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Moderation: Introduction

Moderation: Introduction. David A. Kenny. What Is Moderation. The causal relationship from a causal variable or X to an outcome or Y changes as a function of a moderator or M. X and M interact to cause Y. Effect of stress on mood is moderated by gender. Causation and Correlation.

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Moderation: Introduction

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  1. Moderation: Introduction David A. Kenny

  2. What Is Moderation The causal relationship from a causal variable or X to an outcome or Ychanges as a function of a moderator or M. • X and M interact to cause Y. • Effect of stress on mood is moderated by gender.

  3. Causation and Correlation • Need to know causal direction of the X to Y relationship. • If X is a manipulated variable, there should be no relationship between X and M. • Unlike mediation, there is no reason why necessarily X and M should be correlated.

  4. Timing of Measurement • Typically M is measured before or at the same time as X. • Will discuss whether a moderator can be caused by X when we discuss Assumptions.

  5. Statistical Estimation • Typically estimated as the interaction between X and M • Y = aX + bM + cXM + E a = “main effect” of X b = “main effect” of M c = interaction between X and M • Important to include both X and M in the model. • Will discuss the Interpretation in another webinar.

  6. Linearity • Using an product term implies a linear relationship between M and X to Y relationship. • The effect of X on Y changes by a constant amount as M increases or decreases • For example: the effect of Stress on Marital Satisfaction changes by the same amount for every year married.

  7. Statistical Estimation • What was described has been called moderated regression analysis. • One equation • Moderation as an interaction • Problematic alternatives • Separate slopes • Difference in correlations • Median split

  8. Separate Slopes? • M is categorical. • Slope computed for each group in separate analyses. • Difficult to test for moderation and less power. • Is the correct analysis when there are heterogeneous errors.

  9. Separate Correlations? • Categorical moderator. • Compute the correlation between X and Y to determine moderation within each category. • Problem: Differences in X variance. • If men have more variance on X than women, then women would likely have a weaker correlation (restriction in range).

  10. Median Split? • M is measured at the interval level of measurement. • A questionable way to measure and test for moderation is to split M at the mediation and compute slopes for X to Y above and below the split value. • Big loss in power (see Aiken & West).

  11. Flipping X and M • Because XM is an interaction, it can be interpreted as the effect of X depends on M or the that the effect of M depends on X. • Either a different discipline or a rethinking might lead to treating X as the moderator instead of M. • Sometimes this is a useful exercise.

  12. Diagrams of Moderation

  13. .5 .7

  14. Key Resource • Aiken, L. S., & West, S. G. (1991). Multiple regression: Testing and interpreting interactions. Newbury Park, CA: Sage.

  15. Additional Webinars • Interpretation • Assumptions • Effect Size and Power • ModText

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