# Statistics: Mediation and moderation

### From MathWiki

For an interesting critique of traditional mediation analyses see Gelman, Andrew & Jennifer Hill (2007) *DataAnalysisUsingRegressionand Multilevel/HierarchicalModels* (*http://www.stat.columbia.edu/~gelman/arm/*), 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 (*http://content.apa.org/journals/psp/51/6/1173.pdf*) to the article, York connection required)

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

- Mediation (
*http://davidakenny.net/cm/mediate.htm*) - Moderation (
*http://davidakenny.net/cm/moderation.htm*)

David Kenny's home page (*http://davidakenny.net/kenny.htm*) also contains very interesting links to related topics.

- Other links:
- For perhaps the most up-to-date and comprehensive web site on mediation have a look at David MacKinnon's: http://www.public.asu.edu/~davidpm/ripl/mediate.htm
- Nice summary in Q and A form: http://www.public.asu.edu/~davidpm/ripl/q&a.htm
- Using the bootstrap to estimate mediation: PSYC_6140:_Mediation_R_script.