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 *
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Sample Size Used: 283515
Simulations: 1000
My questions are:
- Can I claim full mediation with this output, given that the ACME is statistically significant and the ADE is not?
- If so, how to explain that the proportion mediated of the effect is 66.79% and not 100%?