## Usual Dietary Intakes: Details of the Method

### Estimating Usual Intakes of Foods

If estimating usual intakes of foods (or any dietary component not consumed daily), follow these steps:

#### Step 1

**Fit a two-part statistical model with correlated person-specific effects**

*Usual Intake = Probability x Amount*

- Part I: Estimates the probability of consuming a food using logistic regression with a person-specific random effect (multiple or no covariates may be used).
- Part II: Specifies the consumption-day
*amount*of a food using the 24HR data on a transformed scale (multiple or no covariates may be used). - Part I and Part II are linked by:
- allowing the two person-specific effects to be correlated, and
- including the same covariates in both parts of the model.

Estimated Model Parameters

#### Step 2

**Estimate final products depending on application of interest**

- If evaluating covariate effects:
- Test significance of model parameters associated with the covariates of interest for both parts of the model.

- If estimating the distribution of usual intake:
- Estimate each individual's linear predictors for Part I and Part II of the model.
- Generate random effects using 100 pseudo-persons for each individual.
- Add random effects to the linear predictors and back-transform the amount estimate to original scale.
- Estimate mean, standard deviation, and percentiles empirically.

- If estimating individual intake:
- Estimate each individual's linear predictors for Part I and Part II of the model.
- Evaluate a ratio of integrals, integrating over the person specific effects, using adaptive Gaussian quadrature to obtain the final estimate.

### Estimating Usual Intakes of Nutrients

If estimating usual intakes of nutrients (or any dietary component consumed daily), the steps are simpler because there is no need to model probability. Therefore, a two-part model is not needed in Step 1.

#### Step 1

**Fit a statistical model with person-specific effects**

- Specify the consumption-day
*amount*of a nutrient using the 24HR data on a transformed scale (multiple or no covariates may be used).

Estimated Model Parameters

#### Step 2

**Estimate final products depending on application of interest**

- If evaluating covariate effects:
- Test significance of model parameters associated with the covariates of interest.

- If estimating the distribution of usual intake:
- Estimate each individual's linear predictor.
- Generate random effect using 100 pseudo-persons for each individual.
- Add random effect to the linear predictor and back-transform the amount estimate to original scale.
- Estimate mean, standard deviation, and percentiles empirically.

- If estimating individual intake:
- Estimate each individual's linear predictor.
- Evaluate a ratio of integrals, integrating over the person specific effect, using adaptive Gaussian quadrature to obtain the final estimate.