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
the internal breakpoints that define the
spline. The default is
degree of the piecewise polynomial—default is
boundary points at which to anchor the B-spline
basis (default the range of the non-
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.
Boundary.knots are set inside
bs() now uses a ‘pivot’ inside the respective boundary
knot which is important for derivative evaluation. In R versions
<= 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
Douglas Bates and Bill Venables. Tweaks by R Core, and a patch
fixing extrapolation “outside”
Boundary.knots by Trevor
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)))
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