slp: Shifted Legendre Polynomials
In qrcm: Quantile Regression Coefficients Modeling

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Computes shifted Legendre polynomials.

1	slp(p, k = 3, intercept = FALSE)

`p`	the variable for which to compute the polynomials. Must be `0 <= p <= 1`.
`k`	the degree of the polynomial.
`intercept`	logical. If `TRUE`, the polynomials include the constant term.

Shifted Legendre polynomials (SLP) are orthogonal polynomial functions in (0,1) that can be used to build a spline basis, typically within a call to iqr. The constant term is omitted unless intercept = TRUE: for example, the first two SLP are (2*p - 1, 6*p^2 - 6*p + 1), but slp(p, k = 2) will only return (2*p, 6*p^2 - 6*p).

An object of class “slp”, i.e., a matrix with the same number of rows as p, and with k columns named slp1, slp2, ... containing the SLP of the corresponding orders. The value of k is reported as attribute.

The estimation algorithm of iqr is optimized for objects of class “slp”, which means that using formula.p = ~ slp(p, k) instead of formula.p = ~ p + I(p^2) + ... + I(p^k) will result in a quicker computation, even with k = 1, with equivalent results. The default for iqr is formula.p = ~ slp(p, k = 3).

Paolo Frumento paolo.frumento@unipi.it

Refaat El Attar (2009), Legendre Polynomials and Functions, CreateSpace, ISBN 978-1-4414-9012-4.

plf, for piecewise linear functions in the unit interval.

  p <- seq(0,1,0.1)
  slp(p, k = 1) # = 2*p
  slp(p, k = 1, intercept = TRUE) # = 2*p - 1 (this is the true SLP of order 1)
  slp(p, k = 3) # a linear combination of (p, p^2, p^3), with slp(0,k) = 0