This thesis is centered on the evaluation of direct and indirect effects via mediation analysis. A researcher is usually interested in assessing to what extent an exposure variable affects an outcome. However, identifying the overall effect does not answer questions concerning how and why such an effect arises. Single mediation analysis decomposes the overall effect of the exposure on the outcome into an indirect and a direct effect. The former refers to the to the effect of the exposure on the outcome due to a third variable, the mediator, which is supposed to fall in the pathway. The latter effect is the effect of the exposure on the outcome after keeping the mediator to whatever value might be of interest. Specifically, we derived novel exact parametric decompositions of the total effect into direct and indirect effect for binary random variables, both in the counterfactual and path-analysis frameworks. In the single mediation context, we derive parametric expressions of the counterfactual entities and their relationships with the associational definitions coming from the path analysis context. We apply these methodological results on a dataset coming from a randomly allocated microcredit program in Bosnia-Herzegovina to evaluate the effect on client’s bankability. We re-analyse the data, in order to build a mediation scheme that allows a better understanding of the main effect of the study, by assuming business ownership as a possible mediator. We also implement a simulation study to compare the proposed estimator to several competing ones. When multiple mediators are involved, we found alternative definitions for the decomposition of the total effect. These new definitions are more appropriate for variables modelled as a recursive system of univariate logistic regressions. Thus, by making use of graphical models, the overall effect was defined as the sum of the direct, indirect effects and a residual term that is null under certain hypotheses. In general, these expressions are written such that one can maintain the link between effects and their corresponding coefficients in logistic regression models assumed in the system.
Counterfactual Graphical Models for Longitudinal Mediation Analysis With Unobserved Confounding
