df2lambda: Convert Degrees of Freedom to a Smoothing Parameter Value
In fda: Functional Data Analysis

Description Usage Arguments Details Value See Also Examples

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 multipler $lambda$.

1 2	df2lambda(argvals, basisobj, wtvec=rep(1, n), Lfdobj=0, df=nbasis)

`argvals`	a vector containing rgument 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
plot(hgtffd)