Week 8 - MMR

Question 1

• Explain what it means to find an interaction in multiple regression 
(x1)

Answer 1

• Relationship between a criterion and a predictor varies as a function of a second predictor

Question 2

• Explain what a moderator is and what it does 
(x1)

Answer 2

A second predictor that enhances, attenuates or puts ‘boundary conditions’ on the focal relationship (between predictor and criterion)

Question 3

• Identify the graphic representation for moderation 
(x3)

Answer 3

The t-bar:
Instead of 2 predictors leading independently to the criterion (Y),
One is direct, and other leads to the connection
And direct effect of moderator is also tested

Question 4

What are the key characteristics of moderation? (x4, plus e.g. x1)

Answer 4

o Focus is on the direct X - Y relationship: Z adjusts it
o At low Z, the X - Y relationship is different compared to the X - Y relationship at high Z
o Moderator doesn’t explain X - Y relationship (no “because”)
o Moderator often uncorrelated with IV
o e.g., family emergency à well-being, moderated by exercise

Question 5

What are the key characteristics of mediation? (x4, plus e.g. x1)

Answer 5

o Focus on the indirect relationship of X - Y via M
o X causes Y because X causes M, which in turn causes Y
o Mediator M is associated with IV (+ or - correlation)
o If the hypothesis has ‘because’ in it, we’re moving away from moderation and into mediation
o Which has a casual change in it
o e.g., exercise - lower stress - higher well-being

Question 6

• List the two questions we ask in moderated regression, and (briefly) how we would 
answer them 
(x5, x3)

Answer 6

Does the XZ interaction contribute significantly to prediction of Y?
o In hierarchical regression:
o Enter direct effects in 1st block
o Enter interaction term in 2nd block
o Significant R2ch indicates a significant interaction
How do we interpret effect Z has on the X - Y relationship?
o In ANOVA, we examine simple effects of IV1 at different levels of IV2
o Similarly, in moderated regression, we examine the simple slopes of X-Y lines at different values of Z

Question 7

• List the 4 steps in testing for moderation 


Answer 7

1. Centre X and Z, calculate interaction term
2. Test for significance of interaction - does addition of interaction term at step 2 account for more variance in total model?
3. If interaction is significant, test for simple slopes (similar to simple effects in ANOVA)
4. Plot interaction on graph

Question 8

• Explain which variables we would mean-centre (x2), how? (x1) and what does this mean? (x2)

Answer 8

The focal IV and the moderator - X and Z
Subtract mean for each variable from each score on that predictor
Those who scored at mean will get zero - data centred around zero

Question 9

• List the two benefits of mean-centering 
(x4, x3)

Answer 9

Reduces multicollinearity:

• Positive interaction term by multiplying them together
• That doesn’t correlate with Iv/moderator it represents
• (crossing originals = multicollinearity between predictors)

Easier to interpret coefficients in presence of interaction:

• b (coefficient) changes at levels of Z
• Centreing makes b the X-Y relationship at Z-bar (0) so direct effect coefficients more meaningful

Question 10

• Explain which statistics are changed by mean-cantering (x2)

Answer 10

Mean of X and Z - now all zero

Correlations between X, Z and criterion (Y)

Question 11

• Explain which statistics stay the same after mean-cantering (x2)

Answer 11

DV mean - no need to centre, as no collinearity

SDs of scales - variance unaffected

Question 12

• Explain how we would test for the significance of the interaction term 
(x2)

Answer 12

By adding it at step 2 in HMR (MMR)

after X and Z, at step 1

Question 13

• Explain which part of the output we would examine to determine whether the
interaction is in fact significant, and what statistics we would report 
(x2)

Answer 13

Step 2 R2ch, Fch, p-value

at step 1, results identical to SMR with the two predictors - main effects

Question 14

• Explain what simple slopes are (x1)

Answer 14

The slopes of X-Y relationship at particular level of Z

Question 15

• Explain why we test simple slopes (x1)

Answer 15

They let us examine IV-DV relationship at different levels of the continuous moderator

Question 16

• Explain how we choose simple slopes to test (x1)

Answer 16

High and low levels (+/- 1 SD) of mean of moderator (Z)

Question 17

• List the three steps in testing simple slopes 


Answer 17

Create 2 new variables, at high and low Z

Get cross products of new moderator variables

• Originally did centred EV and moderator
• Now do centred IV and centred high moderator to get interaction term for high
• And same for low

Regress Y on IV for each of the 2 Z values
*2 separate MMRs

Question 18

• Explain what a significant simple slope tells you 
(x2)

Answer 18

That the b (regression coefficient) for that slope is significantly different from zero -
That there is a significant relationship between X and Y at that level of Z

Question 19

• Explain why we need to plot simple slopes, and how we would do it 
(x1, x2)

Answer 19

Because it’s hard to interpret simple slopes by equations alone
By hand, substituting constant and b, and a high and low value of X, into regression equation for each slope
Or with excel graphing…

Question 20

What is meant by ‘enhancing or attenuating relationships’? 
(x1)

Answer 20

Strengthened or reduced/buffered against at particular levels of the moderator (Z) in MMR

Question 21

What is meant by ‘decomposing an interaction’? (x1)

Answer 21

To examine the simple slopes in MMR

Question 22

Identify the linear model for moderation (x5)

Answer 22

Ŷ = b1X  + b2Z  + b3XZ  + a
Ŷ - predicted score
b1X - slope by X score
b2Z - slope 2 by Z score
b3XZ - slope3 by the interaction of XZ
a - y-intercept

Question 23

Which scores correlate with the interaction term in MMR? (x1)
Which don’t? (x2)

Answer 23

Criterion (Y)

X (focal) and Z (moderator)

Question 24

What betas should we report in MMR? (x1, explain x3)

Answer 24

Those of the simple slopes
NOT the interaction
*Even experts struggle to interpret it,
*And a ‘positive/negative’ interaction is meaningless