mediation: multiple variables david a. kenny. 2 mediation webinars four steps indirect effect causal...

Mediation: Multiple Variables

David A. Kenny

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Mediation Webinars

• Four Steps

• Indirect Effect

• Causal Assumptions

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The Mediational Model

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Multiple Xs• Consider two Xs.

– happens when X is categorical and there are more than two treatment groups

• Now two indirect effects of a1b and a2b (and two direct effects of c1

ʹ

and c1ʹ)

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Formative Variable

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Multiple Mediators• Consider two mediators, M1 and

M2,• Now two indirect effects a1b1 and

a2b2.• Can test:

–Is the sum different from zero?–Is each different from zero?–Is one larger than the other?

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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).

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Dual Mediation with No Intervention Effect

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Mediation with No Intervention Effect

Note that total effect of X on Y is .25 + (-.25) = 0! 9

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Causal Chains• One mediator causes another

X M1 M2 Y

• Indirect effect the product of three terms: ab1b2

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Multiple Outcomes• Consider two outcomes.

• Now two indirect effects ab1 and ab2.

• Consider combining outcome variables into a single variable, e.g., as a latent variables.

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X

U1

U2

MLatent

YLatent

M1

e1

1

1

M2

e21

M3

e31

Y1

e4

1

1

Y2

e51

Y3

e61

a b

c' 1

1

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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.

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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.

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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.

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Same Covariates in Both the M and Y Equations?• Trim?• Sample size and number of

covariate issues.

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Thank You!