Question about interactions in regression

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Ninja say what!?!
#1
So recently, I was told that when using regression with interactions, a main term must always be put in the model. I brought up a situation where I thought you might not need to use a main term, but was told you still have to. Thought I'd share it with you guys to see what you think.

Picture a clinical trial. A control and a treatment group are formed that are exchangeable. The outcome of interest (lets say height) is exactly the same between the two groups. You want to see how the treatment affects height over time (i.e. repeated measures). A model you could set up is:

E[Y] = B0 + B1(Time) + B2(group) + B3(Time*group)

My argument was that since you've verified that both groups start with the same measure of the dependent variable, there is no need to at in the main term for group (i.e. B2(group)). You'd really just be interested in the interaction. I was told that the interpretation of interaction still requires you to have two beta coefficients though.

Do you guys agree?

PS. I know that there will be correlation from the repeated measures. That's a separate issue that I'm conveniently ignoring for now though.
 

fed1

TS Contributor
#2
Your right but yet you are wrong i think.

If the treatment groups are equivalent at baseline then the estimated main effect of group is going to be 0 and the test of the interaction is going to be very similar whether you assume the main effect is 0 or not.

The problem is that if you assume the main effect of group is 0, then the test of the interaction is a 2 df of freedom hypothesis (assuming that there are only two levels of group and time) whereas it was the one df of freedom hypothesis before. The two hypothesis tests are not identically equal.