bs: B-Spline Basis for Polynomial Splines

Description

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

Usage

bs(x, df = NULL, knots = NULL, degree = 3, intercept = FALSE,
   Boundary.knots = range(x))

Arguments

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.

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 also Boundary.knots.

degree

degree of the piecewise polynomial---default is 3 for cubic splines.

intercept

if TRUE, an intercept is included in the basis; default is FALSE.

Boundary.knots

boundary points at which to anchor the B-spline basis (default 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.

Value

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 predict.bs().

Details

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. When Boundary.knots are set inside range(x), bs() now uses a ‘pivot’ inside the respective boundary knot which is important for derivative evaluation. In R versions \(\le\) 3.2.2, the boundary knot itself had been used as pivot, which lead to somewhat wrong extrapolations.

References

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.

Examples

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)))