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
df
rather 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
, takes the number of inner knots aslength(knots)
. If that is zero as per default, that corresponds todf = 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
3
for 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-
NA
data). If bothknots
andBoundary.knots
are supplied, the basis parameters do not depend onx
. Data can extend beyondBoundary.knots
.
Details
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.
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)
# 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)))
# }