1. Moderation & Mediation
…but mostly moderation

2. Moderation vs. Mediation
Generally we ask a question like
“Does X predict or cause Y?”
We clearly have to move beyond these simple questions
Moderators address “when” or “for whom” X causes Y
Mediators address “how” or “why” X causes Y

3. Moderators
A moderator is a variable that alters the direction or strength of the relationship between a predictor and an outcome
Really, it is just an interaction – the effect of one variable depends on the level of another
E.g. Interested not only on the effect of social support on depression levels, but whether this differs if the person is male or female

4. Mediators
A mediator variable explains the relationship between a predictor and an outcome
E.g. Interested in whether or not males and females have differing levels of depression because of differing levels of social support

6. Moderator OR Mediator Consider the effect of gender on depression
Social support could be considered either a moderator OR a mediator
It depends on the theory being tested
Gender as a Moderator
The effect of social support on depression varies depending on gender
Gender as a Mediator
Social support has an effect on depression mainly because of an underlying difference between social support levels of males and females

7. Moderator Effects
We use multiple regression to examine moderator effects
This protects the ‘continuous’ nature of the predictor (explanatory) variables
Avoid ‘grouping’ continuous data so that you can do an ANOVA
Unfortunately, this is a very common practice

8. Example Predictor – Unhelpful Social Support Outcome – Depression
Moderator – Gender
Hypothesis
Because relationships are more important to women than men (Cross & Madson, 1997), the relation between social support and depression may be stronger for women than for men
So positive relation between support and depression
The effect is larger for females than men

9. Designing the Experiment

10. Designing a test of Moderator Effects
It is important that potential moderator effects are selected apriori
In particular, the type of interaction effect should be hypothesised
Types of interaction
Enhancing
Buffering
Antagonistic

11. Types of Interactions Enhancing Buffering Antagonistic
Increasing moderator further increases the effect of predictor
Buffering
Increasing moderator decreases the effect of predictor (i.e. lessens the size of the effect)
Antagonistic
Increasing moderator reverses the effect of predictor (e.g. high support makes counselling bad)

12. Detecting Interactions
In nonexperimental situations generally only 20-34% power
To maximise this,
equate sample size between groups
Reliable measures (e.g. from 1 to .8 halves power)
Outcome variable can’t be too coarse (predictor and moderator variables each have 5-point likert measures, then outcome variable should be 25-point)

13. Simulated Data
Good reliability coefficients for social support and depression measures (i.e. alpha coefficients of 0.8)
Support measure was on a 5-point Likert scale
Outcome measure (of depression) was on a 10-point Likert scale
Equal numbers of males and females

14. Analysing the Data

15. Coding Categorical Variables
If we have categorical variables then we need to represent this as ‘code’ variables
The number of code variables we need is the number of levels of the categorical variable minus one
Gender has 2 levels
So we need 1 code variable

16. Code Variables Type of coding based on question Dummy coding
Comparisons with base or control group
Female = 1 and Male = 0
Effects coding
Comparisons with grand mean
Female = 1 and Male = -1
Contrast coding

17. Let’s Look at this Open XYZ.sav How is the Gender variable coded?
Which sort of coding is this?
How could we change it to be Dummy coding?

18. Centering Continuous Variables
In multiple regression all sorts of problems are related to having explanatory variables which are highly correlated
Interaction terms are often highly correlated with the terms from which they are created
To decrease the correlation we use centred or standardised variables

19. Let’s do this
Our moderator variable, Unhelpful Social Support, is a continuous variable
Let’s standardise it
To do this
Get the mean of support variable
Get the standard deviation of support variable
Create a new variable std_support which is equal to
( Actual Score – Mean Score ) / SD Score
std_support is our standardised version of support
Look at the values in this column. Any ideas on what they mean?

20. Create Product Term
Create a new variable by multiplying together the predictor variable and the moderator variable
For example, to get an ‘interaction’ or ‘product’ term we multiply together gender variable and standardised social support variable

21. Let’s do this Create a new variable interact which is equal to
std_support * gender
Now we have all that we need to see whether or not gender has a moderating effect on the effect of unhelpful social support on depression

22. Entering variables into Regression
First enter the predictor and moderator variables
Then enter the ‘interaction’ variables
Example
First enter the gender variable and the social support variable
Then enter the newly-created product variable

23. Let’s do this
Do a regression with std_support and gender as the explanatory variables and depression as the response variable
Now do another regression which is the same as the first regression, but includes our newly-created interact variable

24. Interpreting the Results

25. Three Steps Interpret the effects of predictor and moderator variables
Test the significance of moderator effect
Plot significant moderator effect

26. Predictor/Moderator Effects
Regression coefficients are representative of the effect of that variable when all other variables are set at 0
For categorical variables what 0 means will depend on the coding used
For continuous variables that are centred, 0 represents the average of that variable.
In this case regression coefficients represent the effect of one variable at the average level of the other variable
Only interpret the regression coefficients AFTER interaction term is added

27. Our Predictor/Moderator effects
Let’s look at the ‘full’ model
What is the regression coefficient for Gender?
What does this mean?
What is the regression coefficient for Social Support?

28. Significance of Interaction
We want to look at whether adding the interaction lead to a significant improvement in how well the regression is performing
R2 tells us how much variance in depression scores our regression model is explaining
If the interaction is improving the regression, then we expect R2 to increase
This increase should be significant

29. The F test
where f is the number of parameters in the full model (i.e. with interaction effects), r is the number of parameters in the reduced model (i.e. without interaction effects) and N is sample size

30. We can do this
Change in R2 due to the addition of interaction term = .046 (from .105)
F(1,316)=17.12, p < .001
So interaction term is significant

31. Interpreting Moderator Effects
If the interaction is significant then we can look at the effect of our predictor variable at representative levels of the moderator variable
For example, we could look at the relationship between gender and depression at ‘low’, ‘medium’ and ‘high’ levels of social support

32. Interpret Interaction
We could get some predicted values and plot them
For example, we could calculate Depression for -1,0 and 1 sd from the average Support scores for both males and females
If we wanted Depression Score for average Support Score for males we would have
Depression = *(-1) * *(-1*0) = 5.17
Depression score for Support Score -1 sd from mean and for females we would have
Depression = 5.09 – 0.08*(1) *(-1) *(-1*1)=4.55

33. Interaction plot
If we got all six values and plotted them what would we get?
The six values are
low ss
mean
high
men
5.09
5.17
5.25
women
4.55
5.01
5.47

34. Interpret Interaction
This process reveals the ‘simple’ regressions
In other words, when gender = -1 (male) then the regression equation is
When gender = 1 (female) then we have
Note that the regression coefficient for males is smaller, but the intercept is higher
What does this mean?

35. Mediator Effects
briefly

36. Mediator Effects
Social support as a mediator of the effect of gender on depression
This means that social support is the underlying cause for the relationship between gender and depression
Males and females have different levels of social support and this causes the difference in depression levels

37. Mediator in Regression
We observe a relationship between gender and depression
e.g. males show higher levels of depression
We can use regression to see this relationship

38. Mediator in Regression
We also observe that there is a significant relationship between social support and gender
e.g. males have lower levels of social support
And that social support and depression levels are also related
e.g. higher social support have lower depression

39. Mediator in Regression
If social support is a mediator then including both variables in the one regression will greatly reduce the relationship between gender and depression

40. Mediator in Regression
Firstly
Males have higher depression levels
But
Males have lower support
Lower support means higher depression
When we use both gender and support to explain depression levels the effect of gender disappears (or is greatly reduced)

41. Confounding variables
Look suspiciously like mediator variables
The key difference is that if we have a confound variable then there is no way that the predictor variable (gender) could have caused changes in mediator/confounding (social support).
If introducing social support removes the relationship between gender and depression, but it is not possible that gender could cause differences in social support then social support is a confounding variable.

42. Real Example
Relationship between type of tobacco use and cancer mortality rate
Found those that used pipe or cigar had higher death rates (35.5%) than those who smoked cigarettes (20.5%)
Are there differences between individuals who smoke pipes or cigars to those who smoke cigarettes?
AGE – average ages were 70 and 51
Tobacco type doesn’t cause age changes
So Tobacco type is a confound