6. Interactions: Categorical*Continuous Flashcards
What is an interaction?
When the effects of one predictor on the outcome differ across levels of another predictor
How is the slope impacted when the interacting variable changes?
Slope will change as value of interacting variable changes
What is a categorical*continuous interaction?
Slope of regression between continuous predictor and outcome is different across levels of a categorical predictor
What is the model equation for interactions and what does each coefficient mean?
yi = B0 + B1xi + B2zi + b3xzi + Ei
B0 = value of y when x & z = 0
B1xi = Effect of x slope when z = 0
B2zi = Difference in intercept between z = 0 and z = 1 when x = 0 as z is a binary variable
B3xzi = Difference in slope across levels of Z
How do you plot a categorical*continuous interaction?
Simple Slopes
- Regression of outcome y on a predictor of x at specific values of z
- When calculating, the regression equation is rearranged
predicted y = (b1 + b3z) + (B2z + b0)
so
predicted y = coefficients for slope + coefficients for intercept
What are marginal effects?
Marginal effects tells us how a dependent variable (outcome) changes when a specific independent variable (explanatory variable) changes. Other covariates are assumed to be held constant.
Effect is not held constant because x is conditional on z
What type of effects will there be if there is an interaction vs there isn’t an interaction?
If interaction = Marginal/Conditional Main effects
If not interaction = Main effects
What happens to the effects we must include when we have a higher order term/interaction in the model?
Must include main effects
If we don’t include them then a single term reflects them all
If there is a known interaction we must include it, otherwise Beta 1 and Beta 2 = Inaccurate
What is mean centering?
What we do with mean-centering is to calculate the average value of each variable and then subtract it from the data. This implies that each column will be transformed in such a way that the resulting variable will have a zero mean.
Why do we centre predictors?
Meaningful interpretation
- Interpretation of model with interaction involves evaluation when other variance = 0
- For continuous variables - 0 needs to be a meaningful point
Reduces multi-collinearity
- ## x and z are by definition correlated with xz (produced multicollinearity which undermines statistical significance of IV)
What is the impact of centering?
Moves where 0 is = Impacts estimates
Beta are marginal effects where variance = 0
Shows how DV changes as variance changes
What type of effects are b1 and b2 in a model that is testing an interaction?
Conditional (marginal) effects as the effect of one IV is conditioned on the other
