smooth.monotone | Language Reference for FDA Library
|
This function is identical to
smooth.monotone
, but uses
code written in C+ to speed computation. The following material is
identical to that for
smooth.monotone
.
When the discrete data that are observed reflect a smooth strictly increasing or strictly decreasing function, it is often desirable to smooth the data with a strictly monotone function, even though the data themselves may not be monotone due to observational error. An example is when data are collected on the size of a growing organism over time. This function computes such a smoothing function, but, unlike other smoothing functions, for only for one curve at a time.
The smoothing function minimizes a weighted error sum of squares criterion. This minimization requires iteration, and therefore is more computationally intensive than normal smoothing.
smooth.monotone(x, y, wt=rep(1,nobs), WfdParobj, zmat=matrix(1,nobs,1), conv=.0001, iterlim=20, active=c(F,rep(T,ncvec-1)), dbglev=1)
iternum+1
by 5 matrix containing the iteration
history.
The smoothing function f(x) is determined by three objects that need to be estimated from the data:
In addition, it is possible to have the intercept
b0
depend in turn on the values of one or more covariates through the
design matrix
>Zmat
>as follows:
b0 = Zc. In this case, the single
intercept coefficient is replaced by the regression coefficients
in vector c multipying the design matrix.
# Estimate the acceleration functions for growth curves # See the analyses of the growth data. # 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) # First set up a basis for monotone smooth # We use b-spline basis functions of order 6 # Knots are positioned at the ages of observation. norder <- 6 nbasis <- nage + norder - 2 wbasis <- create.bspline.basis(rng, nbasis, norder, age) # starting values for coefficient cvec0 <- matrix(0,nbasis,1) Wfd0 <- fd(cvec0, wbasis) # set up functional parameter object Lfdobj <- 3 # penalize curvature of acceleration lambda <- 10^(-0.5) # smoothing parameter growfdPar <- fdPar(Wfd0, Lfdobj, lambda) # Set up wgt vector wgt <- rep(1,nage) # Smooth the data for the first girl hgt1 = hgtf[,1] result <- smooth.monotoneC(age, hgt1, wgt, growfdPar) # Extract the functional data object and regression # coefficients Wfd <- result$Wfdobj beta <- result$beta # Evaluate the fitted height curve over a fine mesh agefine <- seq(1,18,len=101) hgtfine <- beta[1] + beta[2]*eval.monfd(agefine, Wfd) # Plot the data and the curve plot(age, hgt1, type="p") lines(agefine, hgtfine) # Evaluate the acceleration curve accfine <- beta[2]*eval.monfd(agefine, Wfd, 2) # Plot the acceleration curve plot(agefine, accfine, type="l") lines(c(1,18),c(0,0),lty=4)