bs {splines}  R Documentation 
Generate the Bspline basis matrix for a polynomial spline.
bs(x, df = NULL, knots = NULL, degree = 3, intercept = FALSE,
Boundary.knots = range(x), warn.outside = TRUE)
x 
the predictor variable. Missing values are allowed. 
df 
degrees of freedom; one can specify 
knots 
the internal breakpoints that define the
spline. The default is 
degree 
degree of the piecewise polynomial—default is 
intercept 
if 
Boundary.knots 
boundary points at which to anchor the Bspline
basis (default the range of the non 
warn.outside 

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.
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()
.
Douglas Bates and Bill Venables. Tweaks by R Core, and a patch
fixing extrapolation “outside” Boundary.knots
by Trevor
Hastie.
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.
ns
, poly
, smooth.spline
,
predict.bs
, SafePrediction
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)))