[Mediation-information] Question when applying Causal Mediation Analysis
Teppei Yamamoto
teppei at MIT.EDU
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/
====================================
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