<div>Dear Chris-</div><div><br></div><div>Thanks for your email pasted below. You should join our listserv, <a href="mailto:mediation-information@r-forge.wu-wien.ac.at">mediation-information@r-forge.wu-wien.ac.at</a></div>
<div><br></div><div>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.</div>
<div><br></div><div>Dustin</div><div><br></div><div>****</div><div><br></div><span class="Apple-style-span" style="font-family:arial,sans-serif;font-size:13px;border-collapse:collapse;color:rgb(34,34,34)"><div>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.</div>
<div><br></div><div>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.</div>
<div><br></div><div>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!</div>
<div><br></div><div><br></div></span>Dustin Tingley<br>Government Department<br>Harvard University<br><a href="http://scholar.harvard.edu/dtingley" target="_blank">http://scholar.harvard.edu/dtingley</a><br>