  Functional concurrent, or varying-coefficient, regression models are commonly
used in biomedical and clinical settings to investigate how the relation
between an outcome and observed covariate varies as a function of another
covariate. In this work, we propose a Bayesian nonparametric approach to
investigate how clusters of these functional relations evolve over time. Our
model clusters individual functional trajectories within and across time
periods while flexibly accommodating the evolution of the partitions across
time periods with covariates. Motivated by mobile health data collected in a
novel, smartphone-based smoking cessation intervention study, we demonstrate
how our proposed method can simultaneously cluster functional trajectories,
accommodate temporal dependence, and provide insights into the transitions
between functional clusters over time.
