Description Usage Arguments Details Author(s) References See Also Examples
These functions compute the basis of piecewiselinear spline such that,
depending on the argument marginal
, the coefficients can be
interpreted as (1) slopes of consecutive spline segments, or (2) slope change
at consecutive knots.
1 2 3 4 5 
x 
numeric vector, the variable 
knots 
numeric vector of knot positions 
marginal 
logical, how to parametrize the spline, see Details 
names 
character, vector of names for constructed variables 
q 
numeric, a single scalar greater or equal to 2 for a number of
equalfrequency intervals along 
na.rm 
logical, whether 
... 
other arguments passed to 
n 
integer greater than 2, knots are computed such that they cut

If marginal
is FALSE
(default) the coefficients of the spline
correspond to slopes of the consecutive segments. If it is TRUE
the
first coefficient correspond to the slope of the first segment. The
consecutive coefficients correspond to the change in slope as compared to the
previous segment.
Function qlspline
wraps lspline
and calculates the knot
positions to be at quantiles of x
. If q
is a numerical scalar
greater or equal to 2, the quantiles are computed at seq(0, 1,
length.out = q + 1)[c(1, q+1)]
, i.e. knots are at q
tiles of the
distribution of x
. Alternatively, q
can be a vector of values
in [0; 1] specifying the quantile probabilities directly (the vector is
passed to argument probs
of quantile
).
Function elspline
wraps lspline
and computes the knot positions
such that they cut the range of x
into n
equalwidth intervals.
This function is inspired by Stata command mkspline
and function ares::lspline
from Junger & Ponce de
Leon (2011). As such, the implementation follows Greene
(2003), chapter 7.2.5
Poirier, Dale J., and Steven G. Garber. (1974) "The Determinants of Aerospace Profit Rates 19511971." Southern Economic Journal: 228238.
Greene, William H. (2003) Econometric analysis. Pearson Education
Junger & Ponce de Leon (2011) "ares: Environment air pollution epidemiology: a library for timeseries analysis". R package version 0.7.2 retrieved from CRAN archives.
See the package vignette.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34  # Data from a quadratic polynomial
set.seed(666)
x < rnorm(100, 5, 2)
y < (x5)^2 + rnorm(100)
plot(x, y)
#  Marginal and nonmarginal parametrisations
m.nonmarginal < lm(y ~ lspline(x, 5))
m.marginal < lm(y ~ lspline(x, 5, marginal=TRUE))
# Slope of consecutive segments
coef(m.nonmarginal)
# Slope change and consecutive knots
coef(m.marginal)
# Identical predicted values
identical( fitted(m.nonmarginal), fitted(m.marginal))
#  Different ways to place knots
# Manually: knots at x=4 and x=6
m1 < lm(y ~ lspline(x, c(4, 6)))
# 2 knots at terciles of 'x'
m2 < lm(y ~ qlspline(x, 3))
# 3 knots dividing range of 'x' into 4 equalwidth intervals
m3 < lm(y ~ elspline(x, 4))
# Graphically
ox < seq(min(x), max(x), length=100)
lines(ox, predict(m1, data.frame(x=ox)), col="red")
lines(ox, predict(m2, data.frame(x=ox)), col="blue")
lines(ox, predict(m3, data.frame(x=ox)), col="green")
legend("topright",
legend=c("m1: lspline", "m2: qlspline", "m3: elspline"),
col=c("red", "blue", "green"),
bty="n", lty=1)

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