[Mediation-information] treatment interactions in mediation

[dustin tingley]

Dear Chris-

Thanks for your email pasted below. You should join our listserv,
mediation-information at r-forge.wu-wien.ac.at

We have not done anything yet regarding the issue of interaction between
treatments, so I'm at least not much help there. You are correct that your
"fix" does not completely capture the interactive aspect of what you're
interested in. Regarding sensitivity analysis for non-binary treatments, no
this is not possible yet within our framework. One intuition for this is
that one can always increase the magnitude of the treatment contrast to get
less sensitive results if you use the same sensitivity setup. We've talked
about this a bit awhile ago, but our more recent work has dealt with other
issues. I cc my coauthors lest they have some additional ideas.

Dustin

****

I wonder if I could get your guidance about the larger issue of how to
think about mediation given the complex nature of our experimental
treatments.  In brief, the study is about talk and influence in
deliberating groups.  My co-authors and I have run an experiment in which
we've randomly assigned individuals to groups that deliberate and make
decisions.  The experimental treatments involve both the decision rule
followed by the group (unanimous or majority) and the gender composition of
the group (somewhere between 0 and 5 women).  In the mediation analysis,
we're only looking at mixed-gender groups.  Our hypothesis is that our two
treatments interact to affect both the gender gap in speaking behavior in
the group (how much more the average man speaks than the average woman) and
the gender gap in influence in the group (how much more likely men are than
women to be seen as the most influential member of the group).  There is a
statistically significant interaction between these treatments and both
speaking behavior and influence.  In terms of mediation, we think that the
gender gap in speaking behavior mediates the relationship between our
experimental conditions (including the interaction between the conditions)
and the gender gap in influence in the group.

The challenge, then, is that analyzing mediation is complex because we are
looking at multiple treatments and the interaction between them.  When it
comes to the sensitivity analysis, if I'm understanding the documentation
correctly, we're limited by the fact that the treatment is not just a dummy
variable, and we can't specify anything other than a 0-1 treatment.  The
key interaction term in our models (unanimous rule dummy x number of women
in the mixed-gender groups) runs between 0 and 4.  When I use the mediate
command, I can specify the interaction term to be the treatment and to
analyze the difference between 0 and 4 on that variable (in essence
pretending 0 is a control and 4 is a treatment), though that method (at
least as I understand it) won't fully capture the interactive nature of the
treatment effects because the main effects of these interacted terms aren't
included.

In essence, we can show that our treatments interact to affect both the
gender gap in speaking time and the gender gap in influence.  When the
gender gap in speaking time is included in models of the gender gap in
influence, the effect of our experimental treatments is greatly attenuated
and the effect of the gender gap in speaking behavior is large and
statistically significant.  This appears to be initial evidence of
mediation (following the basic Baron-Kenny approach).  But estimating ACME
and the sensitivity analysis is more challenging given that we care about
both treatments and their interaction.  Any thoughts you might have about
how to approach this situation (and, more specifically how to satisfy a
reviewer who really wants us to run your sensitivity analysis) would be
great!


Dustin Tingley
Government Department
Harvard University
http://scholar.harvard.edu/dtingley
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