poly
Compute Orthogonal Polynomials
Returns or evaluates orthogonal polynomials of degree 1 to
degree over the specified set of points x: these are all
orthogonal to the constant polynomial of degree 0. Alternatively,
evaluate raw polynomials.
- Keywords
- math
Usage
poly(x, …, degree = 1, coefs = NULL, raw = FALSE, simple = FALSE)
polym (…, degree = 1, coefs = NULL, raw = FALSE)# S3 method for poly
predict(object, newdata, …)
Arguments
- x, newdata
a numeric vector at which to evaluate the polynomial.
xcan also be a matrix. Missing values are not allowed inx.- degree
the degree of the polynomial. Must be less than the number of unique points when
rawis false, as by default.- coefs
for prediction, coefficients from a previous fit.
- raw
if true, use raw and not orthogonal polynomials.
- simple
logical indicating if a simple matrix (with no further
attributesbutdimnames) should be returned. For speedup only.- object
an object inheriting from class
"poly", normally the result of a call topolywith a single vector argument.- …
poly,polym: further vectors.predict.poly: arguments to be passed to or from other methods.
Details
Although formally degree should be named (as it follows
…), an unnamed second argument of length 1 will be
interpreted as the degree, such that poly(x, 3) can be used in
formulas.
The orthogonal polynomial is summarized by the coefficients, which can
be used to evaluate it via the three-term recursion given in Kennedy
& Gentle (1980, pp.343--4), and used in the predict part of
the code.
poly using … is just a convenience wrapper for
polym: coef is ignored. Conversely, if polym is
called with a single argument in … it is a wrapper for
poly.
Value
For poly and polym() (when simple=FALSE and
coefs=NULL as per default):
A matrix with rows corresponding to points in x and columns
corresponding to the degree, with attributes "degree" specifying
the degrees of the columns and (unless raw = TRUE)
"coefs" which contains the centering and normalization
constants used in constructing the orthogonal polynomials and
class c("poly", "matrix").
For poly(*, simple=TRUE), polym(*, coefs=<non-NULL>),
and predict.poly(): a matrix.
Note
This routine is intended for statistical purposes such as
contr.poly: it does not attempt to orthogonalize to
machine accuracy.
References
Chambers, J. M. and Hastie, T. J. (1992) Statistical Models in S. Wadsworth & Brooks/Cole.
Kennedy, W. J. Jr and Gentle, J. E. (1980) Statistical Computing Marcel Dekker.
See Also
cars for an example of polynomial regression.
Examples
library(stats)
# NOT RUN {
od <- options(digits = 3) # avoid too much visual clutter
(z <- poly(1:10, 3))
predict(z, seq(2, 4, 0.5))
zapsmall(poly(seq(4, 6, 0.5), 3, coefs = attr(z, "coefs")))
zm <- zapsmall(polym ( 1:4, c(1, 4:6), degree = 3)) # or just poly():
(z1 <- zapsmall(poly(cbind(1:4, c(1, 4:6)), degree = 3)))
## they are the same :
stopifnot(all.equal(zm, z1, tol = 1e-15))
## poly(<matrix>, df) --- used to fail till July 14 (vive la France!), 2017:
m2 <- cbind(1:4, c(1, 4:6))
pm2 <- zapsmall(poly(m2, 3)) # "unnamed degree = 3"
stopifnot(all.equal(pm2, zm, tol = 1e-15))
options(od)
# }