Marginal log-linear models and mediation analysis

Abstract

After reviewing some not well known results about marginal log-linear models, the paper derives some new ones and shows how they might be relevant in mediation analysis when all variables are categorical. By focusing on the interactions between treatment and response, both marginally and jointly with respect to the mediating variables, a new relation between these parameters is derived. In addition, the paper describes a new class of models in which linear constraints may be imposed simultaneously on these two sets of interaction parameters. An application to education transmission from parents to their children is used as an illustration.