  It is often of interest to perform clustering on longitudinal data, yet it is
difficult to formulate an intuitive model for which estimation is
computationally feasible. We propose a model-based clustering method for
clustering objects that are observed over time. The proposed model can be
viewed as an extension of the normal mixture model for clustering to
longitudinal data. While existing models only account for clustering effects,
we propose modeling the distribution of the observed values of each object as a
blending of a cluster effect and an individual effect, hence also giving an
estimate of how much the behavior of an object is determined by the cluster to
which it belongs. Further, it is important to detect how explanatory variables
affect the clustering. An advantage of our method is that it can handle
multiple explanatory variables of any type through a linear modeling of the
cluster transition probabilities. We implement the generalized EM algorithm
using several recursive relationships to greatly decrease the computational
cost. The accuracy of our estimation method is illustrated in a simulation
study, and U.S. Congressional data is analyzed.
