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This isn't really a statistical problem, more like a curiosity. In any case, comments much appreciated.

I read a paper where they hypothesize the following:

Hypothesis 1. Z moderates the relationship between X and Y. When Z is high, the positive relationship between X and Y is stronger at intermediate levels of X than at lower or higher levels of X; when Z is low, X has a positive linear relationship with Y.

They tested this hypothesis by including in the regression equation of Y the interaction between X^3 and Z. My simple question is, according to this hypothesis, shouldn't they have included an X^2 x Z term instead - because the relationship that they are describing in the hypothesis seems more curvilinear/quadratic than cubic.

Thanks!

andree
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  • @whuber I am pretty sure this is what they hypothesized and that is how they tested it. So, the model included X, Z, the power terms of X, and the interaction between the X x Z, X^2 x Z, and X^3 x Z in explaining Y. I've seen this before so I don't have a problem with the terms they included. I'm just curious whether they should have looked at the quadratic instead of the cubic X x Z interaction predicting Y. Alternatively, what should they have used to model the nonlinear relationship? – andree Dec 01 '16 at 19:54
  • I apologize--I mixed up my understanding of $X$ and $Z$ in the descriptions. I'm just going to delete that comment (and take a break for awhile!). – whuber Dec 01 '16 at 19:56

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