To control or not to control? A modeller’s dilemma

Michel Mouchart, Université Catholique de Louvain
Guillaume Wunsch, Université Catholique de Louvain
Federica Russo, University of Amsterdam

As the justification for inclusion or exclusion of control variables is very often limited or absent in many population studies, the paper examines the issue of control in complex systems with multiple causes and multiple outcomes. It builds upon the directed acyclic graphs approach to causality, on the one hand, and upon the tradition of structural/causal modelling in economics and social science, on the other hand. The paper begins with elementary three-variable saturated and unsaturated models, and then examines more complex systems, including models with collider and with latent confounder. The paper proposes two simple rules for selecting the variables to be controlled for when studying either the direct effect of a cause on an outcome or the total effect taking multiple causal paths into account. The challenge for the model builder in population science consists in developing structural models specifying the mechanism and sub-mechanisms - and their role-function – standing for the data generating process.