One of the important problems that psychologists face (especially clinical psychologists) is a regression situation where the independent variables appear to interact with one another. You might find, for example, that there is a relationship between stress and symptoms when you look at uncontrollable events, but that there is no relationship between those variables when you look at controllable events. Or, you might find that there is little relationship between past childhood sexual abuse and subsequent recurrence of abuse when children come from families with strong parenting skills, but a strong relationship when parenting skills are absent. Both of these situations involve a moderating variable (control or parenting) that is categorical, but there is no reason why this analysis can’t use continuous moderator variables such as social support.
For this exercise we are going to use a data set from Compas, Wagner, and some other guy on the relationship between hassles, symptoms, and social support. These are almost the actual data, though I have fudged them up just a tiny bit to make them look nicer. The data file is located on Gumby and is named hassles.sav. The data were collected from incoming college freshmen when they came to an orientation session in June. (I have lost the subsequent September and December data). The variables are Daily Hassles, Major Life Events, Symptoms, and Social Support.
If there is a moderating effect of social support, we should find what Anova would call an interaction. In regression we can model this interaction simply by taking the product of SocSupp and Hassles (our dependent variables), and using all three variables to predict Symptoms.
Start by creating a variable called SupXHas, which is the product of SocSupp and Hassles. Then run the multiple regression of Symp = Hassles + SocSupp + SupXHas. In doing so, ask SPSS to print out the correlation matrix and the collinearity diagnostics.
What does the correlation matrix tell you?
What is the multiple R?
What do the tolerances tell you?
In the "paper" on the Shape and Weight Self-esteem Index I discussed centering the data. Do that next. Center both Hassles and SocSupp by subtracting their means from all observations (call them Centhass and CentSupp. Next form the product of those two centered variables and call in CentInt. Now run the regression over again.
What has changed?
What has stayed the same?
What can you conclude?
Now we will graph the result, which will allow us a nice clean view of the interaction. This is a bit tricky, but you can do it if you follow the steps shown below. (There is a shortcut, but I don’t think it reveals as much about what is happening.)
Write out the regression equation to two or three decimal places using the centered variables.
Print out any SPSS output you want to save, and then start a new SPSS file.
Select 5 different values for CentSupp that span the general range of values for that variable.
(Do this by getting descriptive statistics on CentSupp and finding representative values.)
Select three values of CentHass, one at each end of the distribution and one near the mean.
For a fixed value of CentSupp, calculate predicted values of Symptoms (PredSymp) for low, medium, and high values of Centhass.
Use SPSS to plot PredSymp as Y, CentHass as X with CentSupp entered in the set markers by box..
What would you conclude by looking at this plot?
Can you see the interaction?
What does this tell you about the role of social support?
Why do I refer to social support as a "moderating" variable?
It looks like when you have a lot of hassles, social support is actually a bad thing. Do you really believe this? Why do the results suggest it?
The results follow for those who want to look at them.
Regression using uncentered variables.
2. Regression using centered variables
Plotting Symptoms as a function of hassles, ignoring social support.
I used centered variables.
Plotting Predicted Symptoms as a function of hassles, separately for representative levels of social support.
(At lower left, the lines are, from top to bottom, 4, 2, 0, -2, and -4)
When I use a program called Italassi to plot this, I get a slightly different view of the same thing.
You can see this plot by calling up Italassi.gif.
