Generate the B-spline basis matrix for a natural cubic spline.
ns(x, df = NULL, knots = NULL, intercept = FALSE, Boundary.knots = range(x))
the predictor variable. Missing values are allowed.
degrees of freedom. One can supply
breakpoints that define the spline. The default is no
knots; together with the natural boundary conditions this results in
a basis for linear regression on
boundary points at which to impose the natural
boundary conditions and anchor the B-spline basis (default the range
of the data). If both
ns is based on the function
generates a basis matrix for representing the family of
piecewise-cubic splines with the specified sequence of
interior knots, and the natural boundary conditions. These enforce
the constraint that the function is linear beyond the boundary knots,
which can either be supplied or default to the extremes of the
A primary use is in modeling formula to directly specify a natural spline term in a model: see the examples.
A matrix of dimension
length(x) * df where either
supplied or if
knots were supplied,
df = length(knots) + 1 + intercept.
Attributes are returned that correspond to the arguments to
and explicitly give the
Boundary.knots etc for
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) ns(women$height, df = 5) summary(fm1 <- lm(weight ~ ns(height, df = 5), data = women)) ## To see what knots were selected attr(terms(fm1), "predvars") ## example of safe prediction plot(women, xlab = "Height (in)", ylab = "Weight (lb)") ht <- seq(57, 73, length.out = 200) ; nD <- data.frame(height = ht) lines(ht, p1 <- predict(fm1, nD)) stopifnot(all.equal(p1, predict(update(fm1, . ~ splines::ns(height, df=5)), nD))) # not true in R < 3.5.0
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