Hello,

I once posted this topic on this page but it seems that I put it in the wrong category.

I am studying the model as follows: Y= b0 + b1X2 + b2X + b3Z + b4X*Z+ control var + Err.

(X is the log form of natural Natural numbers).

The regression showed the results as I hypothesized with significant inverted U shape and the effect of moderator Z (assume the magnitude of the coefficients are 1, it can be rewritten as Y= 1 + -X2 + X + Z - X*Z+ control var + Err.)

I also tested the robustness using Sasabuchi(1980) test, the 2 extreme points at Xhigh and Xlow, the turning point are within X range. I then split the data into 2 sub samples: one smaller and one larger than the turning point. The results showed the robustness with the coefficient is positive on the left and negative on the right of the curve.

However, according to Richard et al. (2016), my model should include X2*Z to avoid omitted variable bias. That if X2*Z is not added, just the shift of turning point is tested, the flattening or steepening feature is not.

I'd like to ask if it is possible to examine the model without adding X2*Z? (as its presence messes the results up: The estimates of X2, Z, X*Z and X2*Z are insignificant and some of them flip signs.)

- Is there any other ways to test 2 types of moderations as I expect the curve to shift downward, lower than the original curve (without moderations).

- Does taking logarithm form of X make the presence of X2*Z affect the results?

I appreciate all the helps from you!

Thank you!