1. Testing and Plotting Simple Slopes of Interaction Effects

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

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

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

5. XZXZ 111 248 3721 41040 51365 M = 3M = 7 r xxz =.98 r zxz =.98 XZXZ -2-612 -33 000 133 2612 M = 0 r xxz = 0 r zxz = 0

6. Testing

7. Plotting You’ve found a significant interaction, now what? You’ve found a significant interaction, now what? Plot it Plot it Conflict X Sib Gender (0 = sister; 1 = brother) Conflict X Sib Gender (0 = sister; 1 = brother) Two lines, solve for four points (-1, +1 SD of the continuous variable) Two lines, solve for four points (-1, +1 SD of the continuous variable) y RefXH = b o + b 1 X H + b 2 M Ref + b 3 X H M Ref y RefXH = b o + b 1 X H + b 2 M Ref + b 3 X H M Ref y RefXL = b o + b 1 X L + b 2 M Ref + b 3 X L M Ref y RefXL = b o + b 1 X L + b 2 M Ref + b 3 X L M Ref y OneXH = b o + b 1 X H + b 2 M One + b 3 X H M One y OneXH = b o + b 1 X H + b 2 M One + b 3 X H M One y OneXL = b o + b 1 X L + b 2 M One + b 3 X L M One y OneXL = b o + b 1 X L + b 2 M One + b 3 X L M One Technically all control variables should be in the equation too Technically all control variables should be in the equation too But if you’ve centered all continuous variables then you don’t need to But if you’ve centered all continuous variables then you don’t need to

8. Plotting y RefXH =.30 + (.07*.63) + (.01*0) + (.06*.63*0) y RefXH =.30 + (.07*.63) + (.01*0) + (.06*.63*0) y RefXL =.30 + (.07*-.63) + (.01*0) + (.06*-.63*0) y RefXL =.30 + (.07*-.63) + (.01*0) + (.06*-.63*0) y OneXH =.30 + (.07*.63) + (.01*1) + (.06*.63*1) y OneXH =.30 + (.07*.63) + (.01*1) + (.06*.63*1) y OneXL =.30 + (.07*-.63) + (.01*1) + (.06*-.63*1) y OneXL =.30 + (.07*-.63) + (.01*1) + (.06*-.63*1)

9. Plotting

10. Plotting

11. Plotting Now the 3-way interaction Now the 3-way interaction 4 lines, 8 points (-1, +1 SD for each continuous variable) 4 lines, 8 points (-1, +1 SD for each continuous variable) y XHMHRef = b o + b 1 X H + b 2 M H + b 3 D Ref + b 4 X H M H + b 5 X H D Ref + b 6 M H D Ref + b 7 X H M H D Ref y XHMHRef = b o + b 1 X H + b 2 M H + b 3 D Ref + b 4 X H M H + b 5 X H D Ref + b 6 M H D Ref + b 7 X H M H D Ref y XLMHRef = b o + b 1 X L + b 2 M H + b 3 D Ref + b 4 X L M H + b 5 X L D Ref + b 6 M H D Ref + b 7 X L M H D Ref y XLMHRef = b o + b 1 X L + b 2 M H + b 3 D Ref + b 4 X L M H + b 5 X L D Ref + b 6 M H D Ref + b 7 X L M H D Ref y XHMLRef = b o + b 1 X H + b 2 M L + b 3 D Ref + b 4 X H M L + b 5 X H D Ref + b 6 M L D Ref + b 7 X H M L D Ref y XHMLRef = b o + b 1 X H + b 2 M L + b 3 D Ref + b 4 X H M L + b 5 X H D Ref + b 6 M L D Ref + b 7 X H M L D Ref y XLMLRef = b o + b 1 X L + b 2 M L + b 3 D Ref + b 4 X L M L + b 5 X L D Ref + b 6 M L D Ref + b 7 X L M L D Ref y XLMLRef = b o + b 1 X L + b 2 M L + b 3 D Ref + b 4 X L M L + b 5 X L D Ref + b 6 M L D Ref + b 7 X L M L D Ref y XHMHOne = b o + b 1 X H + b 2 M H + b 3 D One + b 4 X H M H + b 5 X H D One + b 6 M H D One + b 7 X H M H D One y XHMHOne = b o + b 1 X H + b 2 M H + b 3 D One + b 4 X H M H + b 5 X H D One + b 6 M H D One + b 7 X H M H D One y XLMHOne = b o + b 1 X L + b 2 M H + b 3 D One + b 4 X L M H + b 5 X L D One + b 6 M H D One + b 7 X L M H D One y XLMHOne = b o + b 1 X L + b 2 M H + b 3 D One + b 4 X L M H + b 5 X L D One + b 6 M H D One + b 7 X L M H D One y XHMLOne = b o + b 1 X H + b 2 M L + b 3 D One + b 4 X H M L + b 5 X H D One + b 6 M L D One + b 7 X H M L D One y XHMLOne = b o + b 1 X H + b 2 M L + b 3 D One + b 4 X H M L + b 5 X H D One + b 6 M L D One + b 7 X H M L D One y XLMLOne = b o + b 1 X L + b 2 M L + b 3 D One + b 4 X L M L + b 5 X L D One + b 6 M L D One + b 7 X L M L D One y XLMLOne = b o + b 1 X L + b 2 M L + b 3 D One + b 4 X L M L + b 5 X L D One + b 6 M L D One + b 7 X L M L D One

12. Plotting

13. You’ve plotted, now what?

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

15. Probing Remember, ZERO is important Remember, ZERO is important The main effect is the effect when everything else is at zero 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) So,.07 is the slope for those with a sister (it is different than zero) The slope for brothers will be.07 +.06 (but we don’t know it’s standard error) The slope for brothers will be.07 +.06 (but we don’t know it’s standard error)

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

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

18. Probing For Intimacy (continuous) For Intimacy (continuous) Create two new variables to reflect high intimacy and low intimacy Create two new variables to reflect high intimacy and low intimacy -1 & +1 SD -1 & +1 SD This is most common This is most common High Intimacy = mean centered intimacy – 1 SD of intimacy High Intimacy = mean centered intimacy – 1 SD of intimacy Low Intimacy = mean centered intimacy + 1 SD of intimacy Low Intimacy = mean centered intimacy + 1 SD of intimacy Not a typo M = 2.97 +1 SD =.68 -1 SD = -.68 ZERO 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 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 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 For a 3-way interaction you’ll end up testing 4 models One for each slope One for each slope

20. Probing Sibgen (0 = sister; 1 = brother) Sibgen (0 = sister; 1 = brother) SibgenR (0 = brother; 1 = sister) SibgenR (0 = brother; 1 = sister) SibIntH (Intimacy @ +1 SD) SibIntH (Intimacy @ +1 SD) SibIntL (Intimacy @ -1 SD) SibIntL (Intimacy @ -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) 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 Now we know which slopes are different from zero But there’s a whole lot more info here But there’s a whole lot more info here Conflict X Sib Gender Conflict X Sib Gender The blue and grey slopes are different The blue and grey slopes are different Intimacy X Conflict Intimacy X Conflict The green and grey slopes are different The green and grey slopes are different Doesn’t map as cleanly as conflict X sib gender Doesn’t map as cleanly as conflict X sib gender Difference from high to low is greater than 1 (1.38) Difference from high to low is greater than 1 (1.38)

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

24. Mean differences 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 brother is -.13 At low levels of conflict, differences in depression based on high or low intimacy with a sister is -.04 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 low intimacy is.04 The difference in depression based on having a brother or a sister at high intimacy is.08 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 An interaction is like splitting your sample N = 100 N = 100 2-way interaction: N = 50 2-way interaction: N = 50 3-way interaction: N = 25 3-way interaction: N = 25 4-way interaction: N = 12.5 4-way interaction: N = 12.5 Even with a larger sample Even with a larger sample Some groups may be small when using categorical variables Some groups may be small when using categorical variables N = 157 (3 way should have ~39) N = 157 (3 way should have ~39) One group had 20 One group had 20

26. Cautions and Considerations How should you scale your figures? How should you scale your figures? You want to accurately convey your findings You want to accurately convey your findings Possible range Possible range May make it hard to interpret, but is the absolute most honest May make it hard to interpret, but is the absolute most honest Observed range Observed range More realistic than the possible range, may be influenced by outliers More realistic than the possible range, may be influenced by outliers 2 SDs 2 SDs Often a good option giving the picture of what most of your data look like Often a good option giving the picture of what most of your data look like 3 SDs 3 SDs Often a good option giving a better picture of what most of your data look like 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 Non-significant interactions Should they stay or should they go? Should they stay or should they go? If part of a higher order interaction they must stay If part of a higher order interaction they must stay Reason to take out Reason to take out May inflate standard errors May inflate standard errors Especially for probing slopes Especially for probing slopes Reason to leave Reason to leave More clear presentation of analysis More clear presentation of analysis Better for reviewers/readers Better for reviewers/readers My preferred option My preferred option

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

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