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I'm quite new to mediation analysis and try to understand the results I get. I have a new online shop feature I tested in a randomized field experiment. The treated group sees the new feature and the control group does not see the new feature. I now estimated the effect of the new feature on the order value of all customers who order something. For this, I use a Poisson Model that estimates the value of an order in Cents (outcome variable) and the binary treatment variable (cents ~ treatment). The coefficients are as follows:

            Estimate Std. Error z value Pr(>|z|)    
(Intercept) 7.644134   0.001836  4162.7   <2e-16 ***
treatTrue   0.139755   0.002465    56.7   <2e-16 ***

I expect the number of articles a customer visits to be a mediation variable. I checked whether this is a potential mediator by first running a Poisson regression on the number of articles (articles ~ treatment) and see that it is slightly significant:

        Estimate Std. Error z value Pr(>|z|)    
(Intercept)  0.92750    0.05278  17.574   <2e-16 ***
treatTrue   -0.13845    0.07573  -1.828   0.0675 .  

Next, I run a poisson regression on the order value using the mediator (articles) and get the following results:

              Estimate Std. Error z value Pr(>|z|)    
(Intercept)  7.6628604  0.0015380 4982.40   <2e-16 ***
articles     0.0227628  0.0003569   63.77   <2e-16 ***

If I now run the mediation analysis (using the r mediation package), I get the following output:

                        Estimate 95% CI Lower 95% CI Upper p-value    
ACME (control)           -16.2655     -38.0539         5.43    0.14    
ACME (treated)           -18.8448     -44.1006         6.29    0.14    
ADE (control)            330.5374     319.5988       341.73  <2e-16 ***
ADE (treated)            327.9581     317.1875       338.83  <2e-16 ***
Total Effect             311.6926     286.8376       337.21  <2e-16 ***

How do I interpret the absolute values of ACME, ADE, and total effect? I understand that ACME is not significant and it is the Total Effect - ADE. But how do I come from the very first regression (cents ~ treatment) with its estimates of 7.6 for the intercept and 0.14 for the treatment variable to the total effect of 312?

Thank you very much :)

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1 Answer 1

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The mediation package reports all effects as mean differences on the units of the predictor. So the total effect of 312 means the treatment increases the order value by 312 (whatever units those are; "cents", I guess). The coefficient on treatment in a Poisson regression of the outcome on the treatment is the log of the treatment effect on the ratio scale; that is, the treatment has an average outcome $\exp(0.139755)=1.15$ times that of the control group.

Note that the regression of the outcome on the mediator alone is unrelated to mediation analysis; you need to include the treatment variable in that model to arrive at any conclusion about mediation.

I urge you to bootstrap the standard errors since the usual Poisson regression standard errors are very sensitive to the assumptions of Poisson regression (the conditional mean equals the conditional variance).

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