the centering age value, while all individuals in the other group have ages that are either much lower or much higher than the centering value, then the adjustment above will lead to biased inferences about the effect of FSP participation on the prevalence of inadequacy.
Only one covariate has been included in this example. The approach above extends naturally to the case of more than one covariate, and the same centering principle would hold. If, for example, income was a second covariate and if the range of incomes in the sample went from $10,000 to $40,000, then the appropriate centering value for income would be the midpoint ($40,000 − $10,000)/2 + $10,000 = $25,000. In this case, one would be adjusting observed intakes to look like the intakes that would have been observed if all individuals had been 35 years of age and earned $25,000.
The adjustment above relies on the ability to accurately specify a regression model for intake. The model needs to contain all covariates thought to be associated with intake, particularly if they are also thought to be correlated with FSP participation. The estimated regression coefficients will have better statistical properties when intakes are approximately normally distributed.
The hypothetical example below (see also Table 7-3) illustrates the first four steps of this approach to assess whether FSP participation affects the mean intake of the group or the prevalence of inadequacy of nutrient A. In this example, it is suspected that age may influence intake of nutrient A and may also be associated with FSP participation. For each of a large group of individuals, 2 days of intake data are available, and the age of each individual is known. Some are FSP participants (FSP = 1) and others are not (FSP = 0). The overall group mean intake of nutrient A is 772 units. Table 7-3 shows data for six of these individuals.
Step 1. In the first step, a regression model is fitted to the intake data (column 4 of the table). The resulting prediction equation is:
Observed intake = −9 + 21.7 × age + 68.7 × FSP
Step 2. Next, standard predicted intakes are calculated for each individual for each day of intake. The regression coefficient associated with age generated from the intake data is used, but the coefficient for FSP participation and the intercept are not included. The