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In general, I'm wondering if there it is ever better not to use orthogonal polynomials when fitting a regression with higher order variables. In particular, I'm wondering with the use of R:

If poly() with raw = FALSE produces the same fitted values as poly() with raw = TRUE, and poly with raw = FALSE solves some of the problems associated with polynomial regressions, then should poly() with raw = FALSE always be used for fitting polynomial regressions? In what circumstances would it be better not to use poly()?

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2 Answers 2

up vote 6 down vote accepted

Ever a reason? Sure; likely several.

Consider, for example, where I am interested in the values of the raw coefficients (say to compare them with hypothesized values), and collinearity isn't a particular problem. It's pretty much the same reason why I often don't mean center in ordinary linear regression (which is the linear orthogonal polynomial)

They're not things you can't deal with via orthogonal polynomials; it's more a matter of convenience, but convenience, to me is a big reason why I do a lot of things.

That said, I lean toward orthogonal polynomials in many cases while fitting polynomials, since they do have some distinct benefits.

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is it possible to compare the coefficients resulting from an orthogonal polynomial regression to hypothesized values? –  user2374133 Jun 20 at 4:55
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Yes. You can transform them back to the implied coefficients and standard errors from the "raw" polynomials, for example. –  Glen_b Jun 20 at 5:03

Because if your model leaves R when it grows up, you have to remember to pack its centring & normalization constants, & then it has to lug them around the whole time. Imagine coming across it one day hard-coded into SQL, & the horror of realizing it's mislaid them!

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