splines2 (version 0.3.1)

dbs: Derivatives of B-Spline Basis

Description

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. By default, it is 1L for the first derivative.

df

Degree of freedom that equals to the column number of 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 spline. 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 non-negative integer specifying the degree of the piecewise polynomial. The default value is 3 for cubic splines. Zero degree is allowed for piece-wise constant bases.

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 spline basis. By default, they are the range of the non-NA data. 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 with 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 for usage of 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 close form recursion formula. At knots, the derivative is defined to be the right derivative.

References

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

See Also

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

Examples

# NOT RUN {
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))
# }

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