bSpline
B-Spline Basis for Polynomial Splines
This function generates the B-spline basis matrix for a polynomial spline.
Usage
bSpline(x, df = NULL, knots = NULL, degree = 3L, intercept = FALSE,
Boundary.knots = range(x, na.rm = TRUE), ...)Arguments
- x
The predictor variable. Missing values are allowed and will be returned as they were.
- df
Degrees of freedom. One can specify
dfrather thanknots, then the function chooses "df - degree" (minus one if there is an intercept) knots at suitable quantiles ofx(which will ignore missing values). The default,NULL, corresponds to no inner knots, i.e., "degree - intercept". Ifknotswas specified,dfspecified 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. See alsoBoundary.knots.- degree
Non-negative integer degree of the piecewise polynomial. The default value is 3 for cubic splines. Zero degree is allowed for this function, which is the only difference compared with
bsin packagesplines.- intercept
If
TRUE, an intercept is included in the basis; Default isFALSE.- Boundary.knots
Boundary points at which to anchor the B-spline basis. By default, they are the range of the non-
NAdata. If bothknotsandBoundary.knotsare supplied, the basis parameters do not depend onx. Data can extend beyondBoundary.knots.- ...
Optional arguments for future usage.
Details
It is an augmented function of bs in package
splines for B-spline basis that allows piecewise constant (close on
the left, open on the right) spline basis with zero degree. When the
argument degree is greater than zero, it internally calls
bs and generates a basis matrix for representing the
family of piecewise polynomials with the specified interior knots and
degree, evaluated at the values of x. The function has the same
arguments with bs for ease usage.
Value
A matrix of dimension length(x) by
df = degree + length(knots) (plus one if intercept is included).
Attributes that correspond to the arguments specified are returned
for usage of other functions in this package.
See Also
predict.bSpline2 for evaluation at given (new) values;
dbs, deriv.bSpline2 for derivatives;
ibs for integral of B-splines;
mSpline for M-splines;
iSpline for I-splines;
cSpline for C-splines.
Examples
# NOT RUN {
library(splines2)
x <- seq.int(0, 1, 0.01)
knots <- c(0.3, 0.5, 0.6)
bsMat <- bSpline(x, knots = knots, degree = 0, intercept = TRUE)
library(graphics)
matplot(x, bsMat, type = "l", ylab = "Piecewise constant B-spline bases")
abline(v = knots, lty = 2, col = "gray")
# }