1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
|
#
# 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
gcv.sreg<- function(out, lambda.grid = NA, cost = 1,
nstep.cv = 80, rmse = NA, offset = 0, trmin = NA, trmax = NA,
verbose = FALSE, tol = 1e-05,
give.warnings=TRUE) {
tauHat.pure.error <- out$tauHat.pure.error
pure.ss <- out$pure.ss
nt <- 2
np <- out$np
N <- out$N
out$cost <- cost
out$offset <- offset
# find good end points for lambda coarse grid.
if (is.na(trmin))
trmin <- 2.05
if (is.na(trmax))
trmax <- out$np * 0.95
if (is.na(lambda.grid[1])) {
l2 <- sreg.df.to.lambda(trmax, out$xM, out$weightsM)
l1 <- sreg.df.to.lambda(trmin, out$xM, out$weightsM)
lambda.grid <- exp(seq(log(l2), log(l1), , nstep.cv))
}
if (verbose) {
cat("endpoints of coarse lamdba grid", fill = TRUE)
cat(l1, l2, fill = TRUE)
}
# build up table of coarse grid serach results for lambda
# in the matrix gcv.grid
nl <- length(lambda.grid)
V <- V.model <- V.one <- trA <- MSE <- RSS.model <- rep(NA,
nl)
# loop through lambda's and compute various quantities related to
# lambda and the fitted spline.
for (k in 1:nl) {
temp <- sreg.fit(lambda.grid[k], out, verbose = verbose)
RSS.model[k] <- temp$rss
trA[k] <- temp$trace
V[k] <- temp$gcv
V.one[k] <- temp$gcv.one
V.model[k] <- temp$gcv.model
}
# adjustments to columns of gcv.grid
RSS <- RSS.model + pure.ss
tauHat <- sqrt(RSS/(N - trA))
gcv.grid <- cbind(lambda.grid, trA, V, V.one, V.model, tauHat)
dimnames(gcv.grid) <- list(NULL, c("lambda", "trA", "GCV",
"GCV.one", "GCV.model", "tauHat"))
gcv.grid<- as.data.frame( gcv.grid)
if (verbose) {
cat("Results of coarse grid search", fill = TRUE)
print(gcv.grid)
}
lambda.est <- matrix(NA, ncol = 5, nrow = 5,
dimnames = list(
c("GCV","GCV.model", "GCV.one", "RMSE", "pure error"),
c("lambda","trA", "GCV", "tauHat", "converge")))
# now do various refinements for different flavors of finding
# a good value for lambda the smoothing parameter
##### traditional leave-one-out
IMIN<- rep( NA, 5)
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)) )
# 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") )
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")
if( verbose){
print(warningTable)
}
# fill in grid search estimates
for( k in 1:5){
if( !is.na(IMIN[k])){
lambda.est[k,1]<- gcv.grid$lambda[IMIN[k]]
}
}
# now optimze the search producing refined optima
#
# now step through the many different ways to find lambda
# This is the key to these choices:
# 1- the usual GCV proposed by Craven/Wahba
# 2- GCV where data fitting is collapsed to the mean for
# each location and each location is omitted
# 3- True leave-one-out even with replicated observations
# 4- Match estimate of tau to external value supplied (RMSE)
# 5- Match estimate of tau from the estimate based the
# pure error sum of squares obtained by the observations
# replicated at the same locations
#test<- sreg.fit(.1, out)
#print( test)
if(indRefine[1]){
starts <- lambda.grid[IMIN[1] + c(-1,0,1)]
outGs <- golden.section.search(ax=starts[1],bx=starts[2],cx=starts[3],
f=sreg.fgcv, f.extra = out, tol = tol)
lambda.est[1,1]<- outGs$x
lambda.est[1,5]<- outGs$iter
}
if( indRefine[2]) {
starts <- lambda.grid[IMIN[2] + c(-1,0,1)]
outGs <- golden.section.search(ax=starts[1],bx=starts[2],cx=starts[3],
f=sreg.fgcv.model, f.extra = out, tol = tol)
lambda.est[2,1]<- outGs$x
lambda.est[2,5]<- outGs$iter
}
if( indRefine[3]) {
starts <- lambda.grid[IMIN[3] + c(-1,0,1)]
outGs <- golden.section.search(ax=starts[1],bx=starts[2],cx=starts[3],
f=sreg.fgcv.one, f.extra = out, tol = tol)
lambda.est[3, 1] <-outGs$x
lambda.est[3,5]<- outGs$iter
}
if ( indRefine[4] ) {
guess<- gcv.grid$lambda[IMIN[4]]
lambda.rmse <- find.upcross(sreg.fs2hat, out,
upcross.level = rmse^2,
guess = guess, tol = tol * rmse^2)
lambda.est[4, 1] <- lambda.rmse
}
if ( indRefine[5] ) {
guess <- gcv.grid$lambda[IMIN[5]]
lambda.pure.error <- find.upcross(sreg.fs2hat, out,
upcross.level = tauHat.pure.error^2, guess = guess,
tol = tol * tauHat.pure.error^2)
lambda.est[5, 1] <- lambda.pure.error
}
if (verbose) {
cat("All forms of estimated lambdas so far", fill = TRUE)
print(lambda.est)
}
for (k in 1:5) {
lam <- lambda.est[k, 1]
if (!is.na(lam)) {
temp <- sreg.fit(lam, out)
lambda.est[k, 2] <- temp$trace
if ((k == 1) | (k > 3)) {
lambda.est[k, 3] <- temp$gcv
}
if (k == 2) {
lambda.est[k, 3] <- temp$gcv.model
}
if (k == 3) {
lambda.est[k, 3] <- temp$gcv.one
}
lambda.est[k, 4] <- temp$tauHat
}
}
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,
warningTable=warningTable)
}
|
