Simple Moderation (Hayes Model 1)

Use this analysis when you suspect that the relationship between X and Y is not the same for everyone, but varies depending on some third variable. For example, testing whether the effect of exercise on weight loss depends on age, or whether the effect of a drug differs between males and females.

• The outcome variable can be continuous or binary. easyCris uses logistic moderation when the outcome is binary.
• The relationship between predictors and the outcome is appropriately modeled as linear on the fitted scale.
• For linear moderation, residuals should be independent and reasonably homoscedastic.
• The moderator can be continuous, ordinal, or binary categorical.
• Interaction models often induce correlation between main effects and the interaction term. Optional mean-centering can improve interpretability and reduce multicollinearity in some designs.

• If the X*W interaction is statistically significant (p < alpha), the effect of X on Y depends on the level of W. This is the definition of moderation.
• easyCris reports conditional effects of X on Y at the selected or default probe values of W. By default these are the mean of W and +/- 1 SD.
• If the conditional effect is significant at some values of W but not others, X only predicts Y for certain levels of the moderator.
• The interaction-change table keeps the standard displayed headers used by easyCris. For binary outcomes, the underlying change test uses logistic-model likelihood logic even though the table still shows R2-chng, F, and Pr > F.
• For continuous moderators, the Johnson-Neyman technique can identify the exact value of W at which the effect of X on Y transitions from significant to non-significant (region of significance).

• Leaving X and W on their original scales is valid, but it can make the main effects harder to interpret because they are evaluated at W = 0 and X = 0 respectively.
• Optional mean-centering can reduce multicollinearity and improve interpretability, but it does not change whether moderation is present.
• A non-significant interaction does not prove the absence of moderation. Low power (small sample, weak effect) may prevent detection.
• Interpreting main effects of X or W in the presence of a significant interaction is misleading unless the reference point of the other variable is meaningful.
• Testing many potential moderators without correction inflates the Type I error rate. Pre-specify moderators based on theory.

1. easyCris optionally mean-centers X and W when the centering boxes are selected.
2. easyCris creates the interaction term X*W and fits either a linear or logistic moderation model depending on the outcome type.
3. The interaction coefficient b3 is the primary moderation test.
4. easyCris also reports conditional effects of X across the selected or default W probe values. In the current app flow, the default probes are the mean and +/- 1 SD of W.