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Title: Extending latent class models for dealing with multilevel cross-classified data structures Authors:  Silvia Columbu - University of Cagliari (Italy) [presenting]
Nicola Piras - University of Cagliari (Italy)
Jeroen Vermunt - Tilburg University (Netherlands)
Abstract: Latent class models, and mixture models in general, are a well-established statistical approach for clustering. When the data have different levels of units, the mixture model must be formulated in order to accommodate the nesting of the data. One possibility is to extend the model by considering separate mixtures for each level of the structure. Such an extension considers a clustering of lower-level units by also allowing a clustering of higher-levels. The simplest multilevel structure is that of observations hierarchically nested within higher-level units; however, it is also interesting the situation in which the same unit belongs simultaneously to two or more groups, i.e. units are cross-classified. A version of finite mixtures is presented that handles the latter situation, with mixture components for first-level units, and mixture components for the multiple higher-levels. Maximum likelihood estimation through standard EM algorithms is not feasible; therefore, it is proposed the use of a stochastic version which includes a Gibbs sampler in the implementation. Numerical experiments with simulated data of different nature will be presented in order to show the performances of the estimation procedure and the interest in the approach for data clustering.