For a multiple regression analysis of nutrient intakes, the dependent variable is usually the observed individual nutrient intake. In the context of the FSP, the dependent variable would be observed nutrient intakes while predictor variables might include—in addition to food stamp participation—household income, family size, education, region of residence, and other important characteristics influencing nutrient intake. This type of multiple regression analysis typically produces a set of regression coefficients and their standard deviations. On the basis of the estimated coefficient for FSP participation, regression-adjusted differences in mean nutrient intake can be calculated between FSP participants and low-income nonparticipants, controlling for other differences between participants and nonparticipants that may also influence nutrient intake. In addition, just as the mean of observed nutrient intake is an unbiased estimate of mean usual nutrient intake, these regression-adjusted differences in mean observed intakes are unbiased estimates of regression-adjusted mean usual nutrient intake.
Multiple regression analysis of nutrient intakes has been used to assess the relationship between program participation and nutrient intakes in FSP eligible individuals (Gordon et al., 1995; Oliveira and Gunderson, 2000; Rose et al., 1998). Specifically, the regression-adjusted differences in mean intake between program participants and a comparison group of nonparticipants were interpreted, with certain caveats, as the estimated effects of program participation. However, as noted previously, mean intakes cannot be used to assess nutrient adequacy. Similarly, differences in mean intakes between subgroups cannot be used to draw conclusions about the effects of program participation on nutrient adequacy. They can be used only to make inferences about differences in mean intakes between program participants and nonparticipants. The approach described below provides a method of estimating the effect of FSP participation on nutrient adequacy.
As discussed above, multiple regression analysis can be used to estimate differences in mean intakes between two subgroups such as FSP participants and eligible nonparticipants, while controlling for other factors that affect nutrient intake. A more difficult research question, however, is testing the difference between subgroups in the prevalence of apparent nutrient inadequacy, after controlling for