35.2 Multiple Groups

When you suspect that you might have confounding events or selection bias, you can add a control group that did not experience the treatment (very much similar to Difference-in-differences)

The model then becomes

$$\begin{aligned} Y = \beta_0 &+ \beta_1 time+ \beta_2 treatment +\beta_3 \times timesincetreat \\ &+\beta_4 group + \beta_5 group \times time + \beta_6 group \times treatment \\ &+ \beta_7 group \times timesincetreat \end{aligned}$$

where

• Group = 1 when the observation is under treatment and 0 under control

• $\beta_4$ = baseline difference between the treatment and control group

• $\beta_5$ = slope difference between the treatment and control group before treatment

• $\beta_6$ = baseline difference between the treatment and control group associated with the treatment.

• $\beta_7$ = difference between the sustained effect of the treatment and control group after the treatment.