To my knowledge, the total effect in mediation reflects the overall impact of X on Y, including the magnitude of the mediator (M) effects. A mediator is assumed to account for part or all of this impact. In mediation analysis, statistical software typically calculates the total effect as: Total effect = Direct effect + Indirect effect.
When all the effects are positive (i.e., the direct effect of X on Y (c’), the effect of X on M (a), and the effect of M on Y (b)), the interpretation of the total effect is straightforward. However, when the effects have mixed or negative signs, interpreting the total effect can become confusing.
For instance, consider the following model: X: Chronic Stress, M: Sleep Quality, Y: Depression Symptoms. Theoretically, all paths (a, b, c’) are expected to be negative. In this case, the indirect effect (a*b) should be positive. Now, assume the indirect effect is 0.150, and the direct effect is -0.150. The total effect would then be zero. This implies the overall impact of chronic stress on depression symptoms is null, which seems illogical given the theoretical assumptions.
Let’s take another example with mixed signs: X: Social Support, M: Self-Esteem, Y: Anxiety. Here, the paths for a and c’ are theoretically positive, while b is negative. The indirect effect (a*b) should also be negative. If the indirect effect is -0.150 and the direct effect is 0.150, the total effect would again be zero, suggesting no overall impact of social support on anxiety.
This leads to several key questions:
1. Does a negative indirect effect indicate a reduction in the impact of X on Y, or does it merely represent the direction of the association (e.g., social support first improves self-esteem, which in turn reduces anxiety)? If the second case holds, should we consider the absolute value of the indirect effect when calculating the total effect? After all, regardless of the sign, the mediator still helps to explain the mechanism by which X affects Y.
2. If the indirect effect reflects a reduction or increase (based on the coefficient sign) in the impact of X on Y, and this change is explained by the mediator, then the indirect effect should be added to the direct effect regardless of its sign to accurately represent the overall impact of both X and M.
3. My main question is: Should I use the absolute values of all coefficients when calculating the total effect?
Yes, the signs of the direct and indirect effects do matter when calculating the total effect in mediation analysis. Here's how the signs influence the total effect:
Breakdown of Effects in Mediation:
How Signs Matter:
- If both the direct effect and the indirect effect have the same sign (both positive or both negative), the total effect will increase in magnitude.
- If the direct effect and indirect effect have opposite signs, they will work against each other, and the total effect will decrease in magnitude or potentially even change direction (depending on the relative sizes of the effects).
Example:
Interpretation:
- The signs of the direct and indirect effects influence whether the mediator amplifies or reduces the overall effect of the independent variable on the outcome.
- If the signs are opposite, the mediator might be suppressing the effect of X on Y, or even reversing it, depending on the magnitude of the indirect effect.
As explained well by Melisew Wubishet Wuchew you cannot ignore the signs by using absolute values, because the mediator will be a suppressor variable whenever there's an odd number of negative signs (1 or 3 negatives) among the 3 paths. The term "total effect" could be a source of confusion. It might help to think of it as the "apparent effect" that would be seen if the mediator were not controlled. If the mediator is a suppressor variable, failing to control for it yields an apparent effect that is less than the true direct effect.
Many thanks to Burke D. Grandjean and Melisew Wubishet Wuchew for their valuable insights
I came across the paper by Jiang et al. (2021), which provides a straightforward explanation: TOTAL-EFFECT TEST IS SUPERFLUOUS FOR ESTABLISHING COMPLEMENTARY MEDIATION. It has been shown that total-effect test can erroneously reject “competitive mediation”. For “complementary mediation”, however, the situation becomes more complicated. They concluded that "Our results support the growing agreement that total-effect test is unnecessary for establishing any type of mediation."
Jiang, Y., Zhao, X., Zhu, L., Liu, J. S., & Deng, K. (2021). Total-effect test is superfluous for establishing complementary mediation. Statistica Sinica, 31(4), 1961-1983.
https://repository.um.edu.mo/bitstream/10692/25758/4/2019-0150_0326.pdf
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