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-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
- degree of the piecewise polynomial---default is
3for cubic splines.
TRUE, an intercept is included in the basis; default is
- boundary points at which to anchor the B-spline
basis (default the range of the non-
NAdata). If both
Boundary.knotsare supplied, the basis parameters do not depend on
x. Data can extend beyond
bs is based on the function
It generates a basis matrix for
representing the family of piecewise polynomials with the specified
interior knots and degree, evaluated at the values of
primary use is in modeling formulas to directly specify a piecewise
polynomial term in a model. When
Boundary.knots are set inside
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.
A matrix of dimension
c(length(x), df), where either
was supplied or if
knots were supplied,
length(knots) + degree plus one if there is an intercept. Attributes
are returned that correspond to the arguments to
explicitly give the
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.
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)))