R: Compute Orthogonal Polynomials

poly {stats} | R Documentation

## Compute Orthogonal Polynomials

### Description

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.

### Usage

    poly(x, ..., degree = 1, coefs = NULL, raw = FALSE, simple = FALSE)
    polym  (..., degree = 1, coefs = NULL, raw = FALSE)

    ## S3 method for class 'poly'
    predict(object, newdata, ...)

### Arguments

`x, newdata` | a numeric vector at which to evaluate the polynomial. `x` can also be a matrix. Missing values are not allowed in `x`.
`degree` | the degree of the polynomial. Must be less than the number of unique points when `raw` is 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 `attributes` but `dimnames`) should be returned. For speedup only.
`object` | an object inheriting from class `"poly"`, normally the result of a call to `poly` with 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.

### Author(s)

R Core Team. Keith Jewell (Campden BRI Group, UK) contributed improvements for correct prediction on subsets.

### 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

`contr.poly`.

`cars` for an example of polynomial regression.

### Examples

    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)

[Package stats version 4.0.5 Index]