# How to interpret output from "mediation" package - can I claim full mediation?

I have an outcome binary variable Y, a continuous mediator M, a binary treatment T and some covariates C.

I have a linear regression model for the mediator:

$$M = \alpha + \beta T + \delta C$$

and a logistic model for the outcome:

$$\text{logit}(\text{Pr}(Y=1)) = \alpha +\beta T + \gamma M + \delta C$$

Using these two models I have run the mediation package obtaining the following output:

Causal Mediation Analysis

Nonparametric Bootstrap Confidence Intervals with the Percentile Method

Estimate 95% CI Lower 95% CI Upper p-value
ACME (control)           -0.000498    -0.000545         0.00  <2e-16 ***
ACME (treated)           -0.000472    -0.000541         0.00  <2e-16 ***
ADE (control)            -0.000254    -0.000828         0.00   0.442
ADE (treated)            -0.000228    -0.000745         0.00   0.442
Total Effect             -0.000726    -0.001270         0.00   0.016 *
Prop. Mediated (control)  0.685899     0.391613         2.87   0.016 *
Prop. Mediated (treated)  0.650018     0.322575         3.08   0.016 *
ACME (average)           -0.000485    -0.000536         0.00  <2e-16 ***
ADE (average)            -0.000241    -0.000786         0.00   0.442
Prop. Mediated (average)  0.667959     0.358519         2.97   0.016 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Sample Size Used: 283515

Simulations: 1000


My questions are:

1. Can I claim full mediation with this output, given that the ACME is statistically significant and the ADE is not?
2. If so, how to explain that the proportion mediated of the effect is 66.79% and not 100%?

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.

• Thank you very much. You have written "To claim full mediation is to claim that there is no indirect effect". Shouldn't it be "direct effect"? Also "The tests for ADE test the null hypothesis that there is no indirect effect" shouldn't it be "direct effect" here too? Aug 7, 2021 at 20:20
• Yes, sorry, those were mistakes.
– Noah
Aug 7, 2021 at 20:30
• Thank you very much. So in which cases can I claim "full mediation"? How can I test the null hypothesis "the ADE is different than 0" and reject it? Aug 7, 2021 at 20:34
• Look into the equivalence testing literature. It's very hard to claim a parameter is exactly equal to a specific value (i.e., 0).
– Noah
Aug 7, 2021 at 20:53