[R] Orthogonal Polynomials
Douglas Bates
bates at stat.wisc.edu
Tue Oct 8 23:41:50 CEST 2002
"Bliese, Paul D MAJ WRAIR-Wash DC" <Paul.Bliese at NA.AMEDD.ARMY.MIL> writes:
> 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
> Quadratic 1 -1 -1 1
> 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?
I think the only difference is that the columns in the orthogonal
polynomial representation in R are scaled to have unit length. The
rows in the table you give from Kirk's book have lengths sqrt(20), 2,
and sqrt(20) respectively so
> poly(1:4,3)*sqrt(20)
1 2 3
[1,] -3 2.236068 -1
[2,] -1 -2.236068 3
[3,] 1 -2.236068 -3
[4,] 3 2.236068 1
gives you the first and third rows from Kirk in the first and third
columns.
Although there is some slight numerical advantage in having the
columns of a model matrix of comparable length I don't think it would
be noticeable here.
-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-
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
_._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
More information about the R-help
mailing list