A simpler approach for mediation analysis for dichotomous mediators in logistic regression

Mediation is a hypothesized causal chain among three variables. Mediation analysis for continuous response variables is well developed in the literature, and it can be shown that the indirect effect is equal to the total effect minus the direct effect. However, mediation analysis for categorical responses is still not fully developed. The purpose of this article is to propose a simpler method of analysing the mediation effect among three variables when the dependent and mediator variables are both dichotomous. We propose using the latent variable technique which in turn will adjust for the necessary condition that indirect effect is equal to the total effect minus the direct effect. An intensive simulation study is conducted to compare the proposed method with other methods in the literature. Our theoretical derivation and simulation study show that the proposed approach is simpler to use and at least as good as other approaches provided in the literature. We illustrate our approach to test for the potential mediators on the relationship between depression and obesity among children and adolescents compared to the method in Winship and Mare using National children health survey data 2011–2012.