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#
# fields is a package for analysis of spatial data written for
# the R software environment.
# Copyright (C) 2024 Colorado School of Mines
# 1500 Illinois St., Golden, CO 80401
# Contact: Douglas Nychka, douglasnychka@gmail.com,
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with the R software environment if not, write to the Free Software
# Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
# or see http://www.r-project.org/Licenses/GPL-2
##END HEADER
"KrigFindLambda" <- function(out, lambda.grid = NA, cost = 1,
nstep.cv = 200, rmse = NA, verbose = FALSE, tol = 1e-05,
offset = 0, y = NULL, give.warnings = TRUE) {
nt <- out$nt
np <- out$np
N <- out$N
D <- out$matrices$D
# Yet another monster function called by Krig
# but there just many simple steps ...
#
# if a y data vector is not supplied then
# use the one in the Krig object
if (is.null(y)) {
u <- out$matrices$u
tauHat.pure.error <- out$tauHat.pure.error
pure.ss <- out$pure.ss
}
else {
#with new data need to update some statistics.
out2 <- Krig.make.u(out, y = y)
u <- out2$u
tauHat.pure.error <- out2$tauHat.pure.error
pure.ss <- out2$pure.ss
}
if (verbose) {
cat("u used:", fill = TRUE)
print(u)
}
#
# generate a reasonable grid of lambda based on equally spaced
# effective degrees of freedom
if (is.na(lambda.grid[1])) {
temp.df <- seq(nt, (np - offset) * 0.95, , nstep.cv)
temp.df[1] <- temp.df[1] + 0.001
for (k in 1:nstep.cv) {
lambda.grid[k] <- Krig.df.to.lambda(temp.df[k], D)
}
}
# make sure that the grid is in sorted order
lambda.grid <- sort(lambda.grid)
nl <- length(lambda.grid)
nd <- length(D)
V <- V.model <- V.one <- lplike <- trA <- tauHat <- rep(NA,
nl)
Dl <- rep(NA, nd)
#
# this is small little list used to pass information to the
# objective functions
info <- list(matrices = list(D = D, u = u), N = N, nt = nt,
cost = cost, pure.ss = pure.ss, tauHat.pure.error = tauHat.pure.error,
offset = offset)
#
# loop over lambda values for the grid search
for (k in 1:nl) {
#
# all the wonderful things calculated for each lambda
# note the use of the info list.
V[k] <- Krig.fgcv(lambda.grid[k], info)
V.one[k] <- Krig.fgcv.one(lambda.grid[k], info)
V.model[k] <- Krig.fgcv.model(lambda.grid[k], info)
lplike[k] <- Krig.flplike(lambda.grid[k], info)
tauHat[k] <- sqrt(Krig.fs2hat(lambda.grid[k], info))
trA[k] <- Krig.ftrace(lambda.grid[k], D)
}
#
# reformat as a matrix with all these values.
gcv.grid <- cbind(lambda.grid, trA, V, V.one, V.model, tauHat,
lplike)
gcv.grid <- as.data.frame(gcv.grid)
names(gcv.grid) <- c("lambda", "trA", "GCV", "GCV.one", "GCV.model",
"tauHat", "-lnLike Prof")
# find minima over grid ifelse used to avoid 0 length vector from which.min
IMIN<- rep( NA, 6)
IMIN[1]<- which.min( gcv.grid$GCV )
IMIN[2]<- ifelse( is.na(tauHat.pure.error), NA,
which.min(gcv.grid$GCV.model) )
IMIN[3]<- which.min( gcv.grid$GCV.one)
if( is.na( rmse)){
IMIN[4] <- NA
}
else{
rangeShat<- range( gcv.grid$tauHat)
IUpcross<- max( (1:nl)[gcv.grid$tauHat< rmse] )
IMIN[4]<- ifelse( (rangeShat[1]<= rmse)&(rangeShat[2] >=rmse),
IUpcross, NA)
}
IMIN[5]<- ifelse( is.na(tauHat.pure.error), NA,
which.min(abs(gcv.grid$tauHat-tauHat.pure.error)) )
IMIN[6]<- which.min( gcv.grid[["-lnLike Prof"]])
# NOTE IMIN indexes from smallest lambda to largest lambda in grid.
warningTable<- data.frame(
IMIN, IMIN == nl, IMIN==1,
gcv.grid$lambda[IMIN],
gcv.grid$trA[IMIN],
row.names = c("GCV","GCV.model", "GCV.one", "RMSE", "pure error", "REML")
)
warning<- (warningTable[,2]|warningTable[,3])&
(!is.na(warningTable[,1]))
indRefine<- (!warningTable[,2]) & (!warningTable[,3]) &
(!is.na(warningTable[,1]))
warningTable<- cbind( warning, indRefine, warningTable )
names( warningTable)<- c("Warning","Refine","indexMIN", "leftEndpoint", "rightEndpoint",
"lambda","effdf")
# now optimze the search producing refined optima
if (verbose)
print(gcv.grid)
# setup output matrix for refined values
lambda.est <- matrix(NA, ncol = 6, nrow = 6, dimnames = list(
c("GCV", "GCV.model", "GCV.one", "RMSE", "pure error", "REML"),
c("lambda", "trA", "GCV", "tauHat","-lnLike Prof" , "converge")))
# fill in grid search estimates
for( k in 1:6){
if( !is.na(IMIN[k])){
lambda.est[k,1]<- gcv.grid$lambda[IMIN[k]]
}
}
#
# now step through the many different ways to find lambda
# This is the key to these choices:
# 1- the usual GCV proposed by Craven/Wahba
# 2- GCV where data fitting is collapsed to the mean for
# each location and each location is omitted
# 3- True leave-one-out even with replicated observations
# 4- Match estimate of tau to external value supplied (RMSE)
# 5- Match estimate of tau from the estimate based the
# pure error sum of squares obtained by the observations
# replicated at the same locations
# 6- Maxmize the restricted maxmimum likelihood (REML)
# standard GCV w/o replicates
if( verbose){
print( warningTable)
}
if(indRefine[1]){
starts <- lambda.grid[IMIN[1] + c(-1,0,1)]
out <- golden.section.search(ax=starts[1],bx=starts[2],cx=starts[3],
f=Krig.fgcv, f.extra = info, tol = tol)
lambda.est[1,1]<- out$x
lambda.est[1,6]<- out$iter
}
if( indRefine[2]) {
starts <- lambda.grid[IMIN[2] + c(-1,0,1)]
out <- golden.section.search(ax=starts[1],bx=starts[2],cx=starts[3],
f=Krig.fgcv.model, f.extra = info, tol = tol)
lambda.est[2,1]<- out$x
lambda.est[2,6]<- out$iter
}
if( indRefine[3]) {
starts <- lambda.grid[IMIN[3] + c(-1,0,1)]
out <- golden.section.search(ax=starts[1],bx=starts[2],cx=starts[3],
f=Krig.fgcv.one, f.extra = info, tol = tol)
lambda.est[3, 1] <-out$x
lambda.est[3,6]<- out$iter
}
if ( indRefine[6] ){
starts <- lambda.grid[IMIN[6] + c(-1,0,1)]
out <- golden.section.search(ax=starts[1],bx=starts[2],cx=starts[3],
f=Krig.flplike, f.extra = info, tol = tol)
lambda.est[6,1]<- out$x
lambda.est[6,6]<- out$iter
}
if ( indRefine[4] ) {
guess<- gcv.grid$lambda[IMIN[4]]
lambda.rmse <- find.upcross(Krig.fs2hat, info,
upcross.level = rmse^2,
guess = guess, tol = tol * rmse^2)
lambda.est[4, 1] <- lambda.rmse
}
#
# matching estimate of tau from reps.
if ( indRefine[5] ) {
guess <- gcv.grid$lambda[IMIN[5]]
lambda.pure.error <- find.upcross(Krig.fs2hat, info,
upcross.level = tauHat.pure.error^2, guess = guess,
tol = tol * tauHat.pure.error^2)
lambda.est[5, 1] <- lambda.pure.error
}
#
# OK done with all six methods
# NOTE that not all may
# fill in return matrix with all the right stuff
# fill in REML results
lam.ml <- lambda.est[6, 1]
lambda.est[6, 2] <- Krig.ftrace(lam.ml, D)
lambda.est[6, 3] <- Krig.fgcv(lam.ml, info)
lambda.est[6, 4] <- sqrt(Krig.fs2hat(lam.ml, info))
lambda.est[6, 5] <- Krig.flplike(lam.ml, info)
# fill in GCV results
for (k in 1:5) {
lam <- lambda.est[k, 1]
if (!is.na(lam)) {
lambda.est[k, 2] <- Krig.ftrace(lam, D)
if (k == 1 | k > 3) {
lambda.est[k, 3] <- Krig.fgcv(lam, info)
lambda.est[k, 5] <- Krig.flplike(lam, info)
}
if (k == 2) {
lambda.est[k, 3] <- Krig.fgcv.model(lam, info)
}
if (k == 3) {
lambda.est[k, 3] <- Krig.fgcv.one(lam, info)
}
lambda.est[k, 4] <- sqrt(Krig.fs2hat(lam, info))
}
}
# Note that the estimate by default is
# REML == restricted maximum likelihood.
if( give.warnings & any(warningTable$Warning)){
cat("Methods at endpoints of grid search:", fill=TRUE)
print(warningTable[warningTable$Warning,])
}
list(gcv.grid = gcv.grid,
lambda.est = lambda.est, info=info, D=D,
warningTable=warningTable)
}
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