Mediation Analysis in Non-Linear Models with Interactions and an Application to the Relation between Childhood Environment and Fear in Adults

Speaker: Vanessa Didelez, Senior Lecturer in Statistics, Department of Mathematics, University of Bristol


Vanessa Didelez, Senior Lecturer in Statistics, Department of Mathematics, University of Bristol.


It is striking that in every day life as well as in applied research people readily and without much hesitation speak of direct and indirect effects (or more generally: effect mediation) in many different context, while a formal conceptualisation, criteria for identification and estimation of such effects outside of linear models seem surprisingly complicated.

I will discuss a number of issues motivated by some sociological data addressing the effect of childhood environment on fear of violence in adults; the data contain only categorical variables, some of which are ordinal, so that linear additive models are not appropriate and instead an approach based on graphical loglinear modelling is employed. Potential mediating factors are adult living environment and especially actual exposure to violence.

In the general non-linear case, if we want a notion of mediated effects that allows us to say that the total effect is the sum of direct and indirect effects then we have to use what is known as the “natural/pure (in)direct” effect  (Robins and Greenland (1996) and Pearl (2001)). This is based on a nested counterfactual formulation, and it is debatable whether this kind of effect is ever identifiable in any practical situation.

In this presentation I will follow the interpretation of Robins and  Richardson (2011), who show that under an augmented version of a directed acyclic graph model, such a counterfactual quantity can be seen as a manipulable parameter. I will illustrate what this means with a number of small examples and relate it to the design of experiments.

The idea of augmentation can further be used to fit the model and obtain the desired effects along separated pathways. Lange et al. (2012) have suggested this in the context of marginal structural models, while we here follow an approach that is comparable to G-computation.

This is joint work with Svend Kreiner (Biostatistics, Copenhagen).


  • Lange, Vansteelandt, Bekaert (2012).  A simple unified approach for estimating natural direct and indirect effects. To appear in AJE.
  • Pearl (2001). Direct and Indirect Effects. Proceedings of the Seventeenth Conference Annual Conference on Uncertainty in Artificial Intelligence. Morgan Kaufmann, San Francisco, CA, pp. 411-420.
  • Robins and Greenland (1992). Identifiability and Exchangeability for Direct and Indirect Effects. Epidemiology , Vol. 3, No. 2, pp. 143-155.
  • Robins JM, Richardson, TS. (2011). Alternative graphical causal models and the identification of direct effects. In: Causality and Psychopathology: Finding the Determinants of Disorders and Their Cures. P. Shrout, Editor. Oxford University Press. 
Published Mar. 1, 2012 12:58 PM - Last modified May 25, 2012 2:12 PM