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In the United States the preferred method of obtaining dietary intake data isthe 24-hour dietary recall, yet the measure of most interest is usual orlong-term average daily intake, which is impossible to measure. Thus, usualdietary intake is assessed with considerable measurement error. Also, dietrepresents numerous foods, nutrients and other components, each of which havedistinctive attributes. Sometimes, it is useful to examine intake of thesecomponents separately, but increasingly nutritionists are interested inexploring them collectively to capture overall dietary patterns. Consumption ofthese components varies widely: some are consumed daily by almost everyone onevery day, while others are episodically consumed so that 24-hour recall dataare zero-inflated. In addition, they are often correlated with each other.Finally, it is often preferable to analyze the amount of a dietary componentrelative to the amount of energy (calories) in a diet because dietaryrecommendations often vary with energy level. The quest to understand overalldietary patterns of usual intake has to this point reached a standstill. Thereare no statistical methods or models available to model such complexmultivariate data with its measurement error and zero inflation. This paperproposes the first such model, and it proposes the first workable solution tofit such a model. After describing the model, we use survey-weighted MCMCcomputations to fit the model, with uncertainty estimation coming from balancedrepeated replication.

A new multivariate measurement error model with zero-inflated dietary data, and its application to dietary assessment