Mediation: Multiple Variables David A. Kenny

2 Mediation Webinars Four Steps Indirect Effect Causal Assumptions

3 The Mediational Model

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

Formative Variable 5

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 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 Dual Mediation with No Intervention Effect 8

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

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

18 Thank You!