Moderation
E0420
Week 12

Interactions
•Multiple variables in regression = additive effect
•Interaction is different from the additive effect
•When relation between X and Y depends on levels of Z
•Moderation is an interaction
•Polynomial terms are interactions (e.g. x2)
•

Types of interactions
•By number of variables
•2-way interactions
•3-way interactions
•By type of variables
•categorical * categorical
•categorical * continuous
•continuous * continuous

Additive effects
•First-order effects
•For two variables:
•
•Sleep_hrs = B0 + B1Age + B2hrs_inet
•Sleep_hrs = 9.449 - 0.131Age – 0.117hrs_inet
•
•Values:
•Age: 10.5 – 21.29
•Hours on internet: 0 – 7
•







Interaction
•Higher-order effects
•In interaction, the first order effects are conditional (depending on the value of the other IV)
•The conditional association is symmetrical:
• X on Z = Z on x
•Interaction term is entered into regression along with the X and Z variables
•In hierarchical regression, it is better to use the interaction term as a separate step

•
•
•
•.2 association between depression and social skills when anxiety = 0
•.6 association between anxiety and social skills and when depression = 0
•.4 association between depression and anxiety increases by .4 for every unit increase in the
cross-product
•
From Peggy Keller’s Moderation presentation from Spring 2012, University of Kentucky

From Peggy Keller’s Moderation presentation from Spring 2012, University of Kentucky



Interactions in ANOVA
•ANOVA interactions are equal to interactions from regression
•ANOVA can only do interactions with categorical variables
•
•People used to categorize continuous variables = bad idea
•Lower power
•Potentially spurious findings

Mediation vs moderation
•Mediation = explains association
•Moderation = conditions the association
•
•Mediation = a third variable explains the association between the two variables
•Z mediates = Z carries (a part of) an effect between X and Y
•
•Moderation = a third variables influences the strength of the association between the two
variables
•Z moderates – Z makes the association between X and Y become stronger/weaker

X
M
Y
X
M
Y
Mediation
Moderation

Centering
•As mentioned in the previous lecture, centering is necessary for interaction terms
1.Interpretability (if there is no meaningful 0)
•Then, the first order coefficient X represents its value when Z = average (and not 0)
2.To deal with multicollinearity
X
Z
XZ
X_c
Z_c
XZ
0
0
0
-5
-5
25
2
2
4
-3
-3
9
4
4
16
-1
-1
1
6
6
36
1
1
1
8
8
64
3
3
9
10
10
100
5
5
25
r = 0.96
X (M) = 5
X (Z) = 5
r = 0.00
X (M) = 0
X (Z) = 0

Note on centering
•Not needed to center when a meaningful zero or when dichotomous
•No need to center additional IVs in the model that are not part of the interaction term

Plotting the interaction
•Plotting is essential for understanding moderation
•We usually select 2-3 values for the moderator to be plotted
•Those are the lines you see
•For categorical moderator, it would be the categories
•For continuous moderator, most often it is +/- 1SD of moderator (+mean)
•
•

•
From Peggy Keller’s Moderation presentation from Spring 2012, University of Kentucky


Simple slopes
•The slopes that we plot (conditional) can be tested for significance
•The computation of SE is not that straightforward
•Software can be used to test the simple slopes
•PROCESS macro
•Quantpsy.org
•Can obtain CIs and region of significance
•Johnson-Neyman
•

Different types of interactions
Positive synergistic
Negative synergistic
From Peggy Keller’s Moderation presentation from Spring 2012, University of Kentucky

Different types of interactions
Antagonistic
From Peggy Keller’s Moderation presentation from Spring 2012, University of Kentucky

Different types of interactions
Curvilinear by linear interaction
From Peggy Keller’s Moderation presentation from Spring 2012, University of Kentucky

3-way interaction
•X*Z*W
•
Rutten, R., & Gelissen, J. (2008). Technology, talent, diversity and the wealth of European
regions. European Planning Studies, 16(7), 985-1006.