[Mediation-information] Question when applying Causal Mediation Analysis

Thu Sep 8 20:54:50 CEST 2011

ACME is actually equal to ITT (intention to treat) effect when direct 
effect is zero.

In the IV framework, the interest is in estimating the effect of M 
itself on Y (i.e. what if we directly manipulated M) and we could use T 
as an instrument if the exclusion restriction holds, i.e., there is no 
direct effect of T on Y.

In the ACME framework, the interest is in the effect of T on Y through M 
(i.e. what if we manipulate T but held the level of M constant at its 
natural value without manipulation). If there is no direct effect of T 
on Y, all the effects go through M so the total effect of T on Y = the 
ACME of T on Y through M.

The key difference is what causal quantity is being estimated. Under 
some assumptions some of those quantities happen to be equal.

Teppei

(9/8/11 2:16 PM), dustin tingley wrote:
> Francesc-
>
> The practical relationship between causal mediation analysis and IV is
> important.
>
> At one level this turns on whether you are interested in the causal
> effect of the treatment, or, if you are using something as an
> instrument, whether you care about the effect of that instrument (most
> economists do not). My biggest concern is people who actually care about
> the effects of the exogenous variable, but who use IV to identify its
> effect under the exclusion restriction assumption.
>
> I would also refer you to Booil Jo's paper that we cite so you can
> contrast our approach to one that is more in line with IV methods you
> appear more familiar with (we discuss this a bit in the PM paper). Key
> is keeping track of the assumptions you are making across the two
> procedures.
>
> Perhaps my co-authors can add anything.
>
> Dustin
>
> Dustin Tingley
> Government Department
> Harvard University
> http://scholar.harvard.edu/dtingley
>
>
>
> On Thu, Sep 8, 2011 at 1:18 PM, Francesc AMAT
> <Francesc.Amat at nuffield.ox.ac.uk
> <mailto:Francesc.Amat at nuffield.ox.ac.uk>> wrote:
>
>     Dustin,
>
>     How can we really distinguish an "exogenous causal effect" (as we
>     refer to them in the traditional IV frameworks) from an "indirect
>     effect" int he causal mediation analysis framework?
>
>     My trouble is that inn the causal mediation analysis the mediator M
>     is also assumed to be causally prior to the outcome Y.
>
>     But doing the analogy to the IV framework, if the mediator is
>     endogneized using T as an instrument then a standard economsit would
>     say that has found an exogenous effect of M on Y, right?
>
>     best,
>
>     Francesc
>     -----------------------------------------
>     Francesc Amat
>     University of Oxford
>     Nuffield College
>     francesc.amat at nuffield.ox.ac.uk <mailto:francesc.amat at nuffield.ox.ac.uk>
>     ________________________________________
>     From: dustin tingley [dtingley at gov.harvard.edu
>     <mailto:dtingley at gov.harvard.edu>]
>     Sent: 26 August 2011 13:25
>     To: Francesc AMAT; Teppei Yamamoto
>     Subject: Re: Question when applying Causal Mediation Analysis
>
>     Hi-
>     I'm not sure. Can you provide the code for the mediator, outcome
>     model, and when you run mediate as well. Teppei, have you see this?
>     best,
>     Dustin
>
>     Dustin Tingley
>     Government Department
>     Harvard University
>     http://scholar.harvard.edu/dtingley
>
>
>
>     On Fri, Aug 26, 2011 at 7:57 AM, Francesc AMAT
>     <Francesc.Amat at nuffield.ox.ac.uk
>     <mailto:Francesc.Amat at nuffield.ox.ac.uk><mailto:Francesc.Amat at nuffield.ox.ac.uk
>     <mailto:Francesc.Amat at nuffield.ox.ac.uk>>> wrote:
>     Dustin,
>
>
>     I run the causal mediation R package and when doing sensitivity
>     analysis I encounter an error message after using the "medsens" command.
>
>
>     The error message is the following one:
>
>     sens.bout <- medsens(out.y1b, rho.by <http://rho.by><http://rho.by>=
>     0.05, sims = 1000)
>
>     Error in Mmodel.coef.sim * (rho12.sim/sigma.2.sim) %x% t(rep(1, y.k -  :
>       non-conformable arrays
>
>     The mediator is a continuous variable and the outcome is binary. So
>     I use a linear regression model for the mediator model and a probit
>     model for the outcome one. So everything is quite standard.
>
>     Do you know which could be the source of the error?
>
>     Thanks,
>
>     Francesc
>
>     -----------------------------------------
>     Francesc Amat
>     University of Oxford
>     Nuffield College
>     francesc.amat at nuffield.ox.ac.uk
>     <mailto:francesc.amat at nuffield.ox.ac.uk><mailto:francesc.amat at nuffield.ox.ac.uk
>     <mailto:francesc.amat at nuffield.ox.ac.uk>>
>     ________________________________________
>     From: dustin tingley [dtingley at gov.harvard.edu
>     <mailto:dtingley at gov.harvard.edu><mailto:dtingley at gov.harvard.edu
>     <mailto:dtingley at gov.harvard.edu>>]
>     Sent: 24 August 2011 15:21
>     To: Francesc AMAT; Kosuke Imai; Teppei Yamamoto; Luke Keele
>     Subject: Re: Question when applying Causal Mediation Analysis
>
>     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
>     <mailto:Francesc.Amat at nuffield.ox.ac.uk><mailto:Francesc.Amat at nuffield.ox.ac.uk
>     <mailto:Francesc.Amat at nuffield.ox.ac.uk>><mailto:Francesc.Amat at nuffield.ox.ac.uk
>     <mailto:Francesc.Amat at nuffield.ox.ac.uk><mailto:Francesc.Amat at nuffield.ox.ac.uk
>     <mailto: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
>     <mailto:francesc.amat at nuffield.ox.ac.uk><mailto:francesc.amat at nuffield.ox.ac.uk
>     <mailto:francesc.amat at nuffield.ox.ac.uk>><mailto:francesc.amat at nuffield.ox.ac.uk
>     <mailto:francesc.amat at nuffield.ox.ac.uk><mailto:francesc.amat at nuffield.ox.ac.uk
>     <mailto:francesc.amat at nuffield.ox.ac.uk>>>
>
>
>

-- 
====================================
Teppei Yamamoto
Assistant Professor
Department of Political Science
Massachusetts Institute of Technology
http://web.mit.edu/teppei/www/
====================================