A hierarchical Bayesian mixture model for repeated dietary records

Many dietary consumption variables show strong positive skewness or large proportions of zeros. Attempts to normalize such data using transformations such as powers and logarithms can be unsuccessful: this results in poor estimates of their probability distributions, and hence of the proportions of the population whose consumption is beyond recommended limits. As an alternative to such transformations, the use of finite mixtures of standard distributions offers flexible modeling of data having skewed or multi-modal distributions, such as data on dietary consumption. In many dietary studies, individuals are asked to report their consumptions on several days. The use of finite-mixture models for such repeated data requires generalization to take account of the resulting hierarchical structure in the data. We first consider how finite mixture models might be extended to data with repeated records, and then apply a Bayesian version of one such extension to data on the consumption of retinol (Vitamin A) by British adults over 7 consecutive days. We also illustrate how factors such as sex and age may be included in the model. The mixture-model approach is found to provide better estimates than alternative methods of the probability distributions of daily consumptions and of maximum consumption over 7 days.