[R] Summary Orthogonal Polynomials
Douglas Bates
bates at stat.wisc.edu
Wed Oct 9 15:31:47 CEST 2002
Bill.Venables at CMIS.CSIRO.AU writes:
> I agree that it doesn't matter a damn what coding you use, but sometimes it
> is useful to look at an integer version of the contrast matrix just to see
> what's going on. This is useful for teaching. Here is the way I have done
> it in the past using a function from the MASS library. Not automatic, but
> this is not the kind of thing you need to do every day... I have trimmed
> the output a bit to make it more readable, too.
>
> > library(MASS)
> > X <- poly(1:8, 5)
> > dim(X)
> [1] 8 5
>
> > fractions(X/rep(X[1, ], each=nrow(X))) # gets rid of surds.
> 1 2 3 4 5
> [1,] 1 1 1 1 1
> [2,] 5/7 1/7 -5/7 -13/7 -23/7
> [3,] 3/7 -3/7 -1 -3/7 17/7
> [4,] 1/7 -5/7 -3/7 9/7 15/7
> [5,] -1/7 -5/7 3/7 9/7 -15/7
> [6,] -3/7 -3/7 1 -3/7 -17/7
> [7,] -5/7 1/7 5/7 -13/7 23/7
> [8,] -1 1 -1 1 -1
>
> > fractions(X/rep(X[1, ], each = nrow(X)))*7
> 1 2 3 4 5
> [1,] 7 7 7 7 7
> [2,] 5 1 -5 -13 -23
> [3,] 3 -3 -7 -3 17
> [4,] 1 -5 -3 9 15
> [5,] -1 -5 3 9 -15
> [6,] -3 -3 7 -3 -17
> [7,] -5 1 5 -13 23
> [8,] -7 7 -7 7 -7
>
> In fact I find fractions() useful for a lot of things, somewhat to my
> surprise.
I did try fractions() on the example that Paul gave, poly(1:4, 3), and
the result is hard to interpret.
> fractions(poly(1:4, 3))
1 2 3
[1,] -5494877/8191279 1/2 -98209/439204
[2,] -98209/439204 -1/2 208010/310083
[3,] 208010/930249 -1/2 -5494877/8191279
[4,] 208010/310083 1/2 208010/930249
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