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## Estimating Usual Intakes of Foods

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

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### 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 performing calculations related to regression calibration:
- Estimate each individual's linear predictors for Part I and Part II of the model.
- Predict each individualâ€™s usual intake given their reported intake(s). These predictions still have errors and therefore deviate from true individual usual intakes, but under the regression calibration assumptions, those errors do not affect the estimated relationship with health outcome. These predictions should only be used to remove bias from estimated diet-outcome associations; they should not be confused with true individual usual intakes - for example, they should never be used to classify individuals into categories (e.g., quintiles) of usual intake.