Hi, recently I got this questions about Centered Polynomials: Why does JMP only center terms involved in an effect with degree greater than one but not the main effects? Does anybody have an answer to this question?
Thanks,
Volker
Volker,
You would get exactly the same coefficients on the main centered effects as the model without main effects centered. Here is why:
Height = α + β(Weight − Mean_Weight) = α − βMean_Weight + βWeight, = α* + β Weight
where α* =α − β*Mean_Weight. Only the intercept has changed.
This is true with models with centered polynomial and interaction terms—only the intercept shifts but other slope coefficients remain the same with or without the main effects centered.
If you asked me about my preference I'd prefer to have the main effects centered for better interpretation when higher-order and interaction terms are centered. But I guess the main objective for JMP is to reduce multicollinearity when polynomials and interactions are included in a regression model.
Jian
Hi Jian,
that helps, thanks a lot.
