Mediation -- why are effects multiplied and not simply additive? Very simple question: why are effects in path analysis or mediation multiplied and not simply additive?
Imagine the effect of $X \rightarrow Z$ is 2 and the effect of $Z \rightarrow Y$ is 4, then
the total effect of $X \rightarrow Y$ will be $2 \times 4 =8$.
My question is why not $2 + 4$?
Similarly, if X has a direct effect on Y (as in Figure 2), let's say 3, then the total effect will be $3 + (2 \times 4) = 11$



First let's make clear what effect means in this case (I will consider linear dependencies).
If $X$'s effect on $Z$ is 2, this means that changing $X$ by 1 unit changes $Z$ 2 units.
For $Y$, a 1 unit change in $Z$ will result in a change of 4. I.e., When $X$ changes 1 unit then $Z$ changes by 2 units and $Y$ changes 4 units for each unit $Z$ has changes, which is $2\times4=8$.
The second example follows the same way of thinking.
