Generate a Basis Matrix for Natural Cubic Splines
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
dfrather than knots;
df - 1 - interceptknots at suitably chosen quantiles of
x(which will ignore missing values). The default,
df = 1, corresponds to no knots.
- 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
x. Typical values are the mean or median for one knot, quantiles for more knots. See also
TRUE, an intercept is included in the basis; default is
- boundary points at which to impose the natural
boundary conditions and anchor the B-spline basis (default the range
of the data). If both
Boundary.knotsare supplied, the basis parameters do not depend on
x. Data can extend beyond
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) * dfwhere either
dfwas supplied or if
df = length(knots) + 1 + intercept. Attributes are returned that correspond to the arguments to
ns, and explicitly give the
Boundary.knotsetc for use by
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) lines(ht, predict(fm1, data.frame(height = ht))) ## Consistency: x <- c(1:3, 5:6) stopifnot(identical(ns(x), ns(x, df = 1)), identical(ns(x, df = 2), ns(x, df = 2, knots = NULL)), # not true till 2.15.2 !is.null(kk <- attr(ns(x), "knots")), # not true till 1.5.1 length(kk) == 0)