Growth Mixture Modeling with Measurement Selection

Abstract

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.