# Comprehending output from mediation analysis in R

I'm trying to get my head around the mediation package in R, using the vignette for the package.

I'm struggling to understand the output of the mediate() function.

require("mediation")
require("sandwich")
data("framing")
med.fit <- lm(emo ~ treat + age + educ + gender + income, data = framing)
out.fit <- glm(cong_mesg ~ emo + treat + age + educ + gender + income,
data = framing, family = binomial("probit"))
summary(out.fit)
# OR for sending a message to a senator for treated compared to untreated.
exp(as.numeric(coef(out.fit)[3]))

# mediation
med.out <- mediate(med.fit, out.fit, treat = "treat", mediator = "emo",
robustSE = TRUE, sims = 100)
summary(med.out)
...

Estimate 95% CI Lower 95% CI Upper p-value
ACME (control)             0.0802       0.0335       0.1300    0.00
ACME (treated)             0.0808       0.0365       0.1311    0.00
ADE (control)              0.0142      -0.1030       0.1325    0.78
ADE (treated)              0.0147      -0.1137       0.1403    0.78
Total Effect               0.0949      -0.0316       0.2129    0.14
Prop. Mediated (control)   0.7621      -2.0926       4.9490    0.14
Prop. Mediated (treated)   0.7842      -1.9272       4.6916    0.14
ACME (average)             0.0805       0.0350       0.1304    0.00
ADE (average)              0.0145      -0.1087       0.1364    0.78
Prop. Mediated (average)   0.7731      -2.0099       4.8203    0.14
...


Does this mean that 8.08 % of the effect of treatment is mediated through emotional state, among those that are treated? Or is this a change in the coefficient of treat?

If someone could explain the output it would be much appreciated.

What does it mean that ACME (treated) is 0.0808?

0.0808 is the estimated average increase in the dependent variable among the treatment group that arrives as a result of the mediators rather than 'directly' from the treatment.

The dependent variable in this example is the probability of sending a message to a congress member, the mediator is the emotional response generated by the treatment, and the treatment is a framing manipulation. So this number means that of the estimated 0.0949 (the Total Effect) increase in this probability due to framing, an estimated 0.0805 (ACME (average)) is as a result of the emotional changes generated by the framing and the remaining 0.0145 (ADE (average)) is from framing itself.

In short Total Effect = ACME (average) + ADE (average)

However, there is no reason that the average mediation effect (ACME) is the same for people in the treatment group and people in the control, so two mediation effects are estimated: ACME (control) and ACME (treated), which is your 0.0808. The average of these average treatment effects is ACME (average) (which is a bit confusing, I admit). A similar argument holds for the direct effects.

The assumption that there is only one mediation effect and one direct effect in this population is called 'no interference' in the the authors of the package.

It's helpful when interpreting the output to bear in mind the definitions in the accompanying papers and push your ordinary understanding of regression tables into the background a little bit.

One last thing: the proportion of the causal effect of framing that is mediated by emotional response rather than direct would normally be calculated as something like ACME (average) / Total Effect, but here it is not (quite). Some discussion of how to compute this quantity for models where the dependent variable is discrete, as it is here, appears in Appendix G of Imai et al. 2010.

• I'd be interested to know how your interpretation changes when you've got an ACME of -0.08, an ADE of +0.02, and a Total Effect of -0.06. For all continuous variables, I would take this to mean that as the IV increases, the DV decreases .06. Of this movement, an estimated -.08 is due to the Mediator, and the remaining .02 is due to the IV. I me, but you can see that the switching of signs makes it less than intuitive to understand. Mar 31, 2017 at 20:39
• How does it change? It doesn't. One 'route' offsets the other. Personally, I find that mediation is one of those things that gets less, not more intuitive the more you look into it. Apr 4, 2017 at 22:22
• Thanks for the reply. I agree and have come to a similar conclusion over the past few days while researching this question. Apr 4, 2017 at 22:25