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It is often of interest to perform clustering on longitudinal data, yet it isdifficult to formulate an intuitive model for which estimation iscomputationally feasible. We propose a model-based clustering method forclustering objects that are observed over time. The proposed model can beviewed as an extension of the normal mixture model for clustering tolongitudinal data. While existing models only account for clustering effects,we propose modeling the distribution of the observed values of each object as ablending of a cluster effect and an individual effect, hence also giving anestimate of how much the behavior of an object is determined by the cluster towhich it belongs. Further, it is important to detect how explanatory variablesaffect the clustering. An advantage of our method is that it can handlemultiple explanatory variables of any type through a linear modeling of thecluster transition probabilities. We implement the generalized EM algorithmusing several recursive relationships to greatly decrease the computationalcost. The accuracy of our estimation method is illustrated in a simulationstudy, and U.S. Congressional data is analyzed.

Model-Based Longitudinal Clustering with Varying Cluster Assignments