RStats Statistics and Research Camp 2014
Moderation and Mediation
Session 2
Todd Daniel PhD
RStats Institute
Slide 1
Slide 2
“So far, we have been unable to document any
incidents that were sparked by a cellular
telephone. In fact, many researchers have tried
to ignite fuel vapors with a cell phone and
failed.”
Petroleum Equipment Institute
“The wireless industry has done studies on the
potential for wireless phones to create
sparks…there is no documented incident where
the use of a wireless phone was found to cause
a fire or explosion at a gas station.”
Federal Communications Commission
Slide 3
https://www.youtube.com/watch?v=AIlsJPNMQss
Hmmmm…
• More gas station fires occur to women
• Women are more likely to re-enter the car
• Women are less likely to touch the car
when exiting
• Conclusion: static electricity not cell
phones
Isn’t this more useful?
Slide 4
Stats Tell Us What?
Stats tell us what.
Grow from whether and if
to how and when
Slide 5
Next Steps
•
•
•
•
Slide 6
NHST tells us whether
Correlation and Regression tell us if
Mediation answers how
Moderation answers when
Moderation
• The combined effect of two variables on
another
– Conceptually known as moderation
– In statistical terms: an interaction effect
Moderator
Predictor
Slide 7
Outcome
Example
• Do violent video games make teens
aggressive?
• Participants
– 442 youths
• IV: Number of hours spent playing video
games per week
• DV: Aggression
• Moderator: Callous (unemotional) traits
Slide 8
Conceptual moderation model
Callous Traits
Game Playing
Aggression
If callous traits are a moderator then the
strength or direction of the relationship
between game playing and aggression is
affected by callous (unemotional) traits.
Slide 9
Treating callous traits as categorical
Slide
10
Treating callous traits as continuous
Slide
11
The Statistical Moderation Model
Predictor
Moderator
Predictor x Moderator
Slide
12
Outcome
Centering variables
• The interaction term makes the b’s for
the main predictors uninterpretable in
many situations
• For this reason, it is common to transform
the predictors using grand mean centering
• Centering refers to the process of
transforming a variable into deviations
around a fixed point
Slide
13
Output from moderation analysis
Slide
14
Output from moderation analysis II
Slide
15
Output from moderation analysis III
Slide
16
Following up Moderation with
Simple Slopes analysis
Slide
17
Simple slopes
equations of the
regression of
aggression on
video games at
three levels of
callous traits
Slide
18
Reporting moderation analysis
Slide
19
How do I do that?
PROCESS
www.afhayes.com
Plug in for SPSS
Slide
20
Mediation Statistical Model
Mediation: when the relationship between a
predictor variable and outcome variable can
be explained by their relationship to a third
variable (the mediator)
Mediator
a
b
Predictor
Slide
21
c'
c
Outcome
Mediated
Simple Relationship
Relationship
Baron & Kenny, (1986)
• Mediation is tested through three
regression models:
1. Predicting the outcome from the predictor
variable
2. Predicting the mediator from the predictor
variable
3. Predicting the outcome from both the
predictor variable and the mediator
Slide
22
Baron & Kenny, (1986)
Four conditions of mediation:
1. The predictor must significantly predict the
outcome variable.
2. The predictor must significantly predict the
mediator.
3. The mediator must significantly predict the
outcome variable.
4. The predictor variable must predict the outcome
variable less strongly in model 3 than in model 1.
Mediator
Slide
23
a
b
Predictor
Outcome
c'
Limitations of Baron & Kenny’s
(1986) Approach
• How much of a reduction in the relationship
between the predictor and outcome is
necessary to infer mediation?
– people tend to look for a change in significance,
which can lead to the ‘all or nothing’ thinking
that p-values encourage
Slide
24
Sobel Test
• An alternative is to estimate the indirect
effect and its significance using the Sobel
Test (Sobel, 1982)
• If the Sobel test is significant, there is
significant mediation
Slide
25
Effect Sizes of Mediation
Kappa-squared (k2)
Slide
26
(Preacher & Kelley, 2011)
Example of a Mediation Model
Indirect Effect
a
Pornography
Consumption
Relationship
Commitment
c'
Direct Effect
Slide
27
Analysis is conducted in PROCESS
b
Infidelity
Output from Mediation Analysis
Slide
28
Output from Mediation Analysis II
Slide
29
Output from Mediation Analysis III
Slide
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Output from Mediation Analysis IV
Slide
31
Output from Mediation Analysis –
Results of Sobel test
Slide
32
Reporting Mediation Analysis
There was a significant indirect effect of
pornography consumption on infidelity though
relationship commitment, b = 0.127, BCa CI
[0.023, 0.335]. This represents a relatively
small effect, κ2 = .041, 95% BCa CI [.008, .104].
Slide
33
Reporting Mediation Analysis
Model of pornography
consumption as a
predictor of infidelity,
mediated by
relationship
commitment. The
confidence interval for
the indirect effect is a
BCa bootstrapped CI
based on 1000
samples.
Relationship
Commitment
b = -0.47, p = .028
Pornography
Consumption
b = -0.27, p < .001
Infidelity
Direct Effect, b = 0.46, p = .02
Indirect Effect, b = 0.13, 95% CI [0.02, 0.34]
Slide
34
Anything else?
• You can do mediation
and moderation
together
• Conditional Process
Analysis
Slide
35
197 male amateur golfers
Stress at Home
Self-Efficacy
Social Support
Slide
36
Rees & Freeman, 2009
Task Performance
Rationality of argument
Attribution
Interaction w/
Outgroup
Positive or Negative
Slide
37
Popan et al. (2010)
Typicality of
Outgroup Mbr.
Attitude about
Outgroup
White v. Non-White
172 female freshmen
Race
Social anxiety
Parental Attachment
Satisfaction
Slide
38
Parade et al. (2010)
Satisfaction with
Friends
Awareness of
advertising intent
Persuasion
Focus
Was the advertisement
intended to persuade
Persuasive Intent
Advertising Tactic
Brand logos v. Brand logos + slogans
Slide
39
Laran, Dalton, and Andrade (2011)
Slogan did (not) emphasize
saving money
Behavioral
Prime
Willingness to
Spend $
$0 to $500 on imaginary
shopping spree
Take a Break
Slide
40
“Static electricity has caused fires at gas
stations…for this reason, you should not reenter your vehicle while you are refueling,
since static electricity caused by friction from
your clothing’s contact with the car seat can
ignite the gas when you get back out of the
car to complete the refueling process.”
Ohio State Bar Association website
Slide
41