This function generates the B-spline basis matrix for a polynomial spline.

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. Degrees of freedom. One can specify df rather than knots, then the function chooses "df - degree" (minus one if there is an intercept) knots at suitable quantiles of x (which will ignore missing values). The default, NULL, corresponds to no inner knots, i.e., "degree - intercept". If knots was specified, df specified will be ignored. 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 also Boundary.knots. 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 bs in package splines. If TRUE, an intercept is included in the basis; Default is FALSE. Boundary points at which to anchor the B-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 for future 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.

## 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.

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.
library(splines2)
matplot(x, bsMat, type = "l", ylab = "Piecewise constant B-spline bases")abline(v = knots, lty = 2, col = "gray") 