The simple model above is called a measurement error model (Fuller, 1987), because it states that observed intakes measure usual intakes with error. Measurement error, in a statistical sense, denotes a (random) deviation from a variable of interest—in this case the usual intake. The error is modeled as a random variable with zero mean and with a variance that reflects the day-to-day variability in intakes.
The adjustment described by the NRC method is relatively straightforward to implement, once the magnitude of the day-to-day variation in intake has been determined for the group. After any necessary transformations to ensure normality, the difference between each person's intake and the mean intake of the group is multiplied by the ratio of day-to-day variation to the total variation, and then added back to the mean intake for the group. These adjusted intakes can then be transformed back to the original scale, as appropriate, and used for further analyses.
In the NRC method the variance of the measurement error was assumed to be constant across individuals. This means that the NRC method establishes that the day-to-day variability in intakes is constant across individuals. A more general version of this basic method developed at ISU by Nusser and colleagues (1996) does not require the measurement error variance to be constant across individuals.
The Iowa State University Method to Adjust Intake Distributions
In general, the statistical method developed at ISU (Nusser et al., 1996) elaborates on the NRC method and produces estimates of usual intake distributions with good statistical properties. Details about the procedure can be found elsewhere (Guenther et al., 1997; Nusser et al., 1996). The following example illustrates how its use can affect the conclusions drawn when a dietary survey is used to assess intakes for a group.
How large a sample size, and what proportion of replicate observations are needed for the ISU method of estimating usual nutrient intake distributions? An exact answer to this question is difficult to provide. Regarding actual sample size, the performance of the ISU method improves as sample size increases; small sample sizes of