Direct and indirect effects in a logit model

In this presentation, I discuss a method by Erikson et al. (2005) for decomposing a total effect in a logit model into direct and indirect effects, and I propose a generalization of this method. Consider an example where social class has an indirect effect on attending college through academic performance in high school. The indirect effect is obtained by comparing the proportion of lower-class students that attend college with the counterfactual proportion of lower-class students if they had the distribution of performance of the higher-class students. This captures the association between class and attending college because of differences in performance, i.e., the indirect effect. The direct effect of class is obtained by comparing the proportion of higher-class students with the counterfactual proportion of lower-class students if they had the same distribution of performance as the higher-class students. This way, the variable performance is kept constant, and this results in the direct effect. If these comparisons are carried out in the form of log odds ratios, then the total effect will equal the sum of the direct and indirect effects. In its original form, this method assumes that the variable through which the indirect effect occurs is normally distributed. In this article, the method is generalized by allowing this variable to have any distribution, which has the added advantage of simplifying the method.