Utest with moderator effect

[Lily Lin]

Hi Statalist,

I would like to test a U-shaped relationship using utest. There is a moderator in the model.
I am not sure how to put moderator in utest. Has anyone had experience with this?
I have tried to write the code below, but I am not sure whether it is correct.

Dependent variable: Y
Independent variable: X
Moderator: M
Control Variables: A, B, C

Code:

gen X_squard = X^2
reg Y X X_squard M c.X#c.M  c.X_squard#c.M M A B C
utest X X_squard

[Maarten Buis]

With a moderator, there is no longer one shape for the relationship between Y and X but as many as there are levels in the moderator variable M. So you need to think very carefully about what you want to test here. A single test makes no sense in this case. You might be able to do multiple tests for multiple values of M, but I am not certain of the properties of the test in that case. However, before diving into the technicalities, you need to do some deep thinking about the exact null-hypotheses you are testing, what those null-hypotheses mean in your research problem, why you want to do so (and you should seriously consider the possible answer that you may not want to do those tests in this case).