• Using and interpreting interactions

• Two kinds of main effects

  • bivariate association (simple regression) or
  • conditional/additional effects (multiple regression)

Main effects in equation: \(... + \beta_i*X_i +...\)

• Interactions: the effect of one independent variable on the dependent variable varies across levels of another independent variable. Interaction effects as “it depends” effects.

  • e.g. interaction between smoking and inhaling asbestos in their effect on lung cancer risk
  • some sociological examples?

Interactions in equation: \(... + \beta_1*X_1 + \beta_2*X_2 + \beta_3*X_1*X_2 + ...\)

For an interaction of continuous variable with a binary variable, we could also run two separate models. So why not? - one model with interaction term = one fit - one model with interaction term = statistical significance test of the difference of slopes

This can be tricky, we will go through it in the lab part of this session. Also see (Gelman et al., 2020, pp. 134–136) for general comments and (Gelman et al., 2020, pp. 185–187) for the effect of centering variables in models with interactions.