Lecture 10_Interactions

Question 1

What is an Interaction?

Answer 1

Instances when the effect of one variable depends on the value of another
[the effect of one independent variable (IV) on the dependent variable (DV) is not the same across all values of a second IV]
- one IV referred to as a “Moderator” (aka effect modification)

Question 2

How should you prepare variables for interaction testing?

Answer 2

• Categorical variables are represented with dummy variables
• Continuous variables should be mean-centered
• Create a cross-product (interactions) terms

Question 3

What is the purpose of mean-centering continuous variables?

Answer 3

– makes interpretation of regression coefficients easier

– this also reduces unnecessary collinearity when forming product terms for testing interactions

Question 4

What is the process of testing for an interaction?

Answer 4

Use a Hierarchical, or Sequential, Approach:
– Step 1: enter terms for main effects of the two predictors (and possibly covariates)
– Step 2: enter product term representing the interaction ( gives ΔR² for the interaction)
– Step 3: if ΔR² significant, pursue the interaction using simple slopes analysis; otherwise, interpret findings from 1st part (model) of MR

Question 5

What is the rearranged “simple slopes” regression equation?

Answer 5

Y’ = (a + b₂X₂) + ( b₁ + b₃X₂) X₁

intercept and slope regressing Y onto X₁ at a specific value of X₂
In this form, the regression on Y on X₁ depends upon the particular value of X₂ (i.e., 0 or 1) at which the slope of X₁ is being considered.

Question 6

How do you determine if the simple slopes are significantly different from 0?

Answer 6

• Use the covariance matrix of the coefficients to calculate standard errors for simple slopes of X₁ at
different values of X₂
• Simple slopes of X₁ are tested using a t-test with
df = N – k – 1.