# Social Sciences: Setting up equation for difference in differences with multiple treatment groups

The dataset I'm looking at is household energy consumption in a particular area. I'm looking to analyze the effect of interventions which were aimed to reduce energy consumption on particular times of day so that is the effect I'm trying to measure i.e how effective the intervention was.

I have data with 1 control group and 4 treatment groups - each of which differ from the other only marginally. For clarity, in this case the participants who are being studied are intimated of the event through different means - email, SMS etc.

I set up dummy variables for each of my treatment groups as group2, group3, group4 and group5 along with dummies for treatment and post which are named as such.

I just want to make sure that I'm setting up my regression equation correctly.

The equation I have is:

Dependant var. = Treatment + Post + (Group1 + Group2 + Group3 + Group4)*Post


where each of the interaction variables signify the treatments for each of my groups.

Also I'm considering two days of pre-treatment data for my analysis.

My treatment period only lasts for about 3 hours on a particular day so I have - 3 hours the day of and 3 hours for the two days before the event I'm trying to look at.

Any help would be appreciated!

• Are you sure you want "Post" in the denomerator of these quantities? Usually for these types of analyses, it's the outcome variable that's measured at baseline and again at followup (pre/post). Are you sure you are interested in a change from exposure and its relationship to the outcome (presumably measured at followup)? Jul 16, 2015 at 22:02
• I've tagged this post analysis since it concerns analysis of a specific dataset. See the wiki for suggestions on how to edit and improve this post. Jul 16, 2015 at 22:04
• @AdamO, I've modified the question. I didn't mean a denominator. Thanks for adding the analysis tag, I'll keep that in mind going forward. Jul 16, 2015 at 22:07

## 1 Answer

If you are setting up the model in R, you'll notice that the formula you've specified will add the lower level effects for the Post * Group variable and additionally control for indicators of Group1, Group2, Group3, and Group4. This is the right way to go about modeling.

Testing for differences-in-differences is the usual way of analyzing prepost data. Setting up a model with controls for a pre/post indicator, indicators of treatment assignment, and the interaction between pre/post and treatment assignment will give you a T-test of pre/post differences for each group in the estimated effects for the interaction parameter.

Similarly, if you do a nested test for the difference between a reduced model with only treatment assignment and pre/post versus a full model with those effects and the interactions, you will obtain an equivalent to the ANOVA for any treatment having had a difference on testing which is different from control. This can have more power than each individual T-test, as I described above, and solve multiple testing issues.

So the model is almost correct, just be sure to add the lower level effects for group assignment. The reason why they need to be there is to account for spurious baseline differences in individuals who may have been assigned to each group. You make broad assumptions by having the same fitted values for all participants in the baseline measurement.

• Hi @AdamO, thanks for your reply! Having done this, if I wanted to estimate the treatment effect on a particular group here - say Group1, how would I do that with assuming I know the regression coefficients? Jul 30, 2015 at 22:16
• @AshwinShankar it's easiest to do that via fitting a plain ol' t-test w/ just the group1 participants. However, you can also add the terms corresponding to the group1*time interaction to the time factor to get the pre-post differences in only group1 participants. Jul 30, 2015 at 23:36
• Thanks! I figured that's how I should report it. As just measures of Cohen's D for each of my treatment groups. I appreciate the help. Jul 31, 2015 at 0:19