R: B-Spline Basis for Polynomial Splines

bSpline {splines2}

R Documentation

B-Spline Basis for Polynomial Splines

Description

Generates the B-spline basis matrix representing the family of piecewise polynomials with the specified interior knots, degree, and boundary knots, evaluated at the values of x.

Usage

bSpline(
  x,
  df = NULL,
  knots = NULL,
  degree = 3L,
  intercept = FALSE,
  Boundary.knots = NULL,
  ...
)

Arguments

`x`	The predictor variable. Missing values are allowed and will be returned as they are.
`df`	Degree of freedom that equals to the column number of the returned matrix. One can specify `df` rather than `knots`, then the function chooses `df - degree - as.integer(intercept)` internal knots at suitable quantiles of `x` ignoring missing values and those `x` outside of the boundary. If internal knots are specified via `knots`, the specified `df` will be ignored.
`knots`	The internal breakpoints that define the splines. The default is `NULL`, which results in a basis for ordinary polynomial regression. Typical values are the mean or median for one knot, quantiles for more knots.
`degree`	A nonnegative integer specifying the degree of the piecewise polynomial. The default value is `3` for cubic splines. Zero degree is allowed for piecewise constant basis functions.
`intercept`	If `TRUE`, the complete basis matrix will be returned. Otherwise, the first basis will be excluded from the output.
`Boundary.knots`	Boundary points at which to anchor the splines. By default, they are the range of `x` excluding `NA`. If both `knots` and `Boundary.knots` are supplied, the basis parameters do not depend on `x`. Data can extend beyond `Boundary.knots`.
`...`	Optional arguments that are not used.

Details

This function extends the bs() function in the splines package for B-spline basis by allowing piecewise constant (left-closed and right-open except on the right boundary) spline basis of degree zero.

Value

A numeric matrix of length(x) rows and df columns if df is specified or length(knots) + degree + as.integer(intercept) columns if knots are specified instead. Attributes that correspond to the arguments specified are returned mainly for other functions in this package.

References

De Boor, Carl. (1978). A practical guide to splines. Vol. 27. New York: Springer-Verlag.

Examples

library(splines2)

x <- seq.int(0, 1, 0.01)
knots <- c(0.3, 0.5, 0.6)

## cubic B-splines
bsMat <- bSpline(x, knots = knots, degree = 3, intercept = TRUE)

op <- par(mar = c(2.5, 2.5, 0.2, 0.1), mgp = c(1.5, 0.5, 0))
matplot(x, bsMat, type = "l", ylab = "Cubic B-splines")
abline(v = knots, lty = 2, col = "gray")

## reset to previous plotting settings
par(op)

## the first derivaitves
d1Mat <- deriv(bsMat)

## the second derivaitves
d2Mat <- deriv(bsMat, 2)

## evaluate at new values
predict(bsMat, c(0.125, 0.801))

[Package splines2 version 0.4.2 Index]