Multivariate Markov Chain Monte Carlo (MCMC) Method

For more information, read an Overview of the Methods & Calculations.

The steps of the multivariate Markov Chain Monte Carlo (MCMC) method are:

1. Separating. Each HEI dietary constituent must be treated separately. Unlike other methods, dietary constituents are not summed and must be separated for statistical modeling.

   For the HEI-2015, the components and associated dietary constituents are noted below:

   HEI-2015 Components and Associated Dietary Constituents for MCMC Method

   HEI Component	MCMC Variables	Typea	Units	Dietary Constituents
   From FPED (or other food-based database)
   Total Fruits	Whole Fruit	Episodic	cup eq.	Citrus, Melons, Berries + Other Intact Fruits
   	Fruit Juice	Episodic	cup eq.	Fruit Juice
   Whole Fruits	Whole Fruit	Episodic	cup eq.	Citrus, Melons, Berries + Other Intact Fruits
   Total Vegetables	Non-Dark Green Vegetables	Daily	cup eq.	Total Vegetables – Dark Green Vegetablesb
   	Dark Green Vegetables	Episodic	cup eq.	Dark Green Vegetables
   	Legumes (Beans and Peas)	Episodic	cup eq.	Legumes (Beans and Peas)
   Greens and Beans	Dark Green Vegetables	Episodic	cup eq.	Dark Green Vegetables
   	Legumes (Beans and Peas)	Episodic	cup eq.	Legumes (Beans and Peas)
   Whole Grains	Whole Grains	Episodic	oz. eq.	Whole Grains
   Refined Grains	Refined Grains	Daily	oz. eq.	Refined Grains
   Dairy	Dairy	Daily	cup eq.	Total Dairy
   Total Protein Foods	Meat, Poultry and Eggsb	Daily	oz. eq.	Total Meat, Poultry (including organ meats and cured meats) + Eggs
   	Seafood, Soy, and Nuts and Seeds	Episodic	oz. eq.	Seafood (high in n-3) + Seafood (low in n-3) + Soy + Nuts and Seeds
   	Legumes (Beans and Peas)	Episodic	oz. eq.	Legumes (Beans and Peas)
   Seafood and Plant Proteins	Seafood, Soy, and Nuts and Seeds	Episodic	oz. eq.	Seafood (high in n-3) + Seafood (low in n-3) + Soy + Nuts and Seeds
   	Legumes (Beans and Peas)	Episodic	oz. eq.	Legumes (Beans and Peas)
   Added Sugars	Added Sugars	Daily	tsp. eq.*	Added Sugars
   From FNDDS (or other nutrient database)
   Fatty Acids	Fatty Acids	Daily	g	Total Monounsaturated Fatty Acids + Total Polyunsaturated Fatty Acids
   Saturated Fats	Saturated Fats	Daily	g*	Total Saturated Fatty Acids
   Sodium	Sodium	Daily	mg	Sodium
   -----	Energy	Daily	kcal	Total Energy

   cup eq.=cup equivalents; oz. eq.=ounce equivalents; tsp. eq.= teaspoon equivalents; tsp. eq*.=added sugars are calculated in teaspoon equivalents but converted to energy in the scoring process; g=grams; g*= fatty acids are calculated in grams but converted to energy in the scoring process; mg=milligrams

   ^a General guidance on daily vs. episodic. Should be examined for each individual dataset.

   ^b Should be rounded to 2 decimal places and set to 0.00 if value is negative.

2. Modeling. Using a model that: a) transforms data to approximate normality, b) separates within-person from between-person variability, c) models the probability of consumption separately from the consumption day amount for episodically consumed foods, d) allows for correlation among the probability of consumption, the consumption-day amount, and energy among all dietary constituents; usual intakes for each dietary constituent are predicted.

3. Deriving Sums. After usual intake is predicted the constituents are combined to create the variables corresponding to the HEI components.

4. Constructing Ratios. The appropriate ratios are constructed. Usually these are the ratios of the dietary constituents to 1000 kcal of energy, with the exception of fatty acids, which use the ratio of the sum of monounsaturated and polyunsaturated fatty acids to saturated fatty acids. (Also, note two components are expressed on a percent of calories basis. Therefore, grams of saturated fat should be multiplied by 9 to convert g to kcal, and added sugars should be multiplied by 16 to convert teaspoons to kcal, prior to dividing by total energy.) Step 5 and beyond are different depending on purpose; see two options below.

For Describing Dietary Intakes: Other methods are under development by NCI Biometry Research Group to examine the association between diet and another variable. For more information, see their resources on measurement error.

5. Estimating. Generate “pseudo-individuals” from the parameters estimated from the model fit in Step 1.

6. Scoring. For each of the pseudo-individuals, score the ratios according to the scoring standards for each component. The component scores are summed to calculate the total score.

7. Calculating Means. Compute means and percentiles for the population of pseudo-individuals.