  The National Birth Defects Prevention Study (NBDPS) is a case-control study
of birth defects conducted across 10 U.S. states. Researchers are interested in
characterizing the etiologic role of maternal diet, collected using a food
frequency questionnaire. Because diet is multi-dimensional, dimension reduction
methods such as cluster analysis are often used to summarize dietary patterns.
In a large, heterogeneous population, traditional clustering methods, such as
latent class analysis, used to estimate dietary patterns can produce a large
number of clusters due to a variety of factors, including study size and
regional diversity. These factors result in a loss of interpretability of
patterns that may differ due to minor consumption changes.
  Based on adaptation of the local partition process, we propose a new method,
Robust Profile Clustering, to handle these data complexities. Here,
participants may be clustered at two levels: (1) globally, where women are
assigned to an overall population-level cluster via an overfitted finite
mixture model, and (2) locally, where regional variations in diet are
accommodated via a beta-Bernoulli process dependent on subpopulation
differences. We use our method to analyze the NBDPS data, deriving
pre-pregnancy dietary patterns for women in the NBDPS while accounting for
regional variability.
