Testing and Plotting Simple Slopes of Interaction Effects

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

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

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

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

Testing

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

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

Plotting

Plotting

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

Plotting

You’ve plotted, now what?

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

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 .07 + .06 (but we don’t know it’s standard error)

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

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

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

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

Probing Sibgen (0 = sister; 1 = brother) SibgenR (0 = brother; 1 = sister) SibIntH (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)

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)

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

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

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

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

Possible Range Observed Range 2 SDs 3 SDs

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

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

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