# [Rd] poly() can exceed degree k - 1 for k distinct points (PR#11251)

From: <russell-lenth_at_uiowa.edu>
Date: Wed, 23 Apr 2008 19:05:28 +0200 (CEST)

The poly() function can create more variables than can be fitted when there are replicated values. In the example below, 'x' has only 5 distinct values, but I can apparently fit a 12th-degree polynomial with no error messages or even nonzero coefficients:

R> x = rep(1:5,3)
R> y = rnorm(15)
R> lm(y ~ poly(x, 12))

Call:
lm(formula = y ~ poly(x, 12))

Coefficients:

(Intercept) poly(x, 12)1 poly(x, 12)2 poly(x, 12)3

-0.27442 0.35822 -0.26412 2.11780
poly(x, 12)4 poly(x, 12)5 poly(x, 12)6 poly(x, 12)7

1.83117 -0.09260 -0.48572 1.94030   poly(x, 12)8 poly(x, 12)9 poly(x, 12)10 poly(x, 12)11

-0.88297 -1.04556 0.74289 -0.01422
poly(x, 12)12

-0.46548

If I try the same with raw=TRUE, only a 4th-degree polynomial is obtained:

R> lm(y ~ poly(x, 12, raw=TRUE))

Call:
lm(formula = y ~ poly(x, 12, raw = TRUE))

Coefficients:

(Intercept)   poly(x, 12, raw = TRUE)1
9.7527                   -22.0971
poly(x, 12, raw = TRUE)2   poly(x, 12, raw = TRUE)3
15.3293                    -4.1005
poly(x, 12, raw = TRUE)4   poly(x, 12, raw = TRUE)5
0.3686                         NA
poly(x, 12, raw = TRUE)6   poly(x, 12, raw = TRUE)7
NA                         NA
poly(x, 12, raw = TRUE)8   poly(x, 12, raw = TRUE)9
NA                         NA
poly(x, 12, raw = TRUE)10  poly(x, 12, raw = TRUE)11
NA                         NA
poly(x, 12, raw = TRUE)12
NA

I believe that what is needed is a check on the 'rank' result after poly() calls the qr() function.

System info:
R version: 2.6.2
Windows XP Pro; also get same results on Linux x_64 dual-core system.

[I thought I submitted this via the website yesterday, but I can find no trace of it. I apologize if this is a duplicate, but I don't think it is.]

--
Russell V. Lenth, Professor
Department of Statistics
& Actuarial Science            (319)335-0814    FAX (319)335-3017
The University of Iowa           russell-lenth_at_uiowa.edu
Iowa City, IA 52242  USA         http://www.stat.uiowa.edu/~rlenth/

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