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@John recently pointed out to me that R's poly function produces less correlated values (more orthogonal) to fit polynomial predictors, i.e. the transformed predictors have a lower correlation with each other than if I just mean centered the 1st order predictor prior to generating the nth order predictor(s). R's poly accomplishes this using an algorithm from Kennedy, W. J. Jr and Gentle, J. E. (1980) Statistical Computing Marcel Dekker, pg 343-344. I checked the book out from the library, but I have to say that I am not quite following what is going on. I've also made some plots comparing these values to the raw values and I sort of can see what is going on, but I still don't I fully understand it. It seems like the data is being processed and subjected to some transformation that involves the mean of the values and some prediction coefficients. I can always use predict.poly to turn the values from real values to poly values. My question is how should I report the results of a model fit with poly? The raw slope coefficients refer to a transformed value, if I report them, then I assume I should also report some of the coefficients from poly itself as well. Which ones? In any particular format? Is anybody going to really understand them? Is this a compelling reason to stick to raw mean-centered coefficients?

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  • $\begingroup$ Since there was some specific recommendation made in terms of using orthogonal polynomials elsewhere I'm holding off on accepting an answer until I see a response from the opposing camp. Please vote up Frank's answer if you agree with his position. $\endgroup$ – russellpierce Mar 2 '13 at 20:57
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With modern matrix algebra software, I feel that orthogonal polynomials get in the way more than they help. I prefer to use ordinary polynomials for this reason, for example the pol function in the R rms package.

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  • $\begingroup$ BTW something seems to be off with the documentation for the R 2.15.2 / rms_3.6-3 build for Windows. The help file shows \dots rather than the expected $\dots$ for the first listing of Usage, then followed by a more typical usage section for ?pol. $\endgroup$ – russellpierce Mar 2 '13 at 1:24
  • $\begingroup$ Thanks @drknexus. It appears that in R .Rd help files the \dots directive is not supported for the \synopsis environment. I'll change to literal ... $\endgroup$ – Frank Harrell Mar 2 '13 at 13:28

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