When factorial modeling is used to estimate the distribution of requirements from the distributions of the individual components of requirement (e.g., losses, accretion), it is necessary to add the individual distributions. For normal component distributions, this is straightforward since the resultant distribution is also normal, with a mean that is the sum of the component means and a variance (the square of the SD) that is the sum of the individual variances. The ninety-seventh and one-half percentile is then estimated as the mean value plus two SDs.
If the requirement of a nutrient is not normally distributed but can be transformed to normality, its EAR and RDA can be estimated by transforming the data, calculating a fiftieth and a ninety-seventh and one-half percentile, and transforming these percentiles back into the original units. In this case, the difference between the EAR and the RDA cannot be used to obtain an estimate of the CV because skewing is usually present.
If normality cannot be assumed for all of the components of requirement, then Monte Carlo simulation is used for the summation of the components. This approach involves simulation of a large population of individuals (e.g., 100,000) each with his or her own requirement for a particular nutrient. To accomplish this, the component parts of nutrient needs (the factorial components) are treated as coming from independent random distributions.
For example, for basal losses of a nutrient, a distribution of expected losses can be generated. For each individual in the simulated population, a randomly selected basal loss value was drawn from that distribution of nutrient losses. This is done for each component of nutrient need and then these components are summed for each individual yielding the simulated nutrient needs. The total requirement is then calculated for each individual and the median and the ninety-seventh and one-half percentile calculated directly.
Information about the distribution of values for the requirement components is modeled on the basis of known physiology. Monte Carlo approaches may be used in the simulation of the distribution of components; or, where large data sets exist for similar populations (such as growth rates in infants), estimates of relative variability may be transferred to the component in the simulated population (Gentle, 1998). At each step, the goal is to achieve distribution values for the component that reflect not only known physiology or known direct observations, but also values that can be transformed