The issue of control in multivariate systems, A contribution of structural modelling.

This paper builds upon Judea Pearl’s directed acyclic graphs approach to causality and the tradition of structural modelling in economics and social science. The paper re-examines the issue of control in complex systems with multiple causes and outcomes, in a specific perspective of structural modelling. It begins with three-variable saturated and unsaturated models, and then examines more complex systems including models with collider and latent confounder discussed by Pearl. In particular, focusing on the causes of an outcome, the paper proposes two simple rules for selecting the variables to be controlled for when studying the direct effect of a cause on an outcome of interest or the total effect when dealing with multiple causal paths. This paper presents a model building strategy that allows a statistical model to be considered as structural. The challenge for the model builder amounts to developing an explanation through a recursive decomposition of the joint distribution of the variables congruent with background knowledge and stable with respect to specified changes of the environment.