Dear Stata experts,
I am trying to test the effect of a moderator variable Z on the U-shaped relationship between X and Y. Hence, I introduced the interactions between the moderator, Z and X and its square as well as Z's main term. Normally, there is two types of moderation: 1) Turning point shift and 2) flattening or steepening.
The following specification allows for isolated test of each of the moderation types:
To illustrate how the moderator affects the turning point of the U-shaped relationship, we derive the turning point X* by setting the first derivative with respect to X to zero: X* = −𝛽1 − 𝛽3Z / 2𝛽2 + 2𝛽4Z equation(1)
To show how the turning point changes as Z changes, we take the derivative of this equation with respect to Z: 𝛿X/𝛿Z = 𝛽1𝛽4 − 𝛽2𝛽3 / 2 ( 𝛽2 + 𝛽4Z )2 equation (2)
Thus, the turning point shift depends not only on 𝛽3, but also on 𝛽1, 𝛽2, and 𝛽4.
I read that, in order to test formally whether a shift in the turning point occurs, one has to assess whether Equation 2 as a whole is significantly different from zero.
My question is how to test whether equation 2 is statistically different from zero using STATA.
Your answer is highly appreciated!
Thank you in advance
I am trying to test the effect of a moderator variable Z on the U-shaped relationship between X and Y. Hence, I introduced the interactions between the moderator, Z and X and its square as well as Z's main term. Normally, there is two types of moderation: 1) Turning point shift and 2) flattening or steepening.
The following specification allows for isolated test of each of the moderation types:
Code:
Y = 𝛽0 + 𝛽1X + 𝛽2X2 + 𝛽3XZ + 𝛽4X2Z + 𝛽5Z
To show how the turning point changes as Z changes, we take the derivative of this equation with respect to Z: 𝛿X/𝛿Z = 𝛽1𝛽4 − 𝛽2𝛽3 / 2 ( 𝛽2 + 𝛽4Z )2 equation (2)
Thus, the turning point shift depends not only on 𝛽3, but also on 𝛽1, 𝛽2, and 𝛽4.
I read that, in order to test formally whether a shift in the turning point occurs, one has to assess whether Equation 2 as a whole is significantly different from zero.
My question is how to test whether equation 2 is statistically different from zero using STATA.
Your answer is highly appreciated!
Thank you in advance
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