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,
takes the number of inner knots as length(knots). If that is
zero as per default, that corresponds to df = 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 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.
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().
bs is based on the function splineDesign.
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.
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.
# NOT RUN {
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)))
# }