  We discuss functional clustering procedures for nested designs, where
multiple curves are collected for each subject in the study. We start by
considering the application of standard functional clustering tools to this
problem, which leads to groupings based on the average profile for each
subject. After discussing some of the shortcomings of this approach, we present
a mixture model based on a generalization of the nested Dirichlet process that
clusters subjects based on the distribution of their curves. By using mixtures
of generalized Dirichlet processes, the model induces a much more flexible
prior on the partition structure than other popular model-based clustering
methods, allowing for different rates of introduction of new clusters as the
number of observations increases. The methods are illustrated using hormone
profiles from multiple menstrual cycles collected for women in the Early
Pregnancy Study.
