df2lambda {fda}

Convert Degrees of Freedom to a Smoothing Parameter Value

Description

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 $lambda$.

Usage

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

Arguments

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.

Details

The conversion requires a one-dimensional optimization and may be therefore computationally intensive.

Value

a positive smoothing parameter value $lambda$

References

Ramsay, James O., Hooker, Giles, and Graves, Spencer (2009), Functional data analysis with R and Matlab, Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2005), Functional Data Analysis, 2nd ed., Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2002), Applied Functional Data Analysis, Springer, New York.

See Also

lambda2df, lambda2gcv

Examples

#  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(fd(matrix(0,nbasis,1),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)