Convert Degrees of Freedom to a Smoothing Parameter Value
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 $lambda$
# 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)
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