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.

the model matrix, whose columns represent scalar predictors.

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).

Value

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

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.

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

Run this code

# NOT RUN {
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)
# }

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