Test whether the effect of a predictor on an outcome depends on the level of a third (moderating) variable.
Moderation Analysis tests whether the relationship between a predictor (X) and an outcome (Y) varies as a function of a third variable (the moderator, W). A significant X × W interaction indicates that the effect of X on Y depends on the value of W. This is sometimes called an 'interaction effect' in regression. Examples: Does the effect of social support on wellbeing depend on personality (introversion–extraversion)? Does the effect of a training program on performance depend on employees' baseline skill level?
Moderation is tested by adding the X × W product term to the regression model and testing its coefficient. StatRyx mean-centres X and W before forming the product (to reduce multicollinearity) and probes the significant interaction by computing simple slopes of Y on X at low (−1 SD), mean, and high (+1 SD) values of W, following Aiken & West (1991).
A Johnson-Neyman plot identifies the exact range of W values for which the X → Y effect is significant, providing much more nuanced information than the three-group probe.
Moderation tests whether the effect of X on Y depends on a third variable W. It is a regression with an X × W interaction term: a significant interaction means the slope of X changes across values of W. To describe it, probe simple slopes — the effect of X at low (−1 SD), average and high (+1 SD) W — or use the Johnson-Neyman interval, which shows exactly where along W the effect of X becomes significant.
| Predictor | B | SE | t | p | R² |
|---|---|---|---|---|---|
| Social Support (X) | 0.31 | 0.07 | 4.43 | < .001 | |
| Neuroticism (W) | −0.42 | 0.08 | −5.25 | < .001 | |
| X × W (interaction) | −0.31 | 0.08 | −3.88 | < .001 | .07 |
| Model | < .001 | .34 |
Moderation analysis revealed a significant interaction between social support and neuroticism in predicting wellbeing, B = −0.31, SE = 0.08, t(196) = −3.88, p < .001, ΔR² = .07. Simple slopes indicated that social support positively predicted wellbeing for low-neuroticism individuals (b = 0.54, p < .001) but not for high-neuroticism individuals (b = 0.08, p = .43).
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Mean-centering subtracts the variable's mean before forming the product term. It reduces multicollinearity between the main effects and the interaction term and makes the main effect coefficients interpretable as effects at the mean of the moderator.
Rather than probing the interaction at three arbitrary W values, the Johnson-Neyman technique identifies the precise range of W for which the X → Y effect is statistically significant. This gives a much richer picture of the moderation.
Report the interaction coefficient with SE, t and p, the change in R² it adds, then the simple slopes: "The interaction was significant, B = −0.31, SE = 0.08, t(196) = −3.88, p < .001, ΔR² = .06. At high neuroticism the effect of support was weaker (B = 0.12, p = .21) than at low neuroticism (B = 0.54, p < .001)."
Mediation asks how or why X affects Y: through a mechanism M that X changes. Moderation asks when or for whom X affects Y: the strength of the effect depends on W. A mediator is caused by X; a moderator is not.
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