fda (version 2.2.6)

smooth.basisPar: Smooth Data Using a Directly Specified Roughness Penalty

Description

Smooth (argvals, y) data with roughness penalty defined by the remaining arguments.

Usage

smooth.basisPar(argvals, y, fdobj=NULL, Lfdobj=NULL,
      lambda=0, estimate=TRUE, penmat=NULL,
      wtvec=NULL, fdnames=NULL)

Arguments

argvals

a vector of argument values correspond to the observations in array y.

y

an array containing values of curves at discrete sampling points or argument values. If the array is a matrix, the rows must correspond to argument values and columns to replications, and it will be assumed that there is only one variable per

fdobj

One of the following:

• fd

{ a functional data object (class fd) } basisfd{ a functional basis object (class basisfd), which is converted to a functional data object with the identi

Value

• The output of a call to smooth.basis, which is an object of class fdSmooth, being a list of length 8 with the following components:
• fd
  a functional data object that smooths the data.
• df
  a degrees of freedom measure of the smooth
• gcv
  the value of the generalized cross-validation or GCV criterion. If there are multiple curves, this is a vector of values, one per curve. If the smooth is multivariate, the result is a matrix of gcv values, with columns corresponding to variables.
• SSE
  the error sums of squares. SSE is a vector or a matrix of the same size as 'gcv'.
• penmat
  the penalty matrix.
• y2cMap
  the matrix mapping the data to the coefficients.
• argvals, y
  input arguments

item

• Lfdobj
• fourier
• anything else
• lambda
• estimate
• penmat
• wtvec
• fdnames
• reps
• fun

code

y

itemize

• args

Details

1. if(is.null(fdobj))fdobj <- create.bspline.basis(argvals). Else if(is.integer(fdobj)) fdobj <- create.bspline.basis(argvals, norder = fdobj)

2. fdPar

3. smooth.basis

References

Ramsay, James O., and Silverman, Bernard W. (2006), 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

Data2fd, df2lambda, fdPar, lambda2df, lambda2gcv, plot.fd, project.basis, smooth.basis, smooth.fd, smooth.monotone, smooth.pos

Examples

##
## simplest call
##
girlGrowthSm <- with(growth, smooth.basisPar(argvals=age, y=hgtf))
plot(girlGrowthSm$fd, xlab="age", ylab="height (cm)",
         main="Girls in Berkeley Growth Study" )
plot(deriv(girlGrowthSm$fd), xlab="age", ylab="growth rate (cm / year)",
         main="Girls in Berkeley Growth Study" )
plot(deriv(girlGrowthSm$fd, 2), xlab="age",
        ylab="growth acceleration (cm / year^2)",
        main="Girls in Berkeley Growth Study" )
#  Undersmoothed with lambda = 0

##
## Another simple call
##
lipSm <- smooth.basisPar(liptime, lip)
plot(lipSm)
#  Undersmoothed with lambda = 0
plot(smooth.basisPar(liptime, lip, lambda=1e-9))
# more sensible

##
## A third example
##

x <- seq(-1,1,0.02)
y <- x + 3*exp(-6*x^2) + sin(1:101)/2
# sin not rnorm to make it easier to compare
# results across platforms

#  set up a saturated B-spline basis
basisobj101 <- create.bspline.basis(x)
fdParobj101 <- fdPar(basisobj101, 2, lambda=1)
result101  <- smooth.basis(x, y, fdParobj101)

resultP <- smooth.basisPar(argvals=x, y=y, fdobj=basisobj101, lambda=1)
stopifnot(
all.equal(result101, resultP)
)
# TRUE

result4 <- smooth.basisPar(argvals=x, y=y, fdobj=4, lambda=1)
stopifnot(
all.equal(resultP, result4)
)
# TRUE

result4. <- smooth.basisPar(argvals=x, y=y, lambda=1)
stopifnot(
all.equal(resultP, result4.)
)
# TRUE

with(result4, c(df, gcv)) #  display df and gcv measures

result4.4 <- smooth.basisPar(argvals=x, y=y, lambda=1e-4)
with(result4.4, c(df, gcv)) #  display df and gcv measures
# less smoothing, more degrees of freedom, better fit

plot(result4.4)
lines(result4, col='green')
lines(result4$fd, col='green') # same as lines(result4, ...)

result4.0 <- smooth.basisPar(x, y, basisobj101, lambda=0)

result4.0a <- smooth.basisPar(x, y, lambda=0)
stopifnot(
all.equal(result4.0, result4.0a)
)

with(result4.0, c(df, gcv)) #  display df and gcv measures
# no smoothing, degrees of freedom = number of points
# but generalized cross validation = Inf
# suggesting overfitting.

##
## fdnames?
##
girlGrow12 <- with(growth, smooth.basisPar(argvals=age, y=hgtf[, 1:2],
              fdnames=c('age', 'girl', 'height')) )
girlGrow12. <- with(growth, smooth.basisPar(argvals=age, y=hgtf[, 1:2],
    fdnames=list(age=age, girl=c('Carol', 'Sally'), value='height')) )

##
## Fourier basis with harmonic acceleration operator
##
daybasis65 <- create.fourier.basis(rangeval=c(0, 365), nbasis=65)
daytemp.fdSmooth <- with(CanadianWeather, smooth.basisPar(day.5,
       dailyAv[,,"Temperature.C"],
       daybasis65, fdnames=list("Day", "Station", "Deg C")) )