To claim full mediation is to claim that there is no direct effect. The tests for ADE test the null hypothesis that there is no direct effect, but failing to reject the null hypothesis is not the same as accepting the null hypothesis. Indeed, the confidence intervals for the ADE indicate that it is possible the direct effect is larger in magnitude than the indirect effect. The proportion mediated is a point estimate, but you can see that the confidence intervals include 100% mediated (as well as high values, i.e., that the direct and indirect effects are in opposite directions) and 50% mediated (i.e., that the direct and indirect effects are of equal size and direction).
You don't have to use a term like "full mediation" to describe the results in a meaningful and useful way. "We found evidence of mediation, but not of a direct effect." This explains the situation very clearly without using that specific term.
Interaction and mediation are different things.
In mediation, we have a causal pathway where one variable causes the mediator and the mediator causes the outcome.
In interaction, we have a joint action, where two variables are associated with an outcome, but the "effect" of one variable depends on the value of the other variable.
Clearly these are different things. If we were to do a simple simulation, we might proceed as follows, in R.
First we simulate for an interaction:
set.seed(1)
X <- rnorm(500)
Z <- rnorm(500)
Y <- X + Z + X*Z + rnorm(500)
lm(Y ~ X * Z)
And we find:
## Coefficients:
## (Intercept) X Z X:Z
## -0.006785 0.967882 0.927355 0.973669
as expected. In particular, we see that the interaction has an estimate close to 1.
Now, for mediation:
set.seed(1)
X <- rnorm(500)
M <- X + rnom(500)
Y <- X + M + rnorm(500)
Now some care is needed. If we fit the model lm(Y ~ X + M) we obtain:
## Coefficients:
## (Intercept) X M
## -0.005709 1.043180 0.925210
So, here the estimate for X, 1.04 is the direct effect of X on Y, and 0.92 is the indirect (mediated) effect. Typically in inference we would like to total effect, which should obviously be close to 2, and we can obtain that with:
lm(Y ~ X)
## Coefficients:
## (Intercept) X
## -0.04731 1.92853
as expected.
Best Answer
Since you ask this conceptually....
If the results change when you add the mediator, the mediator is doing something, but what? Since the traditional use of the term "mediation" is one that reduces the effect, negative mediation would be one that increases the effect.
As for a real world example.... well, I don't have one that's from actual data, but Google found this article.