  Growth mixture models are an important tool for detecting group structure in
repeated measures data. Unlike traditional clustering methods, they explicitly
model the repeat measurements on observations, and the statistical framework
they are based on allows for model selection methods to be used to select the
number of clusters. However, the basic growth mixture model makes the
assumption that all of the measurements in the data have grouping
information/separate the clusters. In other clustering contexts, it has been
shown that including non-clustering variables in clustering procedures can lead
to poor estimation of the group structure both in terms of the number of
clusters and cluster membership/parameters. In this paper, we present an
extension of the growth mixture model that allows for incorporation of stepwise
variable selection based on the work done by Maugis et al. (2009) and Raftery
and Dean (2006). Results presented on a simulation study suggest that the
method performs well in correctly selecting the clustering variables and
improves on recovery of the cluster structure compared with the basic growth
mixture model. The paper also presents an application of the model to a
clinical study dataset and concludes with a discussion and suggestions for
directions of future work in this area.
