# Simple Mediation Analysis Interpretation

I want to do a mediation analysis for variables Y,X,M in statistical package R.

I have perform the following regression models:

Y=intercept1+a0*X
M=intercept2+a*X
Y=intercept3+c*X+b*M


For the mediation analysis i have used the package: library(mediation)

The results from the estimated parameters from regression models are:

a0=-0.86
a =-1.01
c =-0.19
b = 0.66


The parameter c is non significant (p=0.2).

The results from mediation analysis are:

               Estimate 95% CI Lower 95% CI Upper p-value
ACME             -0.660       -0.878        -0.45  <2e-16 ***

$a_0$ measures the total (direct+indirect) effect of $X$ on $Y$, while $c$ is the direct effect (since you are now including the mediator in the regression). $a_0-c$ then measures the difference between total and direct effect, i.e. the indirect effect: its negative value means you have a negative mediation effect. You have both a total and an indirect negative (and highly significant) effect, while (as you noticed) no significant direct effect. Thus, you have evidence for mediation, and can't reject the hypothesis of complete mediation (i.e., null direct effect).