  Previous likelihood-based linear modeling of nutritional data has been
limited by the availability of software that allows flexible error structures
in the data. We demonstrate the use of a Bayesian modeling approach to the
analysis of such data. Our goal is to model the relationship between the energy
intake derived from Food Frequency Questionnaires (FFQs) and the energy
expenditure estimated from the doubly labeled water method. We consider models
with different distributions for the FFQ energy intake. The models include
previously identified covariates describing social desirability, education and
their possible interaction that are felt to impact the reported FFQ. The models
also include random effects to account for subject specific random variation
(frailty) and also to account for the complex patterns of measurement error
inherent in these data. Issues arising within the work relate both to the
selection of relevant linear and non-linear models, the use of random effects,
and the relevance of goodness-of-fit criteria such as DIC and PPL in assessing
the most appropriate model.
