[Mediation-information] Question when applying Causal Mediation Analysis

[Kosuke Imai]

Francesc,

  In the framework of causal mediation analysis, we do not usually use the phrases such as "exogenous causal effect" or "M and Y are jointly determined".  Instead, you can refer the indirect effect as the causal effect of the treatment T on the outcome Y that is transmitted through the mediator M.  The idea is that T causally affects Y through M.  So, T is causally prior to M (and Y) and M is causally prior to Y. 

Kosuke

Department of Politics
Princeton University
http://imai.princeton.edu

On Sep 2, 2011, at 1:30 PM, Francesc AMAT wrote:

> Kosuke,
> 
> In the Causal Mediation Analysis framework even if we have a statistically sign ACME effect we cannot claim that the mediator (M) has  an "exogenous causal effect" on the outcome Y right?
> 
> And when what we actually mean is the effect of a change of M on Y induced by the Treatment it is still fair to say that M and Y are"jointly determined"? Which is the usual expression that we use when we have an endogenous regressor.
> 
> In other words, to refer to an indirect effect in the CME framework, can we still make use of standard terminology in the IV approaches and claim that because we have a statistically sign indirect effect then the effect of M on Y is not an exogenous causal effect and that instead M and Y are jointly determined? 
> 
> Francesc
> -----------------------------------------
> Francesc Amat
> University of Oxford
> Nuffield College
> francesc.amat at nuffield.ox.ac.uk
> ________________________________________
> From: Kosuke Imai [kimai at princeton.edu]
> Sent: 27 August 2011 01:31
> To: Francesc AMAT
> Cc: Dustin Tingley; Teppei Yamamoto; Luke Keele; mediation-information at r-forge.wu-wien.ac.at
> Subject: Re: Question when applying Causal Mediation Analysis
> 
> You can have significant indirect effect and insignificant total effect at the same time.
> 
> Kosuke
> 
> Department of Politics
> Princeton University
> http://imai.princeton.edu
> 
> On Aug 25, 2011, at 3:04 AM, Francesc AMAT wrote:
> 
>> Dear all,
>> 
>> Thank you all for your quick answers. Indeed, when fitting the model of Y given T and M I find no direct effect of T on Y. So it is not that I "assume" no direct effect, in fact I find evidence of the direct effect being insignificant. But I was more morried about the fact that the "total effect" is also insiginificant. And in any case, yes, I will run IV regressions as an alternative.
>> 
>> Best,
>> 
>> Francesc
>> -----------------------------------------
>> Francesc Amat
>> University of Oxford
>> Nuffield College
>> francesc.amat at nuffield.ox.ac.uk
>> ________________________________________
>> From: Kosuke Imai [kimai at princeton.edu]
>> Sent: 24 August 2011 22:49
>> To: dustin tingley
>> Cc: Francesc AMAT; Teppei Yamamoto; Luke Keele
>> Subject: Re: Question when applying Causal Mediation Analysis
>> 
>> Francesc,
>> 
>> I think Dustin is right.  You can "assume" no direct effect, but at the same time it would be good to show empirically that there is no direct effect by fitting the model of Y given T and M.  And, yes, all of these analyses depend on sequential ignorability and so sensitivity analysis is important.  You may also look at our discussion of natural experiments applied to incumbency advantage to see if any of those research designs, which avoid the reliance on sequential ignorability, is applicable to your research.
>> 
>> Good luck,
>> Kosuke
>> 
>> 
>> Department of Politics
>> Princeton University
>> http://imai.princeton.edu
>> 
>> 
>> On Aug 24, 2011, at 7:21 AM, dustin tingley wrote:
>> 
>>> Francesc--
>>> 
>>> This is a good question, that we often get. If we haven't made it explicit in our APSR paper we might want to (I don't remember).
>>> 
>>> At one level, the answer is pretty simple. If the "direct" effect (which might be thought of as other mechanisms you're not interested in) runs in the opposite direction from your mechanisms--even if it is insignificant--then you might see a total effect be insig but the ACME be significant. We're not the first to point this out, a paper by MacKinnon talks about "effect suppression", which is basically this. More generally, this is one reason why we think that just looking at the ATE might be misleading. Of course, you must in our framework be making the SI assumption. So do the sensitivity analyses and report them!
>>> 
>>> I'm sure we'd all be interested in your paper when you have one to circulate.
>>> 
>>> I cc my co-authors lest they have more to add.
>>> best,
>>> Dustin
>>> 
>>> Dustin Tingley
>>> Government Department
>>> Harvard University
>>> http://scholar.harvard.edu/dtingley
>>> 
>>> 
>>> 
>>> On Wed, Aug 24, 2011 at 8:49 AM, Francesc AMAT <Francesc.Amat at nuffield.ox.ac.uk> wrote:
>>> Dear Prof. Tingley,
>>> 
>>> I am applying your R package for doing causal mediation analysis and I´m following your new APSR piece.
>>> 
>>> My question is rather simple but it remains unclear to me. In the old Baron and Kenny (1986) framework when doing mediation analysis the first standard requirement was that the treatment (T) should significantly affect the outcome (Y) in the abase of the mediator (M) so that there is an effect to be mediated.
>>> 
>>> However, I'm using a natural experiment in which the treatment (T) affects the mediator but not directly the outcome (and even in the absence of the mediator the treatment does not affect the outcome). In other words, when modelling the outcome model when I include the treatment (T) but not the mediator (M) the treatment do not have any significant effect on Y. And indeed, when applying your R package I do find a significant "indirect effect" but a not significant "direct effect".
>>> 
>>> So, rather simply, my question is the following. It is necessary as a pre-condition to apply the causal mediation analysis package to find that the treatment significantly affects the outcome in the absence of the mediator -as it seems to me it was the standard in the Baron and Kenny framework)? Or alternatively, it is perfectly fine to use a treatment (T) such that indirectly affects the outcome (Y) but it does not have a direct effect on Y even when no controlling for the mediator?
>>> 
>>> I have good theoretical reasons to expect such an indirect effect and no reason to think that the treatment should have a direct effect on Y, even when no controlling for the mediator.
>>> 
>>> Many thanks,
>>> 
>>> Francesc
>>> 
>>> -----------------------------------------
>>> Francesc Amat
>>> University of Oxford
>>> Nuffield College
>>> francesc.amat at nuffield.ox.ac.uk
>>> 
>> 
>