1. Testing and Plotting Simple Slopes of Interaction Effects

2. Today’s outline 1) What is an interaction? 2) Testing
3) Plotting (let’s not get bogged down here)
4) Probing (aka testing simple slopes)
5) Cautions and Considerations

3. What is an interaction? For whom, or when
An association differs based on some other variable(s)
It’s all about context

4. Testing Preparing your variables – it’s all about ZERO
Centering is critical for all continuous variables
X1Centered = X1 - Mean of X1

5. X Z XZ 1 2 4 8 3 7 21 10 40 5 13 65
M = 3
M = 7
rxxz = .98
rzxz = .98 X Z XZ -2 -6 12 -1 -3 3 1 2 6
M = 0
rxxz = 0
rzxz = 0

6. Testing

7. Plotting You’ve found a significant interaction, now what? Plot it
Conflict X Sib Gender (0 = sister; 1 = brother)
Two lines, solve for four points (-1, +1 SD of the continuous variable)
yRefXH = bo + b1XH + b2MRef + b3XHMRef
yRefXL = bo + b1XL + b2MRef + b3XLMRef
yOneXH = bo + b1XH + b2MOne + b3XHMOne
yOneXL = bo + b1XL + b2MOne + b3XLMOne
Technically all control variables should be in the equation too
But if you’ve centered all continuous variables then you don’t need to

8. Plotting yRefXH = .30 + (.07*.63) + (.01*0) + (.06*.63*0)
yRefXL = (.07*-.63) + (.01*0) + (.06*-.63*0)
yOneXH = (.07*.63) + (.01*1) + (.06*.63*1)
yOneXL = (.07*-.63) + (.01*1) + (.06*-.63*1)

9. Plotting

10. Plotting

11. Plotting Now the 3-way interaction
4 lines, 8 points (-1, +1 SD for each continuous variable)
yXHMHRef = bo + b1XH + b2MH + b3DRef + b4XHMH + b5XHDRef + b6MHDRef + b7XHMHDRef
yXLMHRef = bo + b1XL + b2MH + b3DRef + b4XLMH + b5XLDRef + b6MHDRef + b7XLMHDRef
yXHMLRef = bo + b1XH + b2ML + b3DRef + b4XHML + b5XHDRef + b6MLDRef + b7XHMLDRef
yXLMLRef = bo + b1XL + b2ML + b3DRef + b4XLML + b5XLDRef + b6MLDRef + b7XLMLDRef
yXHMHOne = bo + b1XH + b2MH + b3DOne + b4XHMH + b5XHDOne + b6MHDOne + b7XHMHDOne
yXLMHOne = bo + b1XL + b2MH + b3DOne + b4XLMH + b5XLDOne + b6MHDOne + b7XLMHDOne
yXHMLOne = bo + b1XH + b2ML + b3DOne + b4XHML + b5XHDOne + b6MLDOne + b7XHMLDOne
yXLMLOne = bo + b1XL + b2ML + b3DOne + b4XLML + b5XLDOne + b6MLDOne + b7XLMLDOne

12. Plotting

13. You’ve plotted, now what?

14. Probing Different than zero? It’s not enough to plot the interaction
But it looks significant!
It’s not enough to plot the interaction
You MUST probe it/test the simple slopes

15. Probing Remember, ZERO is important
The main effect is the effect when everything else is at zero
So, .07 is the slope for those with a sister (it is different than zero)
The slope for brothers will be (but we don’t know it’s standard error)

16. Probing If we recode Sib Gender so that brother = 0
We see that the slope is .13
Now we know the SE (.03)

17. Probing For the 3-way interaction Remember, it’s all about ZERO
We need to recode our two moderators to adjust what zero means
For Sib Gender
0 = 1
1 = 0

18. Probing For Intimacy (continuous) Not a typo
Create two new variables to reflect high intimacy and low intimacy
-1 & +1 SD
This is most common
High Intimacy = mean centered intimacy – 1 SD of intimacy
Low Intimacy = mean centered intimacy + 1 SD of intimacy
Not a typo
ZERO
M = 2.97
+1 SD = .68
-1 SD = -.68
M = 2.97
+1 SD = .68
-1 SD = -.68
M = 2.97
+1 SD = .68
-1 SD = -.68

19. Probing
Re-run your models with your combinations of re-coded variables
Must be done in the step where the interaction is the highest you are testing
For a 3-way interaction you’ll end up testing 4 models
One for each slope

20. Probing Sibgen (0 = sister; 1 = brother)
SibgenR (0 = brother; 1 = sister)
SibIntH +1 SD)
SibIntL -1 SD)
The re-coded variables must replace the old variable every time it is used in that model (the main effect and each interaction)

22. Now we know which slopes are different from zero
But there’s a whole lot more info here
Conflict X Sib Gender
The blue and grey slopes are different
Intimacy X Conflict
The green and grey slopes are different
Doesn’t map as cleanly as conflict X sib gender
Difference from high to low is greater than 1 (1.38)

23. Mean differences
At average levels of conflict, differences in depression based on high or low intimacy with a brother is - .09
At average levels of conflict, differences in depression based on high or low intimacy with a sister is -.08
The difference in depression based on having a brother or a sister is .02 for both high and low intimacy

24. Mean differences
At low levels of conflict, differences in depression based on high or low intimacy with a brother is -.13
At low levels of conflict, differences in depression based on high or low intimacy with a sister is -.04
The difference in depression based on having a brother or a sister at low intimacy is .04
The difference in depression based on having a brother or a sister at high intimacy is .08

25. Cautions and Considerations
An interaction is like splitting your sample
N = 100
2-way interaction: N = 50
3-way interaction: N = 25
4-way interaction: N = 12.5
Even with a larger sample
Some groups may be small when using categorical variables
N = 157 (3 way should have ~39)
One group had 20

26. Cautions and Considerations
How should you scale your figures?
You want to accurately convey your findings
Possible range
May make it hard to interpret, but is the absolute most honest
Observed range
More realistic than the possible range, may be influenced by outliers
2 SDs
Often a good option giving the picture of what most of your data look like
3 SDs
Often a good option giving a better picture of what most of your data look like

27. Possible Range
Observed Range
2 SDs
3 SDs

28. Cautions and Considerations
Non-significant interactions
Should they stay or should they go?
If part of a higher order interaction they must stay
Reason to take out
May inflate standard errors
Especially for probing slopes
Reason to leave
More clear presentation of analysis
Better for reviewers/readers
My preferred option

29. Cautions and Considerations
Checking work
It’s easy to make an error in plotting or probing
From your plotting:
Calculate the rise for each slope
From your probing
Multiply 2 SDs by the unstandardized coefficient for each association
Results from plotting and probing should match

30. Plotting with templates
It’s really awesome
Be careful
Verify
Check against probing