a special implementation of the EM algorithm. However, sometimes the nesting consists of multiple higher levels which are not hierarchically linked, but instead cross-classified, for example, when children are nested 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.