## Task 1: Key Concepts about Evaluating the Effects of Covariates on Usual Intake of a Single Ubiquitously-Consumed Dietary Constituent

The goal of the analysis described in this task is to describe differences in usual intake by personal characteristics or other covariates. These inferences are made for the mean usual intake. To illustrate, we answer the question, ”Does the mean usual intake of calcium from food and beverages in women differ by race or ethnicity?”

Because of the measurement error that arises from the use of 24-hour recalls to measure usual intake, the model partitions between-person from within-person variability (see Module 18 "Model Usual Intake Using Dietary Recall Data", Task 1 for more details on measurement error). To accommodate the skewed consumption amounts, a Box-Cox transformation is used. In particular, the model used is a mixed effects model with a random person-specific effect and a built-in Box-Cox transformation to normality. The Box-Cox parameter (lambda) is estimated during the model fitting procedure at the same time the covariate effects are estimated so that the best transformation is chosen after adjusting for these effects. The person-specific effect is a latent variable that represents an individual’s tendency to eat a particular amount of a food. Balanced Repeated Replication (BRR) (Module 18 "Model Usual Intake Using Dietary Recall Data", Task 4) is used to calculate standard errors that account for the complex sampling design of NHANES.