Moderation

Purpose:

Moderation tests whether the relationship between X and Y changes depending on the level of a third variable — the moderator (W). It answers: does the effect of X on Y depend on W? This is also called an interaction effect. The moderator does not explain how X affects Y — it tells you under what conditions or for whom the effect is stronger, weaker, or reversed.

Mediation vs. moderation: A mediator explains the mechanism (how X affects Y). A moderator specifies when or for whom X affects Y. These are fundamentally different questions.

Context Used:

  • ONE continuous or categorical IV (X)
  • ONE continuous or categorical moderator (W)
  • ONE continuous DV (Y)
  • A theoretical reason to expect the effect of X on Y to differ across levels of W

Common psychology examples:

  • Does social support (W) buffer the effect of stress (X) on depression (Y)?
  • Is the association between parenting warmth (X) and child anxiety (Y) stronger for boys than girls (W)?
  • Does the effect of therapy type (X) on symptom reduction (Y) differ by baseline severity (W)?
Do NOT use moderation if: You have no theory-driven reason to expect the effect to vary — fishing for interactions inflates Type I error | Your sample is small (aim for N ≥ 200) | You want to know why the effect occurs, not when → use mediation instead | You have more than one DV → use MANOVA or SEM

Assumptions:

Moderation is tested through regression, so the same regression assumptions apply:

  • Linearity
  • Independence of residuals
  • Homoscedasticity
  • No excessive multicollinearity: Some correlation between X and the interaction term (X × W) is expected — this is why mean-centering continuous variables before computing the interaction is recommended.

Jamovi Walkthrough:

Requires the medmod module. Install via Modules → jamovi library → search "medmod."

Mean-Centering (recommended before running):

  1. Click "Data" → "Compute"
  2. Create: X_c = X − MEAN(X)
  3. Repeat for the moderator: W_c = W − MEAN(W)

Running the Moderation:

  1. Click "medmod" → "Moderation"
  2. Move the DV into the "Dependent Variable" box
  3. Move the IV (X_c) into the "Predictor" box
  4. Move the moderator (W_c) into the "Moderator" box
  5. Under "Estimates," check "Labels," "Test statistics," and "Confidence interval"
  6. Under "Simple Slopes," check "Simple slopes plot"

R Walkthrough:

library(interactions)

df$X_c <- scale(df$X, center = TRUE, scale = FALSE)
df$W_c <- scale(df$W, center = TRUE, scale = FALSE)
df$XW  <- df$X_c * df$W_c

mod_model <- lm(Y ~ X_c + W_c + XW, data = df)
mcSummary(mod_model)

sim_slopes(mod_model, pred = X_c, modx = W_c, jnplot = FALSE)

Output Interpretation:

Interaction term (X × W):

  • If p < .05 → moderation is significant; the effect of X on Y depends on W.
  • If p > .05 → moderation is not significant; the relationship does not significantly change across levels of W.

Simple slopes: When the interaction is significant, interpret the effect of X on Y at three levels of W: low (−1 SD), mean, and high (+1 SD). A crossover interaction — where the slope reverses direction across levels of W — is the strongest form of moderation.

Simple slopes plot: The most intuitive way to report moderation. Shows the regression line of X on Y separately for low, mean, and high W. Non-parallel lines indicate an interaction. Always include this plot when reporting moderation results.

β and R²: Interpreted the same as in standard regression.

APA Format:

Appropriate data visualization: Simple slopes plot. See APA sample figures.

Sample write-up:

A moderated regression analysis examined whether [W] moderated the relationship between [X] and [Y]. After mean-centering, the interaction term ([X] × [W]) was entered alongside the main effects. The overall model was significant, F(, ) = , p < .05, R² = . The interaction term was significant, b = , t() = , p = , 95% CI [, ]. Simple slopes analysis revealed that the effect of [X] on [Y] was significant at low [W] (b = , p = ) but not at high [W] (b = , p = ).

Note: Report b (unstandardized), t, df, p, and 95% CI for the interaction term. Report simple slopes at all three levels of W.

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