Moderated Mediation (Hayes Model 7)
Mediation & ModerationTests whether the indirect effect of X on Y through mediator M changes as a function of moderator W. easyCris estimates conditional indirect effects and the index of moderated mediation using bootstrap confidence intervals.
When to Use
Use this model when you expect mediation to be present, but only at some levels of a moderator. For example, treatment effects may be mediated by a biomarker only in a specific subgroup.
Assumptions
- Correct causal ordering (X precedes M, which precedes Y).
- No major unmeasured confounding of X-M, M-Y, or X-Y paths.
- Sufficient sample size for bootstrap interval estimation.
- Moderator is correctly specified and measured at baseline or before outcome.
- Mediator and outcome variables can be continuous or binary; easyCris uses logistic modeling where applicable.
Required Inputs
| Input | Type | Notes |
|---|---|---|
| Independent Variable (X) | Numeric / Categorical | Predictor variable |
| Mediator (M) | Numeric / Binary Categorical | Mediator variable |
| Moderator (W) | Numeric / Categorical | Moderator of path a or indirect effect |
| Dependent Variable (Y) | Numeric / Binary Categorical | Outcome variable |
| Covariates (optional) | Numeric / Categorical | Optional control variables |
| Parameter | Default | Options |
|---|---|---|
| Bootstrap Samples | 5000 | 1000 - 10000 |
| Center predictor (X) | Unchecked | Optional mean-centering before fitting the moderated mediation model. |
| Center moderator (W) | Unchecked | Optional mean-centering before fitting the moderated mediation model. |
Output Metrics
| Metric | What it means |
|---|---|
| Path a Coefficients (X, W, X*W) | Effects from the mediator model, including interaction terms. |
| Path b Coefficient | Effect of M on Y controlling for X (and covariates). |
| Path c' (Direct Effect) | Direct effect of X on Y after accounting for mediation pathways. |
| Conditional Indirect Effects at Selected W Values | Estimated indirect effects at the selected or default probe values of W, with bootstrap SE, CI, and bootstrap p-value. By default these probes are the mean and +/- 1 SD of W. |
| Total Indirect Effect | Indirect effect evaluated at the moderator reference point used in the fitted model, with bootstrap SE and confidence interval. |
| Pairwise Contrasts Between Probe Values | Bootstrap contrasts comparing conditional indirect effects across the reported W values. |
| Index of Moderated Mediation | Primary test of whether the indirect effect changes with W. |
| Index Bootstrap CI | Bootstrap confidence interval for the index of moderated mediation. |
Interpretation
- Evidence for moderated mediation is present when the index of moderated mediation confidence interval excludes zero.
- easyCris reports conditional indirect effects at the selected or default probe values of W. In the current app flow, the default probes are the mean of W and +/- 1 SD.
- Conditional indirect effects show where mediation is strongest or weakest across moderator levels.
- A significant indirect effect at one moderator level does not imply significance at all levels.
- Interpret both effect direction and confidence intervals, not p-values alone.
Common Pitfalls
- Cross-sectional data limits causal interpretation of mediated effects.
- Incorrect moderator scaling can make conditional effects hard to interpret. Optional centering can improve interpretability without changing the underlying hypothesis.
- Small samples produce unstable bootstrap intervals for moderated mediation models.
- Including post-treatment covariates can distort mediation estimates.
How It Works
- easyCris optionally mean-centers X and W when the centering boxes are selected.
- easyCris fits the mediator model with X, W, and X*W, then fits the outcome model with X, M, W, and any covariates.
- For binary mediator or outcome variables, easyCris uses logistic modeling where appropriate.
- Bootstrap resampling is used to estimate conditional indirect effects across the selected or default moderator values, the total indirect effect, pairwise contrasts, and the index of moderated mediation confidence interval.
Citations
References
- Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research. Journal of Personality and Social Psychology, 51(6), 1173-1182.
- Hayes, A. F. (2022). Introduction to Mediation, Moderation, and Conditional Process Analysis (3rd ed.). Guilford Press (PROCESS framework).
- Preacher, K. J., Rucker, D. D., & Hayes, A. F. (2007). Addressing moderated mediation hypotheses. Multivariate Behavioral Research, 42(1), 185-227.