## Task 2: Evaluating the Effects of Covariates on Usual Intake of a Single Episodically-Consumed Dietary Constituent

When a dietary component is episodically consumed, as is the case for many food groups and some food groups, a two-part model is used to estimate: (1) the probability of the dietary component being consumed, and (2) the amount of the dietary component consumed on a consumption day. This task describes how to fit the two-part model with covariates and how to evaluate the effects of the covariates on usual intake consumption.

The first part of the model estimates the probability of consuming an episodically-consumed dietary constituent using logistic regression with a person-specific random effect. The second part of the model specifies the consumption-day amount using linear regression with a built in Box-Cox transformation, also with a person-specific random effect. Because of the measurement error that arises from the use of 24-hour recalls to measure usual intake, the amount model partitions between-person from within-person variability. The Box-Cox parameter (lambda) is estimated during the model fitting procedure at the same time the covariate effects are estimated. The person-specific effects are latent variables that represent the deviation of the individual’s probability of consumption and amount of intake from the population mean. Because these effects are specific to individuals, they vary only between individuals; therefore, they capture the between-person variation of usual intake in the population. The two parts of the model—probability and consumption-day amount—are linked by allowing the two person-specific effects to be correlated and by including common covariates (e.g., age, sex) in both parts of the model. Balanced Repeated Replication (BRR) (Module 18 "Model Usual Intake Using Dietary Recall Data", Task 4) is used to calculate standard errors.