18.5 Three-Way Interactions

For models with a second moderator (\(W\)), we examine:

\[ \begin{aligned} Y &= \beta_0 + \beta_1 X + \beta_2 M + \beta_3 W + \beta_4 X \times M \\ &+ \beta_5 X \times W + \beta_6 M \times W + \beta_7 X \times M \times W + \varepsilon \end{aligned} \]

• To interpret three-way interactions, the slope difference test can be used (Dawson and Richter 2006).

References

Dawson, Jeremy F, and Andreas W Richter. 2006. “Probing Three-Way Interactions in Moderated Multiple Regression: Development and Application of a Slope Difference Test.” Journal of Applied Psychology 91 (4): 917.