Statistics: Mediation and moderation

From MathWiki

For an interesting critique of traditional mediation analyses see Gelman, Andrew & Jennifer Hill (2007) DataAnalysisUsingRegressionand Multilevel/HierarchicalModels (, Section 9.8, pp 190 ff, "Intermediate Outcome and Causal Paths". They point out that if the mediator variable also selects different pre-treatment groups then the estimated direct effect of the treatment will also reflect pre-treatment differences conditional on the mediating variable. If it is really desired to test whether the mediating variable is causal then ones needs as careful an analysis as one needs for any causal question with forcibly observational data.

The expressions mediator variable and moderator variable refer to the potential role of variables in a regression model. An article that has had a wide influence in spreading these concepts is

  • Baron, R. M., & Kenny, D. A. (1986). "The moderator-mediator variable distinction in social psychological research: Conceptual, strategic and statistical considerations." Journal of Personality and Social Psychology, 51, 1173-1182. (link ( to the article, York connection required)

David Kenny has created some very interesting web pages on the topic:

  • Mediation (
  • Moderation (

David Kenny's home page ( also contains very interesting links to related topics.