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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. We wereinterested in estimating the population distribution of the Healthy EatingIndex-2005 (HEI-2005), a multi-component dietary quality index involving ratiosof interrelated dietary components to energy, among children aged 2-8 in theUnited States, using a national survey and incorporating survey weights. Wedeveloped a highly nonlinear, multivariate zero-inflated data model withmeasurement error to address this question. Standard nonlinear mixed modelsoftware such as SAS NLMIXED cannot handle this problem. We found that taking aBayesian approach, and using MCMC, resolved the computational issues and doingso enabled us to provide a realistic distribution estimate for the HEI-2005total score. While our computation and thinking in solving this problem wasBayesian, we relied on the well-known close relationship between Bayesianposterior means and maximum likelihood, the latter not computationallyfeasible, and thus were able to develop standard errors using balanced repeatedreplication, a survey-sampling approach.

Estimating the Distribution of Dietary Consumption Patterns