[Mediation-information] Prop. Mediated vs. ACME (average).

[Kosuke Imai]

Prop Mediated is a ratio of two estimates, which are known to have a very
high variance especially when the average treatment effect is not precisely
estimated.  I would focus on the point estimate of this quantity rather
than its CI.  The most important thing is the ACME which have a much more
stable CI.

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

On Tue, Jun 9, 2015 at 10:34 PM, Daniel Newman <dan.newman86 at gmail.com>
wrote:

> Dear mediation gourp,
>
> Firstly, thank you to  Profs. Tingley, Yamamoto, Hirose, Keele, Imai, et
> al. for building this R package.  I have just started using it.
>
> I am a little confused about the difference between  "Prop. Mediated
> (average)"  and  "ACME (average)". Could anybody help explain this to me?
>
> For example, in the mediate summary below, the 95% CIs show that my "Prop.
> Mediated (average)" is significantly greater than zero, but the ACME
> (average) is not significantly greater than zero.
>
> Causal Mediation Analysis
>
> Quasi-Bayesian Confidence Intervals
>
> Mediator Groups: AllConds
>
> Outcome Groups: AllConds
>
> Output Based on Overall Averages Across Groups
>
>                          Estimate 95% CI Lower 95% CI Upper p-value
> ACME (control)            -0.0684      -0.1537       0.0103     0.1
> ACME (treated)            -0.2053      -0.4612       0.0308     0.1
> ADE (control)             -3.0298      -6.8686       0.4929     0.1
> ADE (treated)             -3.1667      -7.1734       0.5134     0.1
> Total Effect              -3.2351      -7.3259       0.5237     0.1
> Prop. Mediated (control)   0.0213       0.0139       0.0291     0.0
> Prop. Mediated (treated)   0.0640       0.0417       0.0873     0.0
> *ACME (average) *           -0.1369      -0.3075       0.0205     0.1
> ADE (average)             -3.0983      -7.0210       0.5032     0.1
> *Prop. Mediated (average)*   0.0427       0.0278       0.0582     0.0
>
>
> This output above was generated from the code below - a mediation model to
> test whether the continuous mediator ("PrePupilDiameter ") mediates the
> relationship between the categorical treatment ("Light") and the continuous
> dependent variable ("RT") :
>
> med.fit<-lmer(PrePupilDiameter ~ Light + (1 | AllConds), data =
> data_LeftTargets, na.action = na.exclude)
> out.fit<-lmer(RT ~ PrePupilDiameter + Light + PrePupilDiameter * Light +
> (1 | AllConds), data = data_LeftTargets, na.action = na.exclude)
> med.out <- mediate(med.fit, out.fit, treat = "Light", mediator =
> "PrePupilDiameter",  control.value = 1, treat.value = 3, sims = 100,
> outcome="RT")
> summary(med.out)
>
> Any help explaining to me the difference between "Prop. Mediated
> (average)"  and  "ACME (average)" would be much appreciated
>
> Cheers
> Dan
>
>
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