Nonlinear interactions in Stata

[Ali Alipour]

Hi,

I have two variables X and Z that are hypothesized to influence Y. The effect of X on Y is nonlinear, that is, X squared is also significant. So we have:

Y = B0 + B ₁X + B ₂X² + B ₃Z

The code in stata (a mixed model regression is as follows): mixed Y c.X##c.X Z

Now if I want to estimate how the interaction effect of X and Z are, that is, how does Z moderate the impact of X on Y, which of the following codes are correct:

1. mixed Y c.X##c.X c.X##c.Z

2. mixed Y c.X##c.X##c.Z

In other words, should I interact Z with X, or should I interact it with X#X again?

As usual, I tag dear Clyde since his comments have always been helpful for me.

[Richard Williams]

You can always try it and see what you get. But I think you want the first one. Otherwise you will get X^2 * Z.

Personally, I like to write things out instead of using the shortcuts. I feel like I am surer of what I am doing. So

mixed Y c.X c.X#c.X c.Z c.X#c.Z