B-Spline Basis for Polynomial Splines

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,
  derivs = 0L,
  integral = FALSE,
  ...
)

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.
derivs: A nonnegative integer specifying the order of derivatives of B-splines. The default value is 0L for B-spline basis functions.
integral: A logical value. If TRUE, the corresponding integrals of spline basis functions will be returned. The default value is FALSE.
...: Optional arguments that are not used.

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.

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.

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))
#>              1         2         3          4         5         6         7
#> [1,] 0.1984954 0.5584491 0.2213542 0.02170139 0.0000000 0.0000000 0.0000000
#> [2,] 0.0000000 0.0000000 0.0000000 0.05628999 0.3604115 0.4564141 0.1268844