1. Mediation: Multiple Variables David A. Kenny

2. 2 Mediation Webinars Four Steps Indirect Effect Causal Assumptions

3. 3 The Mediational Model

4. 4 Multiple Xs Consider two Xs. –happens when X is categorical and there are more than two treatment groups Now two indirect effects of a 1 b and a 2 b (and two direct effects of c 1 ʹ and c 1 ʹ ) 4

5. Formative Variable 5

6. 6 Multiple Mediators Consider two mediators, M 1 and M 2, Now two indirect effects a 1 b 1 and a 2 b 2. Can test: –Is the sum different from zero? –Is each different from zero? –Is one larger than the other? 6

7. 7 Dual Mediation: Special Example of Two Mediators X has two levels Each level is intervention Both equally effective Each works through a different mechanism (i.e., mediator). 7

8. 8 Dual Mediation with No Intervention Effect 8

9. 9 Mediation with No Intervention Effect Note that total effect of X on Y is.25 + (-.25) = 0! 9

10. 10 Causal Chains One mediator causes another X  M 1  M 2  Y Indirect effect the product of three terms: ab 1 b 2 10

11. 11 Multiple Outcomes Consider two outcomes. Now two indirect effects ab 1 and ab 2. Consider combining outcome variables into a single variable, e.g., as a latent variables. 11

13. 13 Covariates Often there are variables in the analysis that need to be controlled: –Demographics –Baseline measures If a covariate interacts with X, it becomes a moderator. 13

14. 14 Why Add Covariates? Causal Inference: Covariate might be an omitted variable or a confounder. Power –If covariate is not correlated with the predictor but with the outcome, it leads to an increase in power. 14

15. 15 Causal Assumptions Generally assumed that covariates only cause M and Y and are not caused by them. Covariates may cause or be caused by X, but that covariation is generally left unanalyzed. 15

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17. 17 Same Covariates in Both the M and Y Equations? Trim? Sample size and number of covariate issues. 17

18. 18 Thank You!