How can I compare the interaction terms of two separate polynomial regressions? Both regressions look like
y = x1 + x2 + (x1)^2 + (x2)^2 + x1*x2
Also, how can two interaction terms from the same regression be compared?
And how would you determine the statistical power for doing so?
Thanks!
Yes, x1*x2 is the interaction terms.
What do you mean with points? All variables will be measured at least on a six-point scale (questionnaire research), many of them on a 20 or 30 point scale.
How would you like (relative) interaction strength:
Interaction = | x1*x2 / (y - x1 - x2 - x12 - x22) | , or just
Interaction = | x1*x2 / y | ?
Thank you for your answers.
>Marek Gutowski: I am only using x1*x2 as in lm(y ~ x1 + x2 + (x1)^2 + (x2)^2 + x1*x2).
>Fausto Galetto: I am not sure how this is relevant, but to estimate a straight line, I use the intercept and slope as in y = ax + b or alternatively two points. I am referring to a typical polynomial regression in the social sciences with survey responses forming the variables.
Are you referring to the sample size? This was the second part of my question: How can I determine the sample size for a power of .90 and a medium size difference?
But for the moment, assume that it consists of at least 200 respondents, i.e., that the matrix is 200x2 with x1 and x2 being the columns.
One way to compare the impact of interaction if your outcome is continuous:
Consider using additive decomposition of interaction. VanderWeele from Harvard has a tutorial on how to do this.
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