refund: pwcv – R documentation

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pwcv

Pointwise cross-validation for function-on-scalar regression

Description

Estimates prediction error for a function-on-scalar regression model by leave-one-function-out cross-validation (CV), at each of a specified set of points.

Usage

pwcv(
  fdobj,
  Z,
  L = NULL,
  lambda,
  eval.pts = seq(min(fdobj$basis$range), max(fdobj$basis$range), length.out = 201),
  scale = FALSE
)

Arguments

`fdobj`	a functional data object (class `fd`) giving the functional responses.
`Z`	the model matrix, whose columns represent scalar predictors.
`L`	a row vector or matrix of linear contrasts of the coefficient functions, to be restricted to equal zero.
`lambda`	smoothing parameter: either a nonnegative scalar or a vector, of length `ncol(Z)`, of nonnegative values.
`eval.pts`	argument values at which the CV score is to be evaluated.
`scale`	logical value or vector determining scaling of the matrix `Z` (see `scale`, to which the value of this argument is passed).

Details

Integrating the pointwise CV estimate over the function domain yields the cross-validated integrated squared error, the standard overall model fit score returned by lofocv.

It may be desirable to derive the value of lambda from an appropriate call to fosr, as in the example below.

Value

A vector of the same length as eval.pts giving the CV scores.

Author(s)

Philip Reiss phil.reiss@nyumc.org

References

Reiss, P. T., Huang, L., and Mennes, M. (2010). Fast function-on-scalar regression with penalized basis expansions. International Journal of Biostatistics, 6(1), article 28. Available at https://works.bepress.com/phil_reiss/16/

Examples

require(fda)
# Canadian weather example from Reiss et al. (2010).
# The first two lines are taken from the fRegress.CV help file (package fda)
smallbasis  <- create.fourier.basis(c(0, 365), 25)
tempfd <- smooth.basis(day.5,
          CanadianWeather$dailyAv[,,"Temperature.C"], smallbasis)$fd

# Model matrices for "latitude" and "region" models
Xreg = cbind(1, model.matrix(~factor(CanadianWeather$region)-1))
Xlat = model.matrix(~CanadianWeather$coord[,1])

# Fit each model using fosr() to obtain lambda values for pwcv()
Lreg = matrix(c(0,1,1,1,1), 1)   # constraint for region model
regionmod = fosr(fdobj=tempfd, X=Xreg, con=Lreg, method="OLS")
cv.region = pwcv(tempfd, Xreg, Lreg, regionmod$lambda)

latmod = fosr(fdobj=tempfd, X=Xlat, method="OLS")
cv.lat = pwcv(tempfd, Xlat, lambda=latmod$lambda)

# The following plots may require a wide graphics window to show up correctly
par(mfrow=1:2)
# Plot the functional data
plot(tempfd, col=1, lty=1, axes=list("axesIntervals"), xlab="", ylab="Mean temperature",
     main="Temperatures at 35 stations")
box()

# Plot the two models' pointwise CV
matplot(regionmod$argvals, cbind(cv.region, cv.lat), type='l', col=1, axes=FALSE,
        xlab="", ylab="MSE.CV", main="Pointwise CV for two models")
legend(250, 40, c('Region', 'Latitude'), lty=1:2)
box()
axis(2)
axisIntervals(1)

refund

Regression with Functional Data

v0.1-23

GPL (>= 2)

Authors

Jeff Goldsmith [aut], Fabian Scheipl [aut], Lei Huang [aut], Julia Wrobel [aut, cre], Chongzhi Di [aut], Jonathan Gellar [aut], Jaroslaw Harezlak [aut], Mathew W. McLean [aut], Bruce Swihart [aut], Luo Xiao [aut], Ciprian Crainiceanu [aut], Philip T. Reiss [aut], Yakuan Chen [ctb], Sonja Greven [ctb], Lan Huo [ctb], Madan Gopal Kundu [ctb], So Young Park [ctb], David L. Miller [ctb], Ana-Maria Staicu [ctb]

Initial release

2020-12-03