Mediation:
Multiple Variables
David A. Kenny
Mediation Webinars
• Four Steps
• Indirect Effect
• Causal Assumptions
2
The Mediational Model
3
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 c1ʹ
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!
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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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e1
1
M1
e2
e3
1
1
M2
M3
1
1
U1
M
Latent
a
b
e4
e5
e6
1
1
1
Y1
Y2
Y3
1
X
c'
Y
Latent
1
U2
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!
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