[Mediation-information] interpretation for mediation effect

[Kosuke Imai]

In statistics, estimating proportion is always tricky because randomness in denominator (especially when the denominator is small like in your case) can contribute a lot to the variation of estimated proportion.  This is what happening here.  You can estimate ACME in a relatively precise manner but you have a hard time estimating the ratio of the ACME over the ATE because both the ACME and ATE are estimated. 

Kosuke

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


On Sep 15, 2011, at 11:52 AM, dustin tingley wrote:

> Hi Weichao-
> 
> If you review the formula for proportion mediated that is in our Psychological Methods paper, this sort of thing can happen when your indirect and direct effects go in different directions, as they do in your case.
> 
> best,
> Dustin
> 
> Dustin Tingley
> Government Department
> Harvard University
> http://scholar.harvard.edu/dtingley
> 
> 
> 
> On Thu, Sep 15, 2011 at 10:55 AM, Weichao Bao <weichaobao at gmail.com> wrote:
> Dear All,
> 
> 
> 
> I am using the mediation package on my research. The outcome is dichotomous and the treatment is continuous. It was run with GAM model.  But I am confused with the following results. It shows all the Mediation Effect_0, Mediation Effect_1,and Mediation Effect (Average) have significant mediation effect based on 95% CI. However, the Proportion of Total Effect via Mediation_0, Proportion of Total Effect via Mediation_1, and Proportion of Total Effect via Mediation (Average) indicate there is no mediation at all based on the 95% confidence interval.  The result is: 
> 
> 
> 
> Mediation Effect_0:  -0.004309 95 % CI  -0.0086640 -0.0007235
> 
> Mediation Effect_1:  -0.006557 95 % CI  -0.014173 -0.001015
> 
> Direct Effect_0:  0.04452 95 % CI  0.001001 0.112969
> 
> Direct Effect_1:  0.04228 95 % CI  0.0009312 0.1061973
> 
> Total Effect:  0.03797 95 % CI  -0.004335  0.101359
> 
> Proportion of Total Effect via Mediation_0:  -0.1069 95 % CI  -1.592  0.817
> 
> Proportion of Total Effect via Mediation_1:  -0.1701 95 % CI  -1.8595  0.8059
> 
> Mediation Effect (Average):  -0.005433 95 % CI  -0.011059 -0.000928
> 
> Direct Effect (Average):  0.0434 95 % CI  0.0009659 0.1098405
> 
> Proportion of Total Effect via Mediation (Average):  -0.1391 95 % CI  -1.7258  0.8114 
> 
> 
> 
> Can somebody help me to explain this?
> 
> 
> 
> Thanks a lot.
> 
> Sincerely,
> 
> 
> Weichao
> 
> 
> 
> 
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