VAF in Mediation Analysis: A Descriptive Index, Not a Decision Criterion
VAF describes the proportion of the total effect transmitted through a mediator when that ratio is meaningful. The indirect effect and its bootstrap confidence interval remain the core evidence for mediation.
Calculate the indirect effect a×b, total effect c = c′ + a×b and VAF = indirect/total. When direct and indirect effects have opposite signs or the total is near 0, VAF can be negative or exceed 100% and should not be used for classification.
Mediation: distinguish direct and indirect effects
- Variable X
Predictor
- Mediator M
The hypothesised intervening pathway
- Outcome Y
Outcome
Conceptual diagram. Assess the indirect effect with uncertainty; VAF is descriptive.
Source: Lê Minh · Conceptual illustration, not software output.1. Direct, indirect and total effects, and VAF
In a simple X → M → Y model, a is the X → M path, b is M → Y conditional on X, and c′ is the direct X → Y effect with M included. The indirect effect is a×b and the total effect is c′ + a×b. VAF = (a×b)/(c′ + a×b).
VAF is only a descriptive ratio. The sampling behavior of a×b is not simply normal, so inference about the indirect effect should use a bootstrap confidence interval rather than testing a and b separately.
| Quantity | Formula | Meaning |
|---|---|---|
| Indirect | a × b | Effect transmitted through M |
| Direct | c′ | X → Y conditional on M |
| Total | c′ + a × b | Total effect in the linear model |
| VAF | Indirect / Total | Descriptive proportion through M when the denominator is meaningful |
2. Why should the 20–80% rule not decide the conclusion?
A common convention calls VAF below 20% no mediation, 20–80% partial mediation, and above 80% full mediation. This classification can contradict the bootstrap CI and ignores uncertainty in the ratio; inference about an indirect effect should rely on its bootstrap CI (Preacher & Hayes, 2008; Zhao et al., 2010).
Modern mediation analysis prioritizes testing the indirect effect directly. A significant direct effect is not a prerequisite for testing the indirect effect, and full/partial labels should not obscure direction, magnitude and mechanism (Zhao et al., 2010).
When c′ and a×b have opposite signs, the total effect may be close to 0 and VAF can be unstable, negative or greater than 100%. Report direct and indirect effects separately rather than forcing a classification.
3. Testing workflow
Establish the mechanism and temporal order
Explain why X affects M and M affects Y; cross-sectional data limit conclusions about mechanisms.
Estimate a, b and c′
Retain the prespecified controls and use the same model.
Bootstrap the indirect effect
Use enough resamples and read the prespecified percentile or bias-corrected CI.
Inspect direction and magnitude
Compare direct, indirect and total effects; distinguish complementary from competitive mediation.
Calculate VAF when appropriate
Use it only as a supplementary description when the total effect is not near 0 and the components have a coherent interpretation.
4. Interpretation using indirect and direct effects
| Indirect | Direct | Description |
|---|---|---|
| Significant | Same sign and significant | Complementary mediation |
| Significant | Opposite signs and significant | Competitive mediation |
| Significant | Nonsignificant | Indirect-only mediation |
| Nonsignificant | Significant | Direct-only nonmediation |
| Nonsignificant | Nonsignificant | No-effect nonmediation |
5. Reporting template
Reporting example in English
The indirect effect X → M → Y was ab = [ ], bootstrap 95% CI [ ; ]. The direct effect was c′ = [ ] and the total effect was c = [ ]. Because the indirect-effect CI [excluded/included] 0, the evidence [supported/did not support] mediation. VAF = [ ] is reported as a descriptive ratio [or was not calculated because direct and indirect effects had opposite signs/the total effect was near 0].
- Test the indirect effect directly using bootstrap inference.
- Do not require a significant total effect first.
- Report a, b, c′, indirect and total effects.
- Do not use VAF when the total is close to 0.
- Do not impose the 20–80% rule as a decision criterion.
- State the design’s causal limitations.
Conclusion
VAF can help illustrate the proportion transmitted through a mediator, but it cannot replace bootstrapping the indirect effect. A defensible conclusion focuses on mechanism, direction, magnitude and uncertainty.
References
- Zhao, X., Lynch, J. G., & Chen, Q. (2010). Reconsidering Baron and Kenny: Myths and truths about mediation analysis. Journal of Consumer Research, 37(2), 197–206.https://doi.org/10.1086/651257
- Preacher, K. J., & Hayes, A. F. (2008). Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models. Behavior Research Methods, 40(3), 879–891.https://doi.org/10.3758/BRM.40.3.879
Methodological note: VAF has no simple distribution and can be highly unstable. Inference about the mediated proportion requires a specialized method and confidence interval rather than a ratio of point estimates alone.