Lecture 11_Interactions and Curvilinear Relations Flashcards
Interactions between 2 continuous variables and Modeling Curvilinear Relations in MLR
Define Interaction.
the effect of one independent variable (IV) on the dependent variable (DV) is not the same across all values of a second IV.
What is moderation?
interactions (often described using “it depends…”)
What is the process to find if a interaction is significant?
Use a Hierarchical or Sequential Approach (advantage because it quantifies the strength of the relationship with ΔR²):
–Step 1: enter terms for main effects of the two predictors (and possibly covariates)
–Step 2: enter product term representing the interaction
–Step 3: If the ΔR² is significant, pursue the interaction using simple slopes analysis. (if not, interpret results from model 1)
What are the Conventional definitions for “high” and “low” scores on a continuous variable?
1 SD above the mean, and 1 SD below the mean, respectively.
What should you first do to continuous variables?
Continuous variables should be mean-centered
– makes interpretation of regression coefficients easier
– this also reduces unnecessary collinearity when forming product terms for testing interactions
How do you interpret the intercept?
The intercept is the estimated value on Outcome when both Predictors have values of 0.0 (i.e., at their means due to centering).
How do you interpret the slope coefficients (b)?
The slope coefficients for each Predictor variable are interpreted as the effects of each variable when the other variable has a value of 0.0, or at its mean.
On a plot of the Simple Regression lines what do the intercepts for each line represent?
the adjusted means for subjects with average values of X₁ at:
-1SD on X₂ and
+1SD on X₂
A basic assumption of regression is …
linearity
How are curves in regression line modeled in MLR?
with higher-order polynomials (i.e. variable interacts with itself … “it depends”)
– first raise a predictor, X, to a power (e.g., X²)
– then add this predictor into the regression model along with the original predictor.
Why are statistically significant curves relatively rare in MLR?
– straight lines are reasonably good approximations
– low statistical power leads to fewer significant curves (less ability to detect)
Where is it possible to calculate and test the significance of the simple linear slope for a curvilinear regression curve?
at any value of X.
