ns
Generate a Basis Matrix for Natural Cubic Splines
Generate the B-spline 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
dfrather than knots;ns()then choosesdf - 1 - interceptknots at suitably chosen quantiles ofx(which will ignore missing values). The default,df = NULL, sets the number of inner knots aslength(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 B-spline basis (default the range of the data). If both
knotsandBoundary.knotsare supplied, the basis parameters do not depend onx. Data can extend beyondBoundary.knots
Details
ns is based on the function splineDesign. It
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
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)
# NOT RUN {
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
# }