Statistical Modelling 10 (2010), 265290
Finite mixture models for clustering multilevel data with multiple
cluster structures
Giuliano Galimberti
Department of Statistics,
University of Bologna
Italy
Gabriele Soffritti
Department of Statistics,
University of Bologna,
via Belle Arti, 41
I40126 Bologna
Italy
eMail: gabriele.soffritti@unibo.it
Abstract:
Finite mixture models are useful tools for clustering two-way datasets
within a sound statistical framework which can assess some important
questions, such as how many clusters are there in the data. Models that
can also be used for clustering multilevel data have been proposed, with
the intent to produce clusterings of units at every level on the basis of
all the available variables, considering the hierarchical structure of the
dataset. This paper introduces a new class of mixture models for datasets
with two levels that makes it possible to discover a clustering of level 2
units and different clusterings of level 1 units corresponding to different
subsets of the variables (multiple cluster structures). This new class is
obtained by adapting a mixture model proposed to identify multiple cluster
structures in a data matrix to the multilevel situation. The usefulness of
the new method is shown using simulated data and a real example.
Keywords:
cluster analysis; cluster structure; mixture model; model selection;
multilevel data
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