# [R] Orthogonal Polynomials

Bliese, Paul D MAJ WRAIR-Wash DC Paul.Bliese at NA.AMEDD.ARMY.MIL
Tue Oct 8 20:55:43 CEST 2002

```Looking to the wonderful statistical advice that this group can offer.

In behavioral science applications of stats, we are often introduced to
coefficients for orthogonal polynomials that are nice integers.  For
instance, Kirk's experimental design book presents the following
coefficients for p=4:

Linear     -3 -1  1  3
Cubic      -1  3 -3  1

In R orthogonal polynomials are not integers. For instance, in R where p =4:

> poly(c(1:4),3)
1    2          3
[1,] -0.6708204  0.5 -0.2236068
[2,] -0.2236068 -0.5  0.6708204
[3,]  0.2236068 -0.5 -0.6708204
[4,]  0.6708204  0.5  0.2236068

Where, of course, column 1 is linear, column 2 Quadratic and 3 cubic.

My experience is that the coding scheme used in R works "better" than the
integer scheme discussed in Kirk for many regression type analyses.

Can anyone enlighten me as to why?

Thanks,

Paul Bliese
Walter Reed Army Institute of Research
-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-
r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html
Send "info", "help", or "[un]subscribe"
(in the "body", not the subject !)  To: r-help-request at stat.math.ethz.ch
_._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._

```