df2lambda | R Documentation |
The degree of roughness of an estimated function is controlled by a smoothing parameter $lambda$ that directly multiplies the penalty. However, it can be difficult to interpret or choose this value, and it is often easier to determine the roughness by choosing a value that is equivalent of the degrees of freedom used by the smoothing procedure. This function converts a degrees of freedom value into a multiplier $lambda$.
df2lambda(argvals, basisobj, wtvec=rep(1, n), Lfdobj=0,
df=nbasis)
argvals |
a vector containing argument values associated with the values to be smoothed. |
basisobj |
a basis function object. |
wtvec |
a vector of weights for the data to be smoothed. |
Lfdobj |
either a nonnegative integer or a linear differential operator object. |
df |
the degrees of freedom to be converted. |
The conversion requires a one-dimensional optimization and may be therefore computationally intensive.
a positive smoothing parameter value $lambda$
lambda2df
,
lambda2gcv
# Smooth growth curves using a specified value of
# degrees of freedom.
# Set up the ages of height measurements for Berkeley data
age <- c( seq(1, 2, 0.25), seq(3, 8, 1), seq(8.5, 18, 0.5))
# Range of observations
rng <- c(1,18)
# Set up a B-spline basis of order 6 with knots at ages
knots <- age
norder <- 6
nbasis <- length(knots) + norder - 2
hgtbasis <- create.bspline.basis(rng, nbasis, norder, knots)
# Find the smoothing parameter equivalent to 12
# degrees of freedom
lambda <- df2lambda(age, hgtbasis, df=12)
# Set up a functional parameter object for estimating
# growth curves. The 4th derivative is penalyzed to
# ensure a smooth 2nd derivative or acceleration.
Lfdobj <- 4
growfdPar <- fdPar(hgtbasis, Lfdobj, lambda)
# Smooth the data. The data for the girls are in matrix
# hgtf.
hgtffd <- smooth.basis(age, growth$hgtf, growfdPar)$fd
# Plot the curves
oldpar <- par(no.readonly=TRUE)
plot(hgtffd)
par(oldpar)
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