ns
Generate a Basis Matrix for Natural Cubic Splines
Generate the Bspline basis matrix for a natural cubic spline.
 Keywords
 smooth
Usage
ns(x, df = NULL, knots = NULL, intercept = FALSE, Boundary.knots = range(x))
Arguments
 x
 the predictor variable. Missing values are allowed.
 df
 degrees of freedom. One can supply
df
rather than knots;ns()
then choosesdf  1  intercept
knots at suitably chosen quantiles ofx
(which will ignore missing values). The default,df = 1
, corresponds to no knots.  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 alsoBoundary.knots
.  intercept
 if
TRUE
, an intercept is included in the basis; default isFALSE
.  Boundary.knots
 boundary points at which to impose the natural
boundary conditions and anchor the Bspline basis (default the range
of the data). If both
knots
andBoundary.knots
are supplied, the basis parameters do not depend onx
. Data can extend beyondBoundary.knots
Details
ns
is based on the function spline.des
. It
generates a basis matrix for representing the family of
piecewisecubic 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
data.
A primary use is in modeling formula to directly specify a natural spline term in a model: see the examples.
Value

A matrix of dimension
length(x) * df
where either df
was
supplied or if knots
were supplied,
df = length(knots) + 1 + intercept
.
Attributes are returned that correspond to the arguments to ns
,
and explicitly give the knots
, Boundary.knots
etc for
use by predict.ns()
.
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)
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)))
Community examples
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