B-Spline Basis for Polynomial Splines

Generate the B-spline basis matrix for a polynomial spline.

bs(x, df = NULL, knots = NULL, degree = 3, intercept = FALSE, Boundary.knots = range(x))
the predictor variable. Missing values are allowed.
degrees of freedom; one can specify df rather than knots; bs() then 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.
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.
degree of the piecewise polynomial---default is 3 for cubic splines.
if TRUE, an intercept is included in the basis; default is FALSE.
boundary points at which to anchor the B-spline basis (default the range of the data). If both knots and Boundary.knots are supplied, the basis parameters do not depend on x. Data can extend beyond Boundary.knots.

bs is based on the function spline.des. It generates a basis matrix for representing the family of piecewise polynomials with the specified interior knots and degree, evaluated at the values of x. A primary use is in modeling formulas to directly specify a piecewise polynomial term in a model.


A matrix of dimension c(length(x), df), where either df was supplied or if knots were supplied, df = length(knots) + degree plus one if there is an intercept. Attributes are returned that correspond to the arguments to bs, and explicitly give the knots, Boundary.knots etc for use by


Hastie, T. J. (1992) Generalized additive models. Chapter 7 of Statistical Models in S eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.

See Also

ns, poly, smooth.spline,, SafePrediction

  • bs
library(splines) require(stats); require(graphics) bs(women$height, df = 5) summary(fm1 <- lm(weight ~ bs(height, df = 5), data = women)) ## example of safe prediction plot(women, xlab = "Height (in)", ylab = "Weight (lb)") ht <- seq(57, 73, length.out = 200) lines(ht, predict(fm1, data.frame(height = ht)))
Documentation reproduced from package splines, version 3.1.0, License: Part of R 3.1.0

Community examples

Looks like there are no examples yet.