Lecture 11: Interaction

Question 1

Interaction

Answer 1

Implies that the effect of one predictor variable depends on the level of another predictor variable.

Question 2

Regression equation with interaction

Answer 2

We add a special building block to our regression equation:

Y = a + b1X1 + b2X2 + b3(X1 * X2)

Question 3

When would you use interaction?

Answer 3

Example: you hypothesise that progressive gender roles will predict greater parental involvement, particularly for men.

This implies an interaction between the predictor “Gender roles” (continuous variable) and “Participants’ biological sex” (dummy variable)

Another example: the personality dimension of “Agreeableness” predicts the number of friends, but only when it’s combined with a high level of extroversion.

To get an interaction term, we take the 2 interacting variables, multiply them together (“the product term”) and add that product term to the regression model.

By incorporating interactions, we can gain deeper insights into the nuanced dynamics between predictors and outcomes in our statistical models.

Question 4

Simple effects analysis

Answer 4

When the interaction between a binary and continuous predictor is significant, we often want to know how big the regression effect of the continuous predictor is in each group of the binary predictor. This is called simple effects analysis.

One way of performing simple effect analysis involves creating dummy variables for both categories of the binary moderator and computing interaction terms with these dummies. Then, specify two regression models with different reference categories. This gives the effect of the continuous moderator for each group, along with a significance test.

Question 5

Centering (with interactions)

Answer 5

When working with interaction between 2 continuous predictors, it’s essential to center the variables. Centering aids interpretability - the effect of one predictor is now given for the average value of the other predictors. Moreover, centering avoids artificial multicollinearity between the two interacting variables and their interaction term.

Question 6

Simple slopes analysis

Answer 6

1. Center the interacting predictors at their mean value
2. Compute the interaction term
3. Determine whether the interaction is significant (if not, you don’t have to do simple slopes analysis)
4. Center the moderator X2 at +1 SD above the mean
5. Re-compute the interaction term
6. Note the effect of X1 for this level of X2
7. Center X2 at -1SD
8. Re-compute the interaction term
9. Note the effect of X1 for this level of X2