bs
B-Spline Basis for Polynomial Splines
Generate the B-spline basis matrix for a polynomial spline.
- Keywords
- smooth
Usage
bs(x, df = NULL, knots = NULL, degree = 3, intercept = FALSE,
Boundary.knots = range(x))Arguments
- x
- the predictor variable. Missing values are allowed.
- df
- degrees of freedom; one can specify
dfrather thanknots;bs()then choosesdf-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. - 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
- degree of the piecewise polynomial---default is
3for cubic splines. - intercept
- if
TRUE, an intercept is included in the basis; default isFALSE. - Boundary.knots
- boundary points at which to anchor the B-spline
basis (default the range of the non-
NAdata). If bothknotsandBoundary.knotsare supplied, the basis parameters do not depend onx. Data can extend beyondBoundary.knots.
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.
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().
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.
See Also
Examples
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)))