Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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()?

share|improve this question
up vote 7 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.

share|improve this answer
is it possible to compare the coefficients resulting from an orthogonal polynomial regression to hypothesized values? – user2374133 Jun 20 '14 at 4:55
Yes. You can transform them back to the implied coefficients and standard errors from the "raw" polynomials, for example. – Glen_b Jun 20 '14 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!

share|improve this answer
Why the down-vote? (Fair enough if it's for the strained humour.) – Scortchi Aug 29 '14 at 14:49

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.