  In the United States the preferred method of obtaining dietary intake data is
the 24-hour dietary recall, yet the measure of most interest is usual or
long-term average daily intake, which is impossible to measure. Thus, usual
dietary intake is assessed with considerable measurement error. Also, diet
represents numerous foods, nutrients and other components, each of which have
distinctive attributes. Sometimes, it is useful to examine intake of these
components separately, but increasingly nutritionists are interested in
exploring them collectively to capture overall dietary patterns. Consumption of
these components varies widely: some are consumed daily by almost everyone on
every day, while others are episodically consumed so that 24-hour recall data
are zero-inflated. In addition, they are often correlated with each other.
Finally, it is often preferable to analyze the amount of a dietary component
relative to the amount of energy (calories) in a diet because dietary
recommendations often vary with energy level. The quest to understand overall
dietary patterns of usual intake has to this point reached a standstill. There
are no statistical methods or models available to model such complex
multivariate data with its measurement error and zero inflation. This paper
proposes the first such model, and it proposes the first workable solution to
fit such a model. After describing the model, we use survey-weighted MCMC
computations to fit the model, with uncertainty estimation coming from balanced
repeated replication.
