Produces the derivatives of given order of B-splines.

## Usage

dbs(
x,
derivs = 1L,
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.

derivs

A positive integer specifying the order of derivative. The default value is 1L for the first derivative.

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.

## 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 provides a more user-friendly interface and a more consistent handling for NA's than splines::splineDesign() for derivatives of B-splines. The implementation is based on the closed-form recursion formula. At knots, the derivative is defined to be the right derivative except at the right boundary knot.

## References

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

bSpline for B-splines; ibs for integrals of B-splines.

## Examples

library(splines2)
x <- seq.int(0, 1, 0.01)
knots <- c(0.2, 0.4, 0.7)
## the second derivative of cubic B-splines with three internal knots
dMat <- dbs(x, derivs = 2L, knots = knots, intercept = TRUE)

## compare with the results from splineDesign
ord <- attr(dMat, "degree") + 1L
bKnots <- attr(dMat, "Boundary.knots")
aKnots <- c(rep(bKnots[1L], ord), knots, rep(bKnots[2L], ord))
res <- splines::splineDesign(aKnots, x = x, derivs = 2L)
stopifnot(all.equal(res, dMat, check.attributes = FALSE))