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In order to account for unobserved heterogeneity in composite structural
equation modeling (composite SEM), clustering techniques have been proposed
[1, 2, 3] differing on the type of optimization and whether the whole model rather
only the structural model is considered. In the latter case, this leads to the application
of the PLS algorithm to create a proxy for each construct as a linear combination
of the indicators in its associated block. Then, as in clusterwise approaches, the
clustering analysis aims to simultaneously partition the individuals into clusters and
optimise the structural model fitted to each of them. We present here the two main
clustering strategies (model-based vs. geometric-based) and their variants. The first
is based on the assumption of multivariate normal mixtures on endogenous variables.
The second is related to the optimisation of a criterion derived from the regression
equations of the structural model. Both are compared on the basis of Monte Carlo
simulated data sets.

PLS-SEM, composite models, model-based clustering