Generate the Bspline basis matrix for a natural cubic spline.
1 2 
x 
the predictor variable. Missing values are allowed. 
df 
degrees of freedom. One can supply 
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 
intercept 
if 
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 
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.
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()
.
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.
bs
, predict.ns
, SafePrediction
1 2 3 4 5 6 7 8 9 10 11  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)))

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