Nothing
R/profiles.R
In geoR: Analysis of Geostatistical Data
"proflik" <-
function(obj.likfit, geodata, coords = geodata$coords,
data = geodata$data,
sill.values,
range.values,
nugget.values,
nugget.rel.values,
lambda.values,
sillrange.values = TRUE,
sillnugget.values = TRUE,
rangenugget.values = TRUE,
sillnugget.rel.values = FALSE,
rangenugget.rel.values = FALSE,
silllambda.values = FALSE,
rangelambda.values = TRUE,
nuggetlambda.values = FALSE,
nugget.rellambda.values = FALSE,
uni.only = TRUE,
bi.only = FALSE,
messages,
...)
{
##
## 1. setting arguments
##
if(missing(messages))
messages.screen <- as.logical(ifelse(is.null(getOption("geoR.messages")), TRUE, getOption("geoR.messages")))
else messages.screen <- messages
if(missing(geodata))
geodata <- list(coords = coords, data = data)
# if(! "package:stats" %in% search()) require(mva)
call.fc <- match.call()
n.cov.pars <- obj.likfit$npars - length(obj.likfit$beta)
if(obj.likfit$transform.info$fix.lambda == FALSE)
n.cov.pars <- n.cov.pars - 1
if(missing(sill.values))
sill.values <- sillrange.values <- sillnugget.values <- FALSE
if(missing(range.values))
range.values <- sillrange.values <- rangenugget.values <- rangelambda.values <- FALSE
if(!is.null(obj.likfit$call$fix.nugget))
if(obj.likfit$call$fix.nugget == TRUE)
nugget.values <- nugget.rel.values <- FALSE
if(missing(nugget.values))
nugget.values <- sillnugget.values <- rangenugget.values <- nuggetlambda.values <- FALSE
if(missing(nugget.rel.values))
nugget.rel.values <- sillnugget.rel.values <- rangenugget.rel.values <- nugget.rellambda.values <- FALSE
if(missing(lambda.values) | obj.likfit$transform.info$fix.lambda) lambda.values <- FALSE
if(uni.only){
sillrange.values <- sillnugget.values <- rangenugget.values <-
sillnugget.rel.values <- rangenugget.rel.values <-
silllambda.values <- rangelambda.values <-
nugget.rellambda.values <- nuggetlambda.values <- FALSE
}
else{
if(all(sillrange.values == TRUE)){
if(all(sill.values == FALSE) | all(range.values == FALSE)){
sillrange.values <- FALSE
stop("if argument sillrange.values = TRUE sill.values and range.values must be provided. Alternatively a matrix can be provided in sillrange.values or set this to FALSE")
}
else
sillrange.values <- as.matrix(expand.grid(sill.values, range.values))
}
if(n.cov.pars == 2){
sillnugget.values <- rangenugget.values <-
sillnugget.rel.values <- rangenugget.rel.values <-
nugget.rellambda.values <- nuggetlambda.values <- FALSE
}
else{
if(all(sillnugget.values == TRUE)){
if(all(sill.values == FALSE) | all(nugget.values == FALSE)){
sillnugget.values <- FALSE
stop("if argument sillnugget.values = TRUE sill.values and nugget.values must be provided. Alternatively a matrix can be provided in sillnugget.values or set this to FALSE")
}
else
sillnugget.values <- as.matrix(expand.grid(sill.values, nugget.values))
}
if(all(rangenugget.values == TRUE)){
if(all(range.values == FALSE) | all(nugget.values == FALSE)){
rangenugget.values <- FALSE
stop("if argument rangenugget.values = TRUE range.values and nugget.values must be provided. Alternatively a matrix can be provided in rangenugget.values or set this to FALSE")
}
else
rangenugget.values <- as.matrix(expand.grid(range.values, nugget.values))
}
if(all(sillnugget.rel.values == TRUE)){
if(all(sill.values == FALSE) | all(nugget.rel.values == FALSE)){
sillnugget.rel.values <- FALSE
stop("if argument sillnugget.rel.values = TRUE sill.values and nugget.rel.values must be provided. Alternatively a matrix can be provided in sillnugget.rel.values or set this to FALSE")
}
else
sillnugget.rel.values <- as.matrix(expand.grid(sill.values, nugget.rel.values))
}
if(all(rangenugget.rel.values == TRUE)){
if(all(range.values == FALSE) | all(nugget.rel.values == FALSE)){
rangenugget.rel.values <- FALSE
stop("if argument rangenugget.rel.values = TRUE range.values and nugget.rel.values must be provided. Alternatively a matrix can be provided in rangenugget.rel.values or set this to FALSE")
}
else
rangenugget.rel.values <- as.matrix(expand.grid(range.values, nugget.rel.values))
}
if(obj.likfit$transform.info$fix.lambda == TRUE){
if(all(nuggetlambda.values == TRUE)){
if(all(lambda.values == FALSE) | all(nugget.values == FALSE)){
nuggetlambda.values <- FALSE
stop("if argument nuggetlambda.values = TRUE lambda.values and nugget.values must be provided. Alternatively a matrix can be provided in nuggetlambda.values or set this to FALSE")
}
else
nuggetlambda.values <- as.matrix(expand.grid(lambda.values, nugget.values))
}
if(all(nugget.rellambda.values == TRUE)){
if(all(lambda.values == FALSE) | all(nugget.rel.values == FALSE)){
nugget.rellambda.values <- FALSE
stop("if argument nugget.rellambda.values = TRUE lambda.values and nugget.rel.values must be provided. Alternatively a matrix can be provided in nugget.rellambda.values or set this to FALSE")
}
else
nugget.rellambda.values <- as.matrix(expand.grid(lambda.values, nugget.rel.values))
}
}
}
if(obj.likfit$transform.info$fix.lambda == TRUE)
silllambda.values <- rangelambda.values <- FALSE
else{
if(all(silllambda.values == TRUE)){
if(all(sill.values == FALSE) | all(lambda.values == FALSE)){
silllambda.values <- FALSE
stop("if argument silllambda.values = TRUE sill.values and lambda.values must be provided. Alternatively a matrix can be provided in silllambda.values or set this to FALSE")
}
else
silllambda.values <- as.matrix(expand.grid(sill.values, lambda.values))
}
if(all(rangelambda.values == TRUE)){
if(all(range.values == FALSE) | all(lambda.values == FALSE)){
rangelambda.values <- FALSE
stop("if argument rangelambda.values = TRUE range.values and lambda.values must be provided. Alternatively a matrix can be provided in rangelambda.values or set this to FALSE")
}
else
rangelambda.values <- as.matrix(expand.grid(range.values, lambda.values))
}
}
}
##
## 2. data preparation
##
trend <- unclass(trend.spatial(trend=obj.likfit$trend, geodata = geodata))
if (nrow(trend) != nrow(coords))
stop("coords and trend have incompatible sizes")
data <- as.vector(data)
dimnames(trend) <- list(NULL, NULL)
if(obj.likfit$transform.info$fix.lambda) {
if(obj.likfit$lambda != 1) {
if(any(data <= 0))
stop("Data transformation not allowed when there are zeros or negative data"
)
if(obj.likfit$lambda == 0)
data <- log(data)
else data <- ((data^obj.likfit$lambda) - 1)/obj.likfit$lambda
}
}
n <- length(data)
dists.vec <- as.vector(dist(coords))
d <- range(dists.vec)
min.dist <- d[1]
max.dist <- d[2]
tausq <- obj.likfit$nugget
sigmasq <- obj.likfit$cov.pars[1]
tausq.rel <- tausq/sigmasq
phi <- obj.likfit$cov.pars[2]
lambda <- obj.likfit$lambda
loglik <- obj.likfit$loglik
sill.total <- sigmasq + tausq
n.uni <- 0
n.bi <- 0
lower.phi <- 0.01 * (min.dist/max.dist)
upper.phi <- 1000 * max.dist
lower.sigmasq <- 0.01 * sill.total
result <- list()
assign(".temp.list", list(n = n,
z = data,
beta.size = dim(trend)[2],
kappa = obj.likfit$kappa,
xmat = trend,
## txmat = t(trend),
method.lik = obj.likfit$method.lik,
dists.lowertri = dists.vec,
cov.model = obj.likfit$cov.model,
fix.lambda = obj.likfit$transform.info$fix.lambda,
lambda = obj.likfit$lambda,
lower.phi = lower.phi,
upper.phi = upper.phi,
lower.sigmasq = lower.sigmasq,
phi.est = phi,
tausq.rel.est = tausq.rel,
tausq.est = tausq,
sigmasq.est = sigmasq), envir=.geoR.env)
if(obj.likfit$transform.info$fix.lambda == TRUE)
eval(substitute(.temp.list$log.jacobian <- xxx, list(xxx=obj.likfit$transform.info$log.jacobian)), envir=.geoR.env)
##
## 3. One-dimentional profile likelihoods
##
##
## 3.1 Profile for sigmasq
##
if(bi.only == FALSE) {
if(any(sill.values != FALSE)) {
n.uni <- n.uni + 1
if(messages.screen) cat("proflik: computing profile likelihood for the sill\n")
if(n.cov.pars == 2) {
if(tausq == 0) {
if(obj.likfit$transform.info$fix.lambda == FALSE) {
ini.grid <- as.matrix(expand.grid(seq(min(range.values),
max(range.values),
l = 5),
seq(-1,1,l = 5)))
}
else {
ini.grid <- as.matrix(seq(min(range.values),
max(range.values),
l = 10))
}
dimnames(ini.grid) <- list(NULL, NULL)
eval(substitute(.temp.list$ini.grid <- xxx, list(xxx= ini.grid)), envir=.geoR.env)
pl.sigmasq <- apply(matrix(sill.values,
ncol = 1), 1, .proflik.aux2, ...)
eval(expression(.temp.list$ini.grid <- NULL), envir=.geoR.env)
}
else {
stop("not yet implemented for fixed nugget != 0")
}
}
if(n.cov.pars == 3) {
if(any(lambda.values != FALSE)) {
ini.grid <- as.matrix(expand.grid(seq(min(range.values),
max(range.values), l = 6),
seq(0, 2 * tausq.rel, l = 4),
seq(-1, 1, l = 5)))
}
else {
ini.grid <- as.matrix(expand.grid(seq(min(range.values),
max(range.values), l = 10),
seq(0, 2 * tausq.rel, l = 4)))
}
dimnames(ini.grid) <- list(NULL, NULL)
eval(substitute(.temp.list$ini.grid <- xxx, list(xxx= ini.grid)), envir=.geoR.env)
pl.sigmasq <- apply(matrix(sill.values, ncol =
1), 1, .proflik.aux9, ...)
eval(expression(.temp.list$ini.grid <- NULL), envir=.geoR.env)
}
v.ord <- order(c(sigmasq, sill.values))
if(obj.likfit$transform.info$fix.lambda == TRUE)
pl.sigmasq <- pl.sigmasq + obj.likfit$transform.info$log.jacobian
result$sill <- list(sill = c(sigmasq, sill.values)[
v.ord], proflik.sill = c(loglik, pl.sigmasq)[
v.ord], est.sill = c(sigmasq, loglik))
}
##
## 3.2 Profile for phi
##
if(any(range.values != FALSE)) {
n.uni <- n.uni + 1
if(messages.screen) cat("proflik: computing profile likelihood for the range\n")
if(n.cov.pars == 2) {
if(tausq == 0) {
eval(expression(.temp.list$nugget <- 0), envir=.geoR.env)
pl.phi <- apply(matrix(range.values,
ncol = 1), 1, .proflik.aux0, ...)
eval(expression(.temp.list$nugget <- NULL), envir=.geoR.env)
}
else {
stop("not yet implemented for fixed nugget != 0"
)
}
}
if(n.cov.pars == 3) {
pl.phi <- apply(matrix(range.values, ncol = 1),
1, .proflik.aux7, ...)
}
v.ord <- order(c(phi, range.values))
if(obj.likfit$transform.info$fix.lambda == TRUE)
pl.phi <- pl.phi + obj.likfit$transform.info$log.jacobian
result$range <- list(range = c(phi, range.values)[
v.ord], proflik.range = c(loglik, pl.phi)[
v.ord], est.range = c(phi, loglik))
}
##
## 3.3 Profile for \tau^2
##
if(n.cov.pars == 3) {
if(any(nugget.values != FALSE)) {
n.uni <- n.uni + 1
if(messages.screen) cat("proflik: computing profile likelihood for the nugget\n"
)
pl.tausq <- apply(matrix(nugget.values, ncol =
1), 1, .proflik.aux11, ...)
v.ord <- order(c(tausq, nugget.values))
if(obj.likfit$transform.info$fix.lambda == TRUE)
pl.tausq <- pl.tausq + obj.likfit$transform.info$log.jacobian
result$nugget <- list(nugget = c(tausq,
nugget.values)[v.ord], proflik.nugget
= c(loglik, pl.tausq)[v.ord],
est.nugget = c(tausq, loglik))
}
##
## 3.4 Profile for relative \tau^2
##
if(any(nugget.rel.values != FALSE)) {
if(messages.screen) cat("proflik: computing profile likelihood for the relative nugget\n"
)
n.uni <- n.uni + 1
pl.tausq.rel <- apply(matrix(nugget.rel.values,
ncol = 1), 1, .proflik.aux5, ...)
v.ord <- order(c(tausq.rel, nugget.rel.values))
if(obj.likfit$transform.info$fix.lambda == TRUE)
pl.tausq.rel <- pl.tausq.rel + obj.likfit$transform.info$log.jacobian
result$nugget.rel <- list(nugget.rel = c(
tausq.rel, nugget.rel.values)[v.ord],
proflik.nugget = c(loglik, pl.tausq.rel
)[v.ord],
est.nugget.rel = c(tausq.rel,loglik))
}
}
##
## 3.5 Profile for \lambda
##
if(any(lambda.values != FALSE)) {
assign(".temp.temp.list", get(".temp.list", envir=.geoR.env))
eval(substitute(.temp.temp.list$coords <- xxx, list(xxx= coords)), envir=.geoR.env)
n.uni <- n.uni + 1
if(messages.screen) cat("proflik: computing profile likelihood for lambda\n"
)
if(n.cov.pars == 2) {
if(tausq == 0) {
eval(expression(.temp.temp.list$fixtau <- TRUE), envir=.geoR.env)
eval(substitute(.temp.temp.list$ini <- xxx, list(xxx= c(sigmasq,phi))), envir=.geoR.env)
pl.lambda <- apply(as.matrix(lambda.values), 1, .proflik.aux23, ...)
}
else {
stop("not yet implemented for fixed nugget != 0")
}
}
if(n.cov.pars == 3) {
eval(expression(.temp.temp.list$fixtau <- FALSE), envir=.geoR.env)
eval(substitute(.temp.temp.list$ini <- xxx, list(xxx= phi)), envir=.geoR.env)
pl.lambda <- apply(matrix(lambda.values,
ncol = 1), 1, .proflik.aux23, ...)
}
v.ord <- order(c(lambda, lambda.values))
result$lambda <- list(lambda = c(lambda,
lambda.values)[v.ord], proflik.lambda
= c(loglik, pl.lambda)[v.ord],
est.lambda = c(lambda, loglik))
remove(".temp.temp.list", inherits=TRUE, envir=.geoR.env)
}
}
##
## 4. Two-dimentional profile likelihoods
##
##
## 4.1 Profile for \sigma^2 and \phi
##
if(uni.only == FALSE){
if(any(sillrange.values != FALSE)) {
n.bi <- n.bi + 1
if(messages.screen) cat("proflik: computing 2-D profile likelihood for the sill and range parameters\n")
if(n.cov.pars == 2) {
if(tausq == 0) {
eval(expression(.temp.list$nugget <- 0), envir=.geoR.env)
if(get(".temp.list", envir=.geoR.env)$fix.lambda == TRUE) {
pl.sigmasqphi <- apply(cbind(0, sillrange.values, 1), 1, loglik.spatial, ...)
}
else {
pl.sigmasqphi <- apply(sillrange.values,
1, .proflik.aux28, ...)
}
eval(expression(.temp.list$nugget <- NULL), envir=.geoR.env)
}
else {
stop("not yet implemented for fixed nugget != 0"
)
}
}
if(n.cov.pars == 3) {
pl.sigmasqphi <- apply(sillrange.values, 1, .proflik.aux13, ...)
}
names(pl.sigmasqphi) <- NULL
if(obj.likfit$transform.info$fix.lambda == TRUE)
pl.sigmasqphi <- pl.sigmasqphi + obj.likfit$transform.info$log.jacobian
result$sillrange <- list(sill = as.numeric(levels(as.factor(sillrange.values[,1]))), range =
as.numeric(levels(as.factor(sillrange.values[,2]))), proflik.sillrange = pl.sigmasqphi,
est.sillrange = c(sigmasq, phi, loglik))
}
##
## 4.2 Profile for \sigma^2 and \tau^2
##
if(any(sillnugget.values != FALSE)) {
n.bi <- n.bi + 1
if(messages.screen) cat("proflik: computing 2-D profile likelihood for the sill and nugget\n")
if(obj.likfit$transform.info$fix.lambda == FALSE)
ini.grid <- as.matrix(expand.grid(seq(min(range.values),
max(range.values), l =
10), seq(-1, 1, l = 5)))
else
ini.grid <- as.matrix(seq(min(range.values),
max(range.values), l = 10))
dimnames(ini.grid) <- list(NULL, NULL)
eval(substitute(.temp.list$ini.grid <- xxx, list(xxx=ini.grid)), envir=.geoR.env)
pl.sigmasqtausq <- apply(sillnugget.values, 1, .proflik.aux15, ...)
eval(expression(.temp.list$ini.grid <- NULL), envir=.geoR.env)
names(pl.sigmasqtausq) <- NULL
if(obj.likfit$transform.info$fix.lambda == TRUE)
pl.sigmasqtausq <- pl.sigmasqtausq + obj.likfit$transform.info$log.jacobian
result$sillnugget <- list(sill = as.numeric(levels(as.factor(sillnugget.values[,1]))), nugget = as.numeric(levels(as.factor(sillnugget.values[,2]))), proflik.sillnugget =
pl.sigmasqtausq, est.sillrange = c(sigmasq,
tausq, loglik))
}
##
## 4.3 Profile for \phi and \tau^2
##
if(any(rangenugget.values != FALSE)) {
n.bi <- n.bi + 1
if(messages.screen) cat("proflik: computing 2-D profile likelihood for the range and nugget\n"
)
eval(substitute(.temp.list$ini.grid <- xxx, list(xxx= as.matrix(seq(sigmasq/4, 5 *
sigmasq, l = 15)))), envir=.geoR.env)
pl.phitausq <- apply(rangenugget.values, 1, .proflik.aux17, ...)
eval(expression(.temp.list$ini.grid <- NULL), envir=.geoR.env)
names(pl.phitausq) <- NULL
if(obj.likfit$transform.info$fix.lambda == TRUE)
pl.phitausq <- pl.phitausq + obj.likfit$transform.info$log.jacobian
result$rangenugget <- list(range = as.numeric(levels(as.factor(rangenugget.values[,1]))), nugget
= as.numeric(levels(as.factor(rangenugget.values[,1]))), proflik.rangenugget =
pl.phitausq, est.rangenugget = c(phi, tausq,
loglik))
}
##
## 4.4 Profile for \sigma^2 and \tau^2_{rel}
##
if(any(sillnugget.rel.values != FALSE)) {
n.bi <- n.bi + 1
if(messages.screen) cat("proflik: computing 2-D profile likelihood for the sill and relative nugget parameters\n"
)
if(get(".temp.list", envir=.geoR.env)$fix.lambda == FALSE)
ini.grid <- as.matrix(expand.grid(seq(min(range.values), max(range.values), l =
10), seq(-1, 1, l = 5)))
else
ini.grid <- as.matrix(seq(min(range.values),
max(range.values), l = 10))
dimnames(ini.grid) <- list(NULL, NULL)
eval(substitute(.temp.list$ini.grid <- xxx, list(xxx= ini.grid)), envir=.geoR.env)
pl.sigmasqtausq.rel <- apply(sillnugget.rel.values, 1,
.proflik.aux19, ...)
eval(expression(.temp.list$ini.grid <- NULL), envir=.geoR.env)
names(pl.sigmasqtausq.rel) <- NULL
if(obj.likfit$transform.info$fix.lambda == TRUE)
pl.sigmasqtausq.rel <- pl.sigmasqtausq.rel + obj.likfit$transform.info$log.jacobian
result$sillnugget.rel <- list(sill = as.numeric(levels(as.factor(sillnugget.rel.values[,1]))),
nugget.rel = as.numeric(levels(as.factor(sillnugget.rel.values[,2]))),
proflik.sillnugget.rel = pl.sigmasqtausq.rel,
est.sillrange.rel = c(sigmasq, tausq.rel,
loglik))
}
##
## 4.5 Profile for \phi and \tau^2_{rel}
##
if(any(rangenugget.rel.values != FALSE)) {
n.bi <- n.bi + 1
if(messages.screen) cat("proflik: computing 2-D profile likelihood for the range and relative nugget parameters\n"
)
pl.phitausq.rel <- apply(rangenugget.rel.values, 1, .proflik.aux30, ...)
names(pl.phitausq.rel) <- NULL
if(obj.likfit$transform.info$fix.lambda == TRUE)
pl.phitausq.rel <- pl.phitausq.rel + obj.likfit$transform.info$log.jacobian
result$rangenugget.rel <- list(range = as.numeric(levels(as.factor(rangenugget.rel.values[,1]))),
nugget.rel = as.numeric(levels(as.factor(rangenugget.rel.values[,2]))),
proflik.rangenugget.rel = pl.phitausq.rel,
"est.rangenugget.rel" = c(phi, tausq.rel,
loglik))
}
}
##
## 4.6 Profile for \sigma^2 and \lambda
##
if(any(silllambda.values != FALSE)) {
n.bi <- n.bi + 1
if(messages.screen) cat("proflik: computing 2-D profile likelihood for the sill and transformation parameters\n"
)
if(n.cov.pars == 2) {
ini.grid <- as.matrix(seq(min(range.values), max(
range.values), l = 10))
dimnames(ini.grid) <- list(NULL, NULL)
eval(substitute(.temp.list$ini.grid <- xxx, list(xxx= ini.grid)), envir=.geoR.env)
if(tausq == 0) {
eval(expression(.temp.list$nugget <- 0), envir=.geoR.env)
pl.sigmasqlambda <- apply(silllambda.values, 1, .proflik.aux24, ...)
eval(expression(.temp.list$ini.grid <- NULL), envir=.geoR.env)
eval(expression(.temp.list$nugget <- NULL), envir=.geoR.env)
}
else {
stop("not yet implemented for fixed nugget != 0"
)
}
}
if(n.cov.pars == 3) {
ini.grid <- as.matrix(expand.grid(seq(min(range.values),
max(range.values), l = 10), seq(0, 1, l = 5)))
dimnames(ini.grid) <- list(NULL, NULL)
eval(substitute(.temp.list$ini.grid <- xxx, list(xxx=ini.grid)), envir=.geoR.env)
pl.sigmasqlambda <- apply(silllambda.values, 1, .proflik.aux27, ...)
eval(expression(.temp.list$ini.grid <- NULL), envir=.geoR.env)
}
names(pl.sigmasqlambda) <- NULL
result$silllambda <- list(sill = as.numeric(levels(as.factor(silllambda.values[,1]))), lambda = as.numeric(levels(as.factor(silllambda.values[,2]))), proflik.silllambda = pl.sigmasqlambda,
est.silllambda = c(sigmasq, lambda, loglik))
}
##
## 4.7 Profile for \phi and \lambda
##
if(any(rangelambda.values != FALSE)) {
eval(substitute(.temp.list$data <- xxx, list(xxx=.temp.list$z)), envir=.geoR.env)
n.bi <- n.bi + 1
cat("proflik: computing 2-D profile likelihood for the range and transformation parameters\n"
)
if(n.cov.pars == 2) {
if(tausq == 0) {
eval(expression(.temp.list$nugget <- 0), envir=.geoR.env)
pl.philambda <- apply(rangelambda.values, 1,
.proflik.aux1, ...)
eval(expression(.temp.list$nugget <- NULL), envir=.geoR.env)
}
else {
stop("not yet implemented for fixed nugget != 0"
)
}
}
if(n.cov.pars == 3) {
pl.philambda <- apply(rangelambda.values, 1, .proflik.aux31, ...)
}
names(pl.philambda) <- NULL
result$rangelambda <- list(range = as.numeric(levels(as.factor(rangelambda.values[,1]))), lambda = as.numeric(levels(as.factor(rangelambda.values[,2]))), proflik.rangelambda = pl.philambda,
est.rangelambda = c(phi, lambda, loglik))
}
##
## 4.8 Profile for \tau^2 and \lambda
##
if(any(nuggetlambda.values != FALSE)) {
n.bi <- n.bi + 1
cat("proflik: computing 2-D profile likelihood for the nugget and transformation parameters\n"
)
pl.nuggetlambda <- apply(nuggetlambda.values, 1, .proflik.aux32, ...)
names(pl.nuggetlambda) <- NULL
result$nuggetlambda <- list(nugget = as.numeric(levels(as.factor(nuggetlambda.values[,1]))), lambda = as.numeric(levels(as.factor(nuggetlambda.values[,2])))
, proflik.nuggetlambda = pl.nuggetlambda,
est.nuggetlambda = c(tausq, lambda, loglik))
}
##
## 4.9 2-D Profile for \tau^2_{rel} and \lambda
##
if(any(nugget.rellambda.values != FALSE)) {
n.bi <- n.bi + 1
pl.nugget.rellambda <- apply(nugget.rellambda.values, 1, .proflik.aux33, ...)
names(pl.nugget.rellambda) <- NULL
result$nugget.rellambda <- list(nugget.rel = as.numeric(levels(as.factor(nugget.rellambda.values[,1]))),
lambda = as.numeric(levels(as.factor(nugget.rellambda.values[,2]))), proflik.nugget.rellambda =
pl.nugget.rellambda, est.nugget.rellambda = c(tausq.rel,
lambda, loglik))
}
result$n.uni <- n.uni
result$n.bi <- n.bi
result$method.lik <- obj.likfit$method.lik
result$call <- call.fc
oldClass(result) <- "proflik"
return(result)
}
".proflik.aux0" <-
function(phi, ...)
{
## This function computes the value of the profile likelihood for the correlation parameter \phi when nugget effect is not included in the model.
## It requires the minimisation of the function wrt \phi for each value of \lambda, if this transformation parameter is included in the model
## This is an auxiliary function called by likfit.proflik
##
if(get(".temp.list", envir=.geoR.env)$fix.lambda == TRUE)
proflik <- .proflik.aux1(philambda = phi)
else {
eval(substitute(.temp.list$phi <- xxx, list(xxx=phi)), envir=.geoR.env)
# proflik <- - (optim(.temp.list$lambda, .proflik.aux1.1, method="L-BFGS-B", lower
# = -2, upper = 2, ...)$value)
proflik <- - (optimise(.proflik.aux1.1, lower = -5, upper = 5, ...)$objective)
return(proflik)
}
}
".proflik.aux1" <-
function(philambda, ...)
{
## This function computes the value of the profile likelihood for the correlation function scale parameter \phi when nugget effect = 0
.temp.list <- get(".temp.list", envir=.geoR.env)
if(length(philambda) == 2) lambda <- philambda[2]
else lambda <- 1
n <- .temp.list$n
main <- .proflik.main(tausq=.temp.list$nugget, sigmasq=1, phi=philambda[1], lambda = lambda)
if(.temp.list$method.lik == "ML") {
proflik <- - (n/2) * log(2 * pi) - main$log.det.to.half -
(n/2) * log(main$ssresmat/n) - (n/2) + main$
log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
proflik <- - ((n - .temp.list$beta.size)/2) * log(2 * pi) - main$
log.det.to.half - ((n - .temp.list$beta.size)/2) * log(main$ssresmat/
n) - (n/2) + 0.5 * sum(log(eigentrem$values)) +
main$log.jacobian
}
return(proflik)
}
".proflik.aux10" <-
function(phitausq.rel.lambda, ...)
{
.temp.list <- get(".temp.list", envir=.geoR.env)
if(length(phitausq.rel.lambda) == 3)
lambda <- phitausq.rel.lambda[3]
else lambda <- 1
phitausq.rel.lambda <- as.vector(phitausq.rel.lambda)
n <- .temp.list$n
phi <- phitausq.rel.lambda[1]
tausq <- phitausq.rel.lambda[2]
sigmasq <- .temp.list$sigmasq
main <- .proflik.main(tausq=tausq, sigmasq=1, phi=phi, lambda = lambda)
if(.temp.list$method.lik == "ML") {
neglik <- (n/2) * log(2 * pi) + main$log.det.to.half +
(n/2) * log(sigmasq) + (0.5/sigmasq) * main$ssresmat -
main$log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
neglik <- ((n - .temp.list$beta.size)/2) * log(2 * pi) + main$
log.det.to.half + ((n - .temp.list$beta.size)/2) * log(sigmasq) +
(0.5/sigmasq) * main$ssresmat - 0.5 * sum(log(eigentrem$
values)) - main$log.jacobian
}
return(as.vector(round(neglik, digits=8)))
}
".proflik.aux11" <-
function(tausq, ...)
{
## This function computes the value of the profile likelihood for the parameter \tau^2.
## It requires the minimisation of the function wrt \sigma^2, \phi and \lambda (if the case) for each value of \tau^2.
## This is an auxiliary function called by proflik.
eval(substitute(.temp.list$nugget <- xxx, list(xxx=as.vector(tausq))), envir=.geoR.env)
.temp.list <- get(".temp.list", envir=.geoR.env)
if(.temp.list$fix.lambda == TRUE) {
sigmasqphi.res <- optim(c(.temp.list$sigmasq.est, .temp.list$phi.est),
.proflik.aux12, method="L-BFGS-B",
lower = c(.temp.list$lower.sigmasq,
.temp.list$lower.phi),
upper=c(+Inf, .temp.list$upper.phi), ...)$value
}
else {
sigmasqphi.res <- optim(c(.temp.list$sigmasq.est, .temp.list$phi.est,
.temp.list$lambda), .proflik.aux12,method="L-BFGS-B",
lower = c(.temp.list$lower.sigmasq, .temp.list$lower.phi, -2),
upper = c( + Inf, .temp.list$upper.phi, 2), ...)$value
}
eval(expression(.temp.list$nugget <- NULL), envir=.geoR.env)
return( - sigmasqphi.res)
}
".proflik.aux1.1" <-
function(lambda, ...)
{
## This function computes the value of the profile likelihood for the correlation function scale parameter \phi when nugget effect = 0
.temp.list <- get(".temp.list", envir=.geoR.env)
phi <- .temp.list$phi
n <- .temp.list$n
main <- .proflik.main(tausq=.temp.list$nugget, sigmasq=1, phi=phi, lambda = lambda)
if(.temp.list$method.lik == "ML") {
neglik <- (n/2) * log(2 * pi) + main$log.det.to.half +
(n/2) * log(main$ssresmat/n) + (n/2) - main$log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
neglik <- ((n - .temp.list$beta.size)/2) * log(2 * pi) + main$
log.det.to.half + ((n - .temp.list$beta.size)/2) * log(main$ssresmat/n) +
(n/2) - 0.5 * sum(log(eigentrem$values)) -
main$log.jacobian
}
return(as.vector(round(neglik, digits=8)))
}
".proflik.aux12" <-
function(sigmasqphi.lambda, ...)
{
## This function computes the value of the profile likelihood for the nugget parameter \tau^2, minimizing the likelihood wrt correlation function scale parameter \phi (range), the random field scale parameter \sigma^2 (sill) and the transformation parameter \lambda.
.temp.list <- get(".temp.list", envir=.geoR.env)
if(length(sigmasqphi.lambda) == 3) lambda <- sigmasqphi.lambda[3]
else lambda <- 1
sigmasqphi.lambda <- as.vector(sigmasqphi.lambda)
n <- .temp.list$n
sigmasq <- sigmasqphi.lambda[1]
phi <- sigmasqphi.lambda[2]
main <- .proflik.main(tausq=.temp.list$nugget, sigmasq=sigmasq, phi=phi, lambda = lambda)
if(.temp.list$method.lik == "ML") {
neglik <- (n/2) * log(2 * pi) +
main$log.det.to.half +
0.5 * (main$ssresmat) -
main$log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
neglik <- ((n - .temp.list$beta.size)/2) * log(2 * pi) +
main$log.det.to.half +
0.5 * (main$ssresmat) -
0.5 * sum(log(eigentrem$values)) -
main$log.jacobian
}
return(as.vector(round(neglik, digits=8)))
}
".proflik.aux13" <-
function(sigmasqphi, ...)
{
## This function computes the value of the 2-D profile likelihood for the parameters \sigma^2 and \phi when the nugget is included.
## It requires the minimisation of the function wrt \tau^2 and \lambda (if the case) for each value of (\sigma^2, \phi)
## This is an auxiliary function called by likfit.proflik
eval(substitute(.temp.list$sigmasqphi <- xxx, list(xxx=as.vector(sigmasqphi))), envir=.geoR.env)
.temp.list <- get(".temp.list", envir=.geoR.env)
if(.temp.list$fix.lambda == TRUE) {
## tausq.res <- optim(.temp.list$tausq.est, .proflik.aux14, method="L-BFGS-B", lower
## = 0, ...)$value
tausq.res <- optimise(.proflik.aux14, lower = 0, upper = .Machine$double.xmax^0.25, ...)$objective
}
else {
tausq.res <- optim(
c(.temp.list$tausq.est, .temp.list$lambda),
.proflik.aux14, method="L-BFGS-B",lower = c(0, -2),
upper = c( +Inf, 2), ...)$value
}
eval(expression(.temp.list$sigmasqphi <- NULL), envir=.geoR.env)
return( - tausq.res)
}
".proflik.aux14" <-
function(tausq.lambda, ...)
{
## This function computes the value of the 2-D profile likelihood for the parameters (\sigma^2, \phi), minimizing the likelihood wrt the nugget parameter \tau^2.
## This functions is called by the auxiliary function .proflik.aux13
.temp.list <- get(".temp.list", envir=.geoR.env)
if(length(tausq.lambda) == 2) lambda <- tausq.lambda[2]
else lambda <- 1
n <- .temp.list$n
tausq <- tausq.lambda[1]
main <- .proflik.main(tausq=tausq, .temp.list$sigmasqphi[1], phi=.temp.list$sigmasqphi[2], lambda = lambda)
if(.temp.list$method.lik == "ML") {
neglik <- (n/2) * log(2 * pi) + main$log.det.to.half + 0.5 *
main$ssresmat - main$log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
neglik <- ((n - .temp.list$beta.size)/2) * log(2 * pi) + main$
log.det.to.half + 0.5 * main$ssresmat - 0.5 * sum(log(
eigentrem$values)) - main$log.jacobian
}
return(as.vector(round(neglik, digits=8)))
}
".proflik.aux15" <-
function(sigmasqtausq, ...)
{
## This function computes the value of the 2-D profile likelihood for the parameters \sigma^2 and \tau^2
## It requires the minimisation of the function wrt \phi and also \lambda (if the case) for each value of (\sigma^2, \tau^2)
## This is an auxiliary function called by likfit.proflik
eval(substitute(.temp.list$sigmasqtausq <- xxx, list(xxx=as.vector(sigmasqtausq))), envir=.geoR.env)
.temp.list <- get(".temp.list", envir=.geoR.env)
ini.lik <- round(100000000. * apply(.temp.list$ini.grid, 1,
.proflik.aux16))
ini <- as.vector(.temp.list$ini.grid[which(ini.lik == min(ini.lik, na.rm = TRUE)),,drop=FALSE][1,])
if(.temp.list$fix.lambda == TRUE) {
# phi.res <- optim(ini, .proflik.aux16, method="L-BFGS-B", lower =
# .temp.list$lower.phi, upper=.temp.list$upper.phi, ...)$value
phi.res <- optimise(.proflik.aux16, lower = .temp.list$lower.phi, upper=.temp.list$upper.phi, ...)$objective
}
else {
phi.res <- optim(ini, .proflik.aux16, method="L-BFGS-B",
lower = c(.temp.list$lower.phi, -2),
upper = c(.temp.list$upper.phi, 2), ...)$value
}
eval(expression(.temp.list$sigmasqtausq <- NULL), envir=.geoR.env)
return( - phi.res)
}
".proflik.aux16" <-
function(phi.lambda, ...)
{
## This function computes the value of the 2-D profile likelihood for the sill and nugget parameters (\sigma^2,\tau^2), minimising the profile likelihood wrt correlation function scale parameter \phi (and the transformation parameter \lambda
## This is an auxiliary function called by likfit.aux15
.temp.list <- get(".temp.list", envir=.geoR.env)
if(length(phi.lambda) == 2) lambda <- phi.lambda[2]
else lambda <- 1
n <- .temp.list$n
phi <- phi.lambda[1]
main <- .proflik.main(tausq=.temp.list$sigmasqtausq[2], sigmasq=.temp.list$sigmasqtausq[1], phi=phi, lambda = lambda)
if(.temp.list$method.lik == "ML") {
neglik <- (n/2) * log(2 * pi) + main$log.det.to.half + 0.5 *
main$ssresmat - main$log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
neglik <- ((n - .temp.list$beta.size)/2) * log(2 * pi) + main$
log.det.to.half + 0.5 * main$ssresmat - 0.5 * sum(log(
eigentrem$values)) -
main$log.jacobian
}
return(as.vector(round(neglik, digits=8)))
}
".proflik.aux17" <-
function(phitausq, ...)
{
## This function computes the value of the 2-D profile likelihood for the parameters (\phi, \tau^2)
## It requires the minimisation of the function wrt \sigma^2 and \lambda (if the case) for each value of (\phi, \tau^2)
## This is an auxiliary function called by likfit.proflik
eval(substitute(.temp.list$phitausq <- xxx, list(xxx=as.vector(phitausq))), envir=.geoR.env)
.temp.list <- get(".temp.list", envir=.geoR.env)
if(.temp.list$fix.lambda == TRUE) {
## ini.lik <- round(100000000. * apply(.temp.list$ini.grid, 1,
## .proflik.aux18))
## ini <- as.vector(.temp.list$ini.grid[which(ini.lik == min(ini.lik, na.rm = TRUE)),,drop=FALSE][1,])
## sigmasq.res <- optim(ini, .proflik.aux18, method="L-BFGS-B",
## lower = .temp.list$lower.sigmasq, ...)$value
sigmasq.res <- optimise(.proflik.aux18, lower = .temp.list$lower.sigmasq, upper = .Machine$double.xmax^0.25, ...)$objective
}
else {
sigmasq.res <- optim(c(.temp.list$sigmasq.est, .temp.list$lambda),
.proflik.aux18, method="L-BFGS-B",
lower = c(.temp.list$lower.sigmasq, -2),
upper = c( + Inf, 2), ...)$value
}
eval(expression(.temp.list$phitausq <- NULL), envir=.geoR.env)
return( - sigmasq.res)
}
".proflik.aux18" <-
function(sigmasq.lambda, ...)
{
## This function computes the value of the 2-D profile likelihood for the range and nugget parameters (\phi, \tau^2), minimising the likelihood wrt the random field scale parameter \sigma^2 (sill) ant the transformation parameter \lambda.
## This is an auxiliary function called by likfit.aux17.
.temp.list <- get(".temp.list", envir=.geoR.env)
if(length(sigmasq.lambda) == 2) lambda <- sigmasq.lambda[2]
else lambda <- 1
n <- .temp.list$n
sigmasq <- sigmasq.lambda[1]
main <- .proflik.main(tausq=.temp.list$phitausq[2], sigmasq=sigmasq, phi=.temp.list$phitausq[1], lambda = lambda)
if(.temp.list$method.lik == "ML") {
neglik <- (n/2) * log(2 * pi) + main$log.det.to.half + 0.5 *
main$ssresmat - main$log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
neglik <- ((n - .temp.list$beta.size)/2) * log(2 * pi) + main$
log.det.to.half + 0.5 * main$ssresmat - 0.5 * sum(log(
eigentrem$values)) -
main$log.jacobian
}
return(as.vector(round(neglik, digits=8)))
}
".proflik.aux19" <-
function(sigmasqtausq.rel, ...)
{
## This function computes the value of the 2-D profile likelihood for the parameters (\sigma^2, \tau^2_{rel})
## It requires the minimisation of the function wrt \phi and \lambda (if the case) for each value of (\sigma^2, \tau^2_{rel})
## This is an auxiliary function called by likfit.proflik
eval(substitute(.temp.list$sigmasqtausq.rel <- xxx, list(xxx=as.vector(sigmasqtausq.rel))), envir=.geoR.env)
.temp.list <- get(".temp.list", envir=.geoR.env)
if(.temp.list$fix.lambda == TRUE) {
## phi.res <- optim(.temp.list$phi.est, .proflik.aux20, method="L-BFGS-B", lower =
## .temp.list$lower.phi, upper=.temp.list$upper.phi, ...)$value
phi.res <- optimise(.proflik.aux20, lower =
.temp.list$lower.phi, upper=.temp.list$upper.phi, ...)$objective
}
else {
phi.res <- optim(c(.temp.list$phi.est, .temp.list$lambda, ...), .proflik.aux20, method="L-BFGS-B",
lower = c(.temp.list$lower.phi, -2),
upper = c(.temp.list$upper.phi, 2), ...)$value
}
eval(expression( .temp.list$sigmasqtausq.rel <- NULL), envir=.geoR.env)
return( - phi.res)
}
".proflik.aux2" <-
function(sigmasq, ...)
{
## This function computes the value of the profile likelihood for the random field scale (variance) parameter \sigma^2 when nugget effect is not included in the model.
## It requires the minimisation of the function wrt \phi and maybe \lambda for each value of \sigma^2
## This is an auxiliary function called by likfit.proflik
##
eval(substitute(.temp.list$sigmasq <- xxx, list(xxx=as.vector(sigmasq))), envir=.geoR.env)
.temp.list <- get(".temp.list", envir=.geoR.env)
ini.lik <- round(100000000. * apply(.temp.list$ini.grid, 1,
.proflik.aux3))
ini <- as.vector(.temp.list$ini.grid[which(ini.lik == min(ini.lik, na.rm = TRUE)),,drop=FALSE][1,])
if(.temp.list$fix.lambda == TRUE) {
## phi.res <- optim(ini , .proflik.aux3, method="L-BFGS-B",
## lower = .temp.list$lower.phi,
## upper=.temp.list$upper.phi, ...)$value
phi.res <- optimise(.proflik.aux3,
lower = .temp.list$lower.phi,
upper=.temp.list$upper.phi, ...)$objective
}
else {
phi.res <- optim(ini, .proflik.aux3, method="L-BFGS-B",
lower = c(.temp.list$lower.phi, -2),
upper = c(.temp.list$upper.phi, 2), ...)$value
}
eval(expression(.temp.list$sigmasq <- NULL), envir=.geoR.env)
return( - phi.res)
}
".proflik.aux20" <-
function(phi.lambda, ...)
{
## This function computes the value of the 2-D profile likelihood for the sill and relative nugget parameters (\sigma^2, \tau^2_{rel}), minimising the likelihood wrt the correlation function scale parameter \phi and the transformation parameter \lambda.
## This is an auxiliary function called by likfit.aux19.
.temp.list <- get(".temp.list", envir=.geoR.env)
phi.lambda <- as.vector(phi.lambda)
if(length(phi.lambda) == 2) lambda <- phi.lambda[2]
else lambda <- 1
sigmasqtausq.rel <- as.vector(.temp.list$sigmasqtausq.rel)
sigmasq <- sigmasqtausq.rel[1]
tausq.rel <- sigmasqtausq.rel[2]
phi <- phi.lambda[1]
n <- .temp.list$n
main <- .proflik.main(tausq=tausq.rel, sigmasq=1, phi=phi, lambda = lambda)
if(.temp.list$method.lik == "ML") {
neglik <- (n/2) * log(2 * pi) +
main$log.det.to.half +
(n/2) * log(sigmasq) +
(0.5/sigmasq) * main$ssresmat -
main$log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
neglik <- ((n - .temp.list$beta.size)/2) * log(2 * pi) +
main$log.det.to.half +
(n/2) * log(sigmasq) +
(0.5/sigmasq) * main$ssresmat -
0.5 * sum(log(eigentrem$values)) -
main$log.jacobian
}
return(as.vector(round(neglik, digits=8)))
}
".proflik.aux21" <-
function(phitausq.rel, ...)
{
## This function computes the value of the 2-D profile likelihood for the parameters (\phi, \tau^2_{rel})
## This is an auxiliary function called by likfit.proflik
.temp.list <- get(".temp.list", envir=.geoR.env)
phitausq.rel <- as.vector(phitausq.rel)
phi <- phitausq.rel[1]
tausq.rel <- phitausq.rel[2]
n <- .temp.list$n
main <- .proflik.main(tausq=tausq.rel, sigmasq=1, phi=phi, lambda = 1)
sigmasq.hat <- main$ssresmat/n
if(.temp.list$method.lik == "ML") {
proflik <- - (n/2) * log(2 * pi) -
main$log.det.to.half -
(n/2) * log(sigmasq.hat) -
(n/2) -
main$log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
proflik <- - ((n - .temp.list$beta.size)/2) * log(2 * pi) -
main$log.det.to.half -
(n/2) * log(sigmasq.hat) -
(n/2) +
0.5 * sum(log(eigentrem$values)) -
main$log.jacobian
}
return(proflik)
}
".proflik.aux21.1" <-
function(lambda, ...)
{
## This function computes the value of the 2-D profile likelihood for the parameters (\phi, \tau^2_{rel})
## This requires minimasation wrt to the transformation parameter \lambda
## This is an auxiliary function called by likfit.proflik
.temp.list <- get(".temp.list", envir=.geoR.env)
n <- .temp.list$n
main <- .proflik.main(tausq = .temp.list$phitausq.rel[2], sigmasq = 1,
phi = .temp.list$phitausq.rel[1], lambda = lambda)
sigmasq.hat <- main$ssresmat/n
if(.temp.list$method.lik == "ML") {
neglik <- (n/2) * log(2 * pi) +
main$log.det.to.half + (n/2) * log(sigmasq.hat) +
(n/2) -
main$log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
neglik <- ((n - .temp.list$beta.size)/2) * log(2 * pi) +
main$log.det.to.half +
(n/2) * log(sigmasq.hat) +
(n/2) -
0.5 * sum(log(eigentrem$values)) -
main$log.jacobian
}
return(as.vector(round(neglik, digits=8)))
}
".proflik.aux22" <-
function(sigmasq, ...)
{
## This function computes the value of the 2-D profile likelihood for the range and nugget parameters (\phi, \tau^2), minimising the likelihood wrt the random field scale parameter \sigma^2 (sill)
## This is an auxiliary function called by likfit.aux17
.temp.list <- get(".temp.list", envir=.geoR.env)
n <- .temp.list$n
main <- .proflik.main(tausq=.temp.list$phitausq[2], sigmasq=sigmasq, phi= .temp.list$phitausq[1], lambda = 1)
if(.temp.list$method.lik == "ML") {
neglik <- (n/2) * log(2 * pi) +
main$log.det.to.half +
0.5 * main$ssresmat -
main$log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
neglik <- ((n - .temp.list$beta.size)/2) * log(2 * pi) +
main$log.det.to.half +
0.5 * main$ssresmat -
0.5 * sum(log(eigentrem$values)) -
main$log.jacobian
}
return(as.vector(round(neglik, digits=8)))
}
".proflik.aux23" <-
function(lambda, ...)
{
## This function computes the value of the profile likelihood for the transformation parameter \lambda
## It requires the minimisation of the function wrt \phi and \tau^2 and sigma^2 for each value of \lambda
## This is an auxiliary function called by proflik
.temp.list <- get(".temp.list", envir=.geoR.env)
.temp.temp.list <- get(".temp.temp.list", envir=.geoR.env)
lambda <- as.vector(lambda)
if(.temp.temp.list$fixtau == FALSE) {
if(lambda == 0)
data.l <- log(.temp.list$z)
else data.l <- ((.temp.list$z^lambda) - 1)/lambda
var.l <- var(data.l)
ini.cov <- c(var.l, .temp.temp.list$ini)
}
else
ini.cov <- .temp.temp.list$ini
if(dim(.temp.list$xmat)[2] == 1 & all(.temp.list$xmat == 1))
trend.mat <- "cte"
else
trend.mat <- ~ (.temp.list$xmat[,-1])
lambda.res <- likfit(coords = .temp.temp.list$coords,
data = .temp.list$z,
ini.cov.pars = ini.cov, trend = trend.mat,
fix.nugget = .temp.temp.list$fixtau,
lik.method = .temp.list$method.lik,
cov.model = .temp.list$cov.model,
kappa = .temp.list$kappa, fix.lambda = TRUE,
lambda = lambda,
messages = FALSE)$loglik
assign(".temp.list", .temp.temp.list, envir=.geoR.env)
return(lambda.res)
}
".proflik.aux24" <-
function(sigmasqlambda, ...)
{
## This function computes the value of the 2-D profile likelihood for the parameters (\sigma^2, \lambda) when there is no nugget effect (\tau^2 = 0, fixed)
## It requires the minimisation of the function wrt \phi for each value of (\sigma^2, \lambda)
## This is an auxiliary function called by proflik
sigmasqlambda <- as.vector(sigmasqlambda)
eval(substitute(.temp.list$sigmasq <- xxx, list(xxx=sigmasqlambda[1])), envir=.geoR.env)
.temp.list <- get(".temp.list", envir=.geoR.env)
lambda <- sigmasqlambda[2]
if(lambda == 1) {
eval(expression(.temp.list$log.jacobian <- 0), envir=.geoR.env)
}
else {
if(any(.temp.list$z <= 0))
stop("Transformation option not allowed when there are zeros or negative data"
)
eval(substitute(.temp.list$log.jacobian <- xxx, list(xxx=sum(log(.temp.list$z^(lambda - 1))))), envir=.geoR.env)
if(lambda == 0)
eval(substitute(.temp.list$z <- xxx, list(xxx=log(.temp.list$z))), envir=.geoR.env)
else eval(substitute(.temp.list$z <- xxx, list(xxx= ((.temp.list$z^lambda) - 1)/lambda)), envir=.geoR.env)
}
ini.lik <- round(100000000. * apply(.temp.list$ini.grid, 1,
.proflik.aux3))
ini <- as.vector(.temp.list$ini.grid[which(ini.lik == min(ini.lik, na.rm = TRUE)),,drop=FALSE][1,])
## phi.res <- optim(ini, .proflik.aux3, method="L-BFGS-B", lower = .temp.list$
## lower.phi, upper = .temp.list$upper.phi, ...)$value
phi.res <- optimise(.proflik.aux3, lower = .temp.list$lower.phi, upper = .temp.list$upper.phi, ...)$objective
eval(expression(.temp.list$log.jacobian <- NULL), envir=.geoR.env)
eval(expression(.temp.list$sigmasq <- NULL), envir=.geoR.env)
eval(substitute(.temp.list$z <- xxx, list(xxx=.temp.list$data)), envir=.geoR.env)
return( - phi.res)
}
".proflik.aux27" <-
function(sigmasqlambda, ...)
{
## This function computes the value of the 2-D profile likelihood for sill \sigma^2 and the transformation parameter \lambda
## It requires the minimisation of the function wrt \phi and \tau^2 and for each value of (\sigma^2,\lambda)
## This is an auxiliary function called by .proflik.
sigmasqlambda <- as.vector(sigmasqlambda)
eval(substitute(.temp.list$sigmasq <- xxx, list(xxx=sigmasqlambda[1])), envir=.geoR.env)
.temp.list <- get(".temp.list", envir=.geoR.env)
lambda <- sigmasqlambda[2]
if(lambda == 1) {
eval(expression(.temp.list$log.jacobian <- 0), envir=.geoR.env)
}
else {
eval(expression(.temp.list$fix.lambda <- TRUE), , envir=.geoR.env)
if(any(.temp.list$z^(lambda - 1) <= 0))
eval(substitute(.temp.list$log.jacobian <- xxx, list(xxx=log(prod(.temp.list$z^(lambda -
1))))), envir=.geoR.env)
else eval(substitute(.temp.list$log.jacobian <- xxx, list(xxx=sum(log(.temp.list$z^(lambda -
1))))), envir=.geoR.env)
if(lambda == 0)
eval(substitute(.temp.list$z <- xxx, list(xxx=log(.temp.list$z))), envir=.geoR.env)
else eval(substitute(.temp.list$z <- xxx, list(xxx=((.temp.list$z^lambda) - 1)/lambda)), envir=.geoR.env)
}
ini.lik <- round(100000000. * apply(.temp.list$ini.grid, 1,
.proflik.aux10))
ini <- as.vector(.temp.list$ini.grid[which(ini.lik == min(ini.lik, na.rm = TRUE)),,drop=FALSE][1,])
phitausq.rel.res <- optim(ini, .proflik.aux10, method="L-BFGS-B",
lower = c(.temp.list$lower.phi,
0), upper=c(.temp.list$upper.phi, 100), ...)$value
eval(expression(.temp.list$log.jacobian <- NULL), envir=.geoR.env)
eval(expression(.temp.list$sigmasq <- NULL), envir=.geoR.env)
eval(substitute(.temp.list$z <- xxx, list(xxx=.temp.list$data)), envir=.geoR.env)
return( - phitausq.rel.res)
}
".proflik.aux28" <-
function(sigmasqphi, ...)
{
## This function computes the value of the 2-D profile likelihood for the random field scale (variance) parameter \sigma^2 and the correlation function parameter \phi when nugget effect is not included in the model.
## It requires the minimisation of the function wrt \lambda for each value of (\sigma^2, \phi)
## This is an auxiliary function called by likfit.proflik
##
## ini.seq <- seq(-1.5, 1.5, l=7)
## .temp.list$sigmasqphi <<- as.vector(sigmasqphi)
## lambda.lik <- apply(as.matrix(ini.seq), 1, .proflik.aux4)
## ini <- ini.seq[lambda.lik == max(lambda.lik)]
## lambda.res <- optim(ini, .proflik.aux4, method="L-BFGS-B", lower = -2.5, upper = 2.5, ...)$value
lambda.res <- optimise(.proflik.aux4, lower = -5, upper = 5, ...)$objective
eval(expression(.temp.list$sigmasqphi <- NULL), envir=.geoR.env)
return( - lambda.res)
}
".proflik.aux30" <-
function(phitausq.rel, ...)
{
## This function computes the value of the profile likelihood for the correlation parameter \phi when nugget effect is not included in the model.
## It requires the minimisation of the function wrt \phi for each value of \lambda, if this transformation parameter is included in the model
## This is an auxiliary function called by likfit.proflik
##
.temp.list <- get(".temp.list", envir=.geoR.env)
if(.temp.list$fix.lambda == TRUE)
proflik <- .proflik.aux21(phitausq.rel = phitausq.rel)
else {
eval(substitute(.temp.list$phitausq.rel <- xxx, list(xxx=phitausq.rel)), envir=.geoR.env)
## proflik <- - (optim(.temp.list$lambda, .proflik.aux21.1, method="L-BFGS-B", lower =
## -2, upper = 2, ...)$value)
proflik <- - (optimise(.proflik.aux21.1, lower = -5, upper = 5, ...)$objective)
eval(expression(.temp.list$phitausq.rel <- NULL), envir=.geoR.env)
}
return(proflik)
}
".proflik.aux3" <-
function(phi.lambda, ...)
{
## This function computer the negative of the likelihood function for the correlation function scale parameter \phi (and maybe the transformation parameter \lambda) only for models with fixed nugget effect (i.e., when it is not a parameter to be estimated)
## This function is used when computing the profile likelihood for \sigma^2
## This is an auxiliary function called by .proflik.aux2
## phi <- pmax(phi, .temp.list$lower.phi)
.temp.list <- get(".temp.list", envir=.geoR.env)
if(length(phi.lambda) == 2)
lambda <- phi.lambda[2]
else lambda <- 1
sigmasq <- .temp.list$sigmasq
phi <- phi.lambda[1]
n <- .temp.list$n
main <- .proflik.main(tausq=0, sigmasq=1, phi=phi, lambda = lambda)
if(.temp.list$method.lik == "ML") {
neglik <- (n/2) * log(2 * pi) +
main$log.det.to.half +
(n/2) * log(sigmasq) + (0.5/sigmasq) * main$ssresmat -
main$log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
neglik <- ((n - .temp.list$beta.size)/2) * log(2 * pi) +
main$log.det.to.half +
((n - .temp.list$beta.size)/2) * log(sigmasq) +
(0.5/sigmasq) * main$ssresmat -
0.5 * sum(log(eigentrem$values)) -
main$log.jacobian
}
return(as.vector(round(neglik, digits=8)))
}
".proflik.aux31" <-
function(philambda, ...)
{
## This function computes the value of the 2-D profile likelihood for range \phi and the transformation parameter \lambda.
## It requires the minimisation of the function wrt \tau^2_{rel} and for each value of (\phi,\lambda).
## This is an auxiliary function called by .proflik.
.temp.list <- get(".temp.list", envir=.geoR.env)
philambda <- as.vector(philambda)
eval(substitute(.temp.list$phi <- xxx, list(xxx= philambda[1])), envir=.geoR.env)
.temp.list$lambda <- philambda[2]
## tausq.rel.res <- optim(.temp.list$tausq.rel.est, .proflik.aux8, method="L-BFGS-B", lower =
## 0, upper=100, ...)$value
tausq.rel.res <- optimise(.proflik.aux8, lower = 0, upper=1000, ...)$objective
eval(expression(.temp.list$phi <- NULL), envir=.geoR.env)
return( - tausq.rel.res)
}
".proflik.aux32" <-
function(tausqlambda, ...)
{
## This function computes the value of the 2-D profile likelihood for nugget \tau^2 and the transformation parameter \lambda.
# It requires the minimisation of the function wrt \phi and \sigma^2 and for each value of (\tau^2,\lambda).
# This is an auxiliary function called by .proflik.
tausqlambda <- as.vector(tausqlambda)
eval(substitute(.temp.list$nugget <- xxx, list(xxx=tausqlambda[1])), envir=.geoR.env)
.temp.list <- get(".temp.list", envir=.geoR.env)
lambda <- tausqlambda[2]
if(lambda == 1) {
eval(expression(.temp.list$log.jacobian <- 0), envir=.geoR.env)
}
else {
if(any(.temp.list$z^(lambda - 1) <= 0))
eval(substitute(.temp.list$log.jacobian <- xxx, list(xxx=log(prod(.temp.list$z^(lambda -
1))))), envir=.geoR.env)
else eval(substitute(.temp.list$log.jacobian <- xxx, list(xxx=sum(log(.temp.list$z^(lambda - 1))))), envir=.geoR.env)
if(lambda == 0)
eval(substitute(.temp.list$z <- xxx, list(xxx=log(.temp.list$z))), envir=.geoR.env)
else eval(substitute(.temp.list$z <- xxx, list(xxx=((.temp.list$z^lambda) - 1)/lambda)), envir=.geoR.env)
}
sigmasqphi.res <- optim(c(.temp.list$sigmasq.est, .temp.list$phi.est), .proflik.aux12, method="L-BFGS-B",
lower = c(.temp.list$lower.sigmasq, .temp.list$
lower.phi), upper=c(+Inf, .temp.list$upper.phi), ...)$value
eval(expression(.temp.list$log.jacobian <- NULL), envir=.geoR.env)
eval(substitute(.temp.list$z <- xxx, list(xxx=.temp.list$data)), envir=.geoR.env)
eval(expression(.temp.list$nugget <- NULL), envir=.geoR.env)
return( - sigmasqphi.res)
}
".proflik.aux33" <-
function(tausq.rellambda, ...)
{
## This function computes the value of the 2-D profile likelihood for nugget \tau^2 and the transformation parameter \lambda.
## It requires the minimisation of the function wrt \phi for each value of (\tau^2,\lambda).
## This is an auxiliary function called by .proflik.
tausq.rellambda <- as.vector(tausq.rellambda)
eval(substitute(.temp.list$nugget.rel <- xxx, list(xxx=tausq.rellambda[1])), envir=.geoR.env)
.temp.list <- get(".temp.list", envir=.geoR.env)
lambda <- tausq.rellambda[2]
if(lambda == 1) {
eval(expression(.temp.list$log.jacobian <- 0), envir=.geoR.env)
}
else {
if(any(.temp.list$z^(lambda - 1) <= 0))
eval(substitute(.temp.list$log.jacobian <- xxx, list(xxx=log(prod(.temp.list$z^(lambda -
1))))), envir=.geoR.env)
else eval(substitute(.temp.list$log.jacobian <- xxx, list(xxx=sum(log(.temp.list$z^(lambda -
1))))), envir=.geoR.env)
if(lambda == 0)
eval(substitute(.temp.list$z <- xxx, list(xxx=log(.temp.list$z))), envir=.geoR.env)
else eval(substitute(.temp.list$z <- xxx, list(xxx=((.temp.list$z^lambda) - 1)/lambda)), envir=.geoR.env)
}
## phi.res <- optim(.temp.list$phi.est, .proflik.aux6, method="L-BFGS-B", lower = .temp.list$
## lower.phi, upper=.temp.list$upper.phi, ...)$value
phi.res <- optimise(.proflik.aux6, lower = .temp.list$lower.phi, upper=.temp.list$upper.phi, ...)$objective
eval(expression(.temp.list$log.jacobian <- NULL), envir=.geoR.env)
eval(expression(.temp.list$nugget.rel <- NULL), envir=.geoR.env)
eval(substitute(.temp.list$z <- xxx, list(xxx=.temp.list$data)), envir=.geoR.env)
return( - phi.res)
}
".proflik.aux4" <-
function(lambda, ...)
{
## This function computer the values of the profile likelihood function for the parameters \phi and \sigma^2 for models with nugget effect = 0, including the tranformation parameter \lambda
## This is an auxiliary function called by .proflik.aux28
##
.temp.list <- get(".temp.list", envir=.geoR.env)
sigmasqphi <- as.vector(.temp.list$sigmasqphi)
sigmasq <- sigmasqphi[1]
phi <- sigmasqphi[2]
n <- .temp.list$n
if(lambda > 0.999 & lambda < 1.001)
lambda <- 1
main <- .proflik.main(tausq=.temp.list$nugget, sigmasq = sigmasq, phi=phi, lambda = lambda)
if(.temp.list$method.lik == "ML") {
neglik <- ((n/2) * log(2 * pi) +
main$log.det.to.half +
0.5 * main$ssresmat -
main$log.jacobian)
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
xx.eigen <- eigen(crossprod(.temp.list$xmat), symmetric = TRUE,
only.values = TRUE)
neglik <- (((n - .temp.list$beta.size)/2) * log(2 * pi) -
0.5 * sum(log(xx.eigen$values)) + main$log.det.to.half +
(0.5) * main$ssresmat + 0.5 * sum(log(eigentrem$values)) + main$log.jacobian)
}
return(as.vector(round(neglik, digits=8)))
}
".proflik.aux5" <-
function(tausq.rel, ...)
{
## This function computes the value of the profile likelihood for the parameter \tau^2_{rel}.
## It requires the minimisation of the function wrt \phi and \lambda (if the case) for each value of \tau^2_{rel}.
## This is an auxiliary function called by .proflik.
eval(substitute(.temp.list$nugget.rel <- xxx, list(xxx=as.vector(tausq.rel))), envir=.geoR.env)
.temp.list <- get(".temp.list", envir=.geoR.env)
if(.temp.list$fix.lambda == TRUE) {
## phi.res <- optim(.temp.list$phi.est, .proflik.aux6, method="L-BFGS-B", lower =
## .temp.list$lower.phi, upper=.temp.list$upper.phi, ...)$value
phi.res <- optimise(.proflik.aux6, lower =
.temp.list$lower.phi, upper=.temp.list$upper.phi, ...)$objective
}
else {
phi.res <- optim(c(.temp.list$phi.est, .temp.list$lambda), .proflik.aux6, method="L-BFGS-B",
lower = c(.temp.list$lower.phi, -2),
upper = c(.temp.list$upper.phi, 2), ...)$value
}
eval(expression(.temp.list$nugget.rel <- NULL), envir=.geoR.env)
return( - phi.res)
}
".proflik.aux6" <-
function(phi.lambda, ...)
{
## This function computes the value of the profile likelihood for the relative nugget parameter \tau^2_{rel}, minimizing the likelihood wrt correlation function scale parameter \phi (range) and the transformation parameter \lambda.
.temp.list <- get(".temp.list", envir=.geoR.env)
if(length(phi.lambda) == 2) lambda <- phi.lambda[2] else lambda <- 1
phi.lambda <- as.vector(phi.lambda)
phi <- phi.lambda[1]
n <- .temp.list$n
main <- .proflik.main(tausq=.temp.list$nugget.rel, sigmasq=1, phi=phi, lambda = lambda)
if(.temp.list$method.lik == "ML") {
neglik <- (n/2) * log(2 * pi) +
main$log.det.to.half +
(n/2) * log(main$ssresmat/n) +
(n/2) -
main$log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
neglik <- ((n - .temp.list$beta.size)/2) * log(2 * pi) +
main$log.det.to.half +
((n - .temp.list$beta.size)/2) * log(main$ssresmat/n) +
(n/2) -
0.5 * sum(log(eigentrem$values)) -
main$log.jacobian
}
return(as.vector(round(neglik, digits=8)))
}
".proflik.aux7" <-
function(phi, ...)
{
## This function computes the value of the profile likelihood for the parameter \phi when the nugget \tau^2 is included in the model
## It requires the minimisation of the function wrt relative \tau^2_{rel} for each value of \phi
## This is an auxiliary function called by .proflik.
eval(substitute(.temp.list$phi <- xxx, list(xxx=as.vector(phi))), envir=.geoR.env)
.temp.list <- get(".temp.list", envir=.geoR.env)
if(.temp.list$fix.lambda) {
eval(expression(.temp.list$lambda <- 1), envir=.geoR.env)
## tausq.rel.res <- optim(.temp.list$tausq.rel.est, .proflik.aux8, method="L-BFGS-B",
## lower = 0, upper=100, ...)$value
tausq.rel.res <- optimise(.proflik.aux8, lower = 0, upper=1000, ...)$objective
eval(expression(.temp.list$lambda <- NULL), envir=.geoR.env)
}
else {
tausq.rel.res <- optim(c(.temp.list$tausq.rel.est, .temp.list$lambda), .proflik.aux8,
method="L-BFGS-B", lower = c(0, -2), upper = c(100, 2), ...)$value
}
eval(expression(.temp.list$phi <- NULL), envir=.geoR.env)
return( - tausq.rel.res)
}
".proflik.aux8" <-
function(tausq.rel.lambda, ...)
{
## This function computes the value of the profile likelihood for the correlation function scale parameter \phi (and lambda), minimizing the likelihood wrt relative nugget parameter \tau^2_{rel}
.temp.list <- get(".temp.list", envir=.geoR.env)
if(length(tausq.rel.lambda) == 2)
lambda <- tausq.rel.lambda[2]
else lambda <- .temp.list$lambda
n <- .temp.list$n
phi <- .temp.list$phi
tausq.rel <- tausq.rel.lambda[1]
main <- .proflik.main(tausq=tausq.rel, sigmasq=1, phi=phi, lambda = lambda)
if(.temp.list$method.lik == "ML") {
neglik <- (n/2) * log(2 * pi) + main$log.det.to.half + (
n/2) * log(main$ssresmat/n) + (n/2) - main$log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
neglik <- (((n - .temp.list$beta.size)/2) * log(2 * pi) + main$
log.det.to.half + ((n - .temp.list$beta.size)/2) * log(main$ssresmat/
n) + (n/2) - 0.5 * sum(log(eigentrem$values))) -
main$log.jacobian
}
return(as.vector(round(neglik, digits=8)))
}
".proflik.aux9" <-
function(sigmasq, ...)
{
## This function computes the value of the profile likelihood for the parameter \sigma^2 when \tau^2 is included in the model
## It requires the minimisation of the function wrt \phi and \tau^2 for each value of \sigma^2
## This is an auxiliary function called by likfit.proflik
eval(substitute(.temp.list$sigmasq <- xxx, list(xxx=as.vector(sigmasq))), envir=.geoR.env)
.temp.list <- get(".temp.list", envir=.geoR.env)
ini.lik <- round(100000000. * apply(.temp.list$ini.grid, 1,
.proflik.aux10))
ini <- as.vector(.temp.list$ini.grid[which(ini.lik == min(ini.lik, na.rm = TRUE)),,drop=FALSE][1,])
if(.temp.list$fix.lambda == TRUE) {
phitausq.rel.res <- optim(ini, .proflik.aux10, method="L-BFGS-B",
lower = c(.temp.list$
lower.phi, 0),
upper=c(.temp.list$upper.phi, 100), ...)$value
}
else {
if(ini[2] == 0) ini[2] <- 0.01
phitausq.rel.res <- optim(ini, .proflik.aux10, method="L-BFGS-B",
lower = c(.temp.list$lower.phi, 0,-2),
upper = c(.temp.list$upper.phi, 100, 2), ...)$value
}
eval(expression(.temp.list$sigmasq <- NULL), envir=.geoR.env)
return( - phitausq.rel.res)
}
"plot.proflik" <-
function(x, pages = c("user", "one", "two"),
uni.only, bi.only, type.bi = c("contour", "persp"),
conf.int = c(0.90,0.95),
yaxis.lims = c("conf.int", "as.computed"),
by.col = TRUE, log.scale = FALSE, use.splines = TRUE,
par.mar.persp = c(0, 0, 0, 0), ask = FALSE,
...)
{
##
## Saving original par() parameters
##
## par.ori <- par(no.readonly = TRUE)
## on.exit(par(par.ori))
##
parask <- par()$ask
par(ask = ask)
on.exit(par(ask = parask))
##
## Checking whether to plot 1D and/or 2D profiles
##
if(missing(uni.only)){
if(x$n.bi == 0) uni.only <- TRUE
else uni.only <- FALSE
}
if(missing(bi.only)){
if(x$n.uni == 0) bi.only <- TRUE
else bi.only <- FALSE
}
if(!is.logical(uni.only))
stop("argument uni.only must be logical (TRUE or FALSE)")
if(!is.logical(bi.only))
stop("argument bi.only must be logical (TRUE or FALSE)")
n.uni <- x$n.uni
n.bi <- x$n.bi
if((uni.only == FALSE) & (bi.only == FALSE))
np <- n.uni + n.bi
if((uni.only == TRUE) & (bi.only == FALSE))
np <- n.uni
if((uni.only == FALSE) & (bi.only == TRUE))
np <- n.bi
if(n.uni == 0 & np > 0) bi.only <- TRUE
if(n.bi == 0 & np > 0) uni.only <- TRUE
##
##
##
if(mode(yaxis.lims) == "character")
yaxis.lims <- match.arg(yaxis.lims)
type.bi <- match.arg(type.bi)
##
## Definig number of pages to place the plots
##
pages <- match.arg(pages)
if(pages == "one") {
if(np >= 1 & np < 4)
par(mfrow = c(np, 1))
if(np >= 4) {
if(by.col == TRUE)
par(mfcol = c(ceiling(np/2), 2))
else par(mfrow = c(ceiling(np/2), 2))
}
}
if(pages == "two") {
if(n.uni > 1 & n.uni < 4)
par(mfrow = c(n.uni, 1))
if(n.uni >= 4)
par(mfrow = c(ceiling(n.uni/2), 2))
}
##
##
##
if(bi.only == FALSE) {
for(i in 1:n.uni) {
if(x$method.lik == "ML")
ylabm <- "profile log-likelihood"
else ylabm <- "profile log-(restricted) likelihood"
if(!is.logical(conf.int) || all(conf.int) != FALSE) {
if(mode(conf.int) != "numeric"| any(conf.int > 1))
stop("argument conf.int must be numerical (scalar or vector) with values between 0 and 1")
conf.int.drop <- x[[i]][[3]][2] - 0.5 * qchisq(conf.int,1)
}
if(all(is.character(yaxis.lims))){
if(yaxis.lims == "conf.int")
lik.lims <- c(min(conf.int.drop),
x[[i]][[3]][2])
else lik.lims <- c(min(x[[i]][[2]]),
x[[i]][[3]][2])
}
else
lik.lims <- yaxis.lims
if(log.scale == TRUE) {
if(use.splines){
nxpoints <- 5*length(x[[i]][[1]])
nodups <- which(duplicated(x[[i]][[1]]) == FALSE)
plot(spline(x = log(x[[i]][[1]][nodups]),
y = x[[i]][[2]][nodups],
n = nxpoints,
method="natural"), type = "l",
xlab = paste("log-",
.proflik.plot.aux1(names(x[[i]])[1])),
ylab = ylabm, ylim = lik.lims)
}
else{
plot(log(x[[i]][[1]]),
x[[i]][[2]],
type = "l",
xlab = paste("log-",
.proflik.plot.aux1(names(x[[i]])[1])),
ylab = ylabm, ylim = lik.lims)
}
lines(log(c(x[[i]][[3]][1], x[[i]][[3]][1])),
c(min(lik.lims), x[[i]][[3]][2]), lty = 2)
}
else {
if(use.splines){
nxpoints <- 5*length(x[[i]][[1]])
nodups <- which(duplicated(x[[i]][[1]]) == FALSE)
plot(spline(x = x[[i]][[1]][nodups],
y = x[[i]][[2]][nodups],
n = nxpoints,
method="natural"),
type = "l",
xlab = .proflik.plot.aux1(names(x[[i]])[1]),
ylab = ylabm, ylim = lik.lims)
}
else{
plot(x[[i]][[1]],
x[[i]][[2]],
type = "l", xlab =
.proflik.plot.aux1(names(x[[i]])[1]),
ylab = ylabm, ylim = lik.lims)
}
lines(c(x[[i]][[3]][1],
x[[i]][[3]][1]),
c(min(lik.lims), x[[
i]][[3]][2]), lty = 2)
}
abline(h = conf.int.drop, lty = 3)
}
}
if(uni.only == FALSE) {
if(pages == "two") {
if(n.bi >= 1 & n.bi < 4)
par(mfrow = c(n.bi, 1))
if(n.bi >= 4)
par(mfrow = c(ceiling(n.bi/2), 2))
}
for(i in 1:n.bi) {
if(type.bi == "contour") {
if(log.scale == TRUE) {
contour(log(x[[(n.uni + i)]][[1]]),
log(x[[(n.uni + i)]][[2]]),
matrix(x[[(n.uni + i)]][[3]],
ncol = length(x[[(n.uni +i)]][[2]])),
xlab = paste("log-", .proflik.plot.aux1(names(x[[(n.uni + i)]][1]))),
ylab = paste("log-", .proflik.plot.aux1(names(x[[(n.uni + i)]][2]))),
...)
points(log(t(x[[(n.uni + i)]][[4]][1:2])))
}
else {
contour(x[[(n.uni + i)]][[1]],
x[[(n.uni + i)]][[2]],
matrix(x[[(n.uni + i)]][[3]],
ncol = length(x[[(n.uni + i)]][[2]])),
xlab = .proflik.plot.aux1(names(x[[(n.uni + i)]][1])),
ylab = .proflik.plot.aux1(names(x[[(n.uni + i)]][2])),
...)
points(t(x[[(n.uni + i)]][[4]][1:2]))
}
}
if(type.bi == "persp") {
cat("For better visualisation arguments for the funtion `persp` can be passed.\nSome relevant argments are: theta, phi, r, d, among others.\n Type help(persp) for a description of the options\n")
if(x$method.lik == "ML")
zlabm <-
"profile log-likelihood"
else zlabm <- "profile log-(restricted) likelihood"
zlimm <- range(x[[(n.uni +
i)]][[3]])
zlimm[1] <- 1.01 * zlimm[1]
minlik <- min(x[[(n.uni + i)]][[3]])
if(log.scale == TRUE) {
persp(log(x[[(n.uni + i)]][[1]]),
log(x[[(n.uni + i)]][[2]]),
matrix(x[[(n.uni + i)]][[3]],
ncol = length(x[[(n.uni + i)]][[2]])),
xlab = .proflik.plot.aux1(paste("log-", names(x[[(n.uni + i)]][1]))),
ylab = paste("log-", .proflik.plot.aux1(names(x[[(n.uni + i)]][2]))),
zlab = zlabm, box = TRUE, ...)
# pp1 <- perspp(x = log(c(x[[(n.uni + i)]][[4]][1],
# min( x[[(n.uni + i)]][[1]]))[c(1, 1, 1, 2)]),
# y = log(c(x[[(n.uni + i)]][[4]][2],
# min(x[[(n.uni + i)]][[2]]))[c(1, 1, 2, 1)]),
# z = c(minlik, x[[(n.uni + i)]][[4]][3])[c(1, 2, 1, 1)], pp)
# segments(log(pp1$x[1]), log(pp1$y[1]), log(pp1$x[2]), log(pp1$y[2]),
# lwd = 2)
}
else {
persp(x = x[[(n.uni + i)]][[1]],
y = x[[(n.uni + i)]][[2]],
z = matrix(x[[(n.uni + i)]][[3]],
ncol = length(x[[(n.uni + i)]][[2]])),
xlab = .proflik.plot.aux1(names(x[[(n.uni + i)]][1])),
ylab = .proflik.plot.aux1(names(x[[(n.uni + i)]][2])),
zlab = zlabm, box = TRUE, ...)
# pp1 <- perspp(x = c(x[[(n.uni + i)]][[4]][1],
# min(x[[(n.uni + i)]][[1]]))[c(1, 1, 1, 2)],
# y = c(x[[(n.uni + i)]][[4]][2],
# min(x[[(n.uni + i)]][[2]]))[c(1, 1,2, 1)],
# z = c(minlik, x[[(n.uni + i)]][[4]][3])[c(1, 2, 1, 1)], pp)
# segments(pp1$x[1], pp1$y[1], pp1$x[2], pp1$y[2], lwd = 2)
}
}
}
}
return(invisible())
}
".proflik.plot.aux1" <-
function(parameter.name)
{
switch(parameter.name,
range = expression(phi),
sill = expression(sigma^2),
lambda = expression(lambda),
nugget = expression(tau^2),
nugget.rel = expression(tau[rel]^2))
}
".proflik.main" <-
function(tausq, sigmasq, phi, lambda)
{
.temp.list <- get(".temp.list", envir=.geoR.env)
z <- .temp.list$z
n <- .temp.list$n
if(lambda == 1){
## log.jacobian <- .temp.list$log.jacobian
log.jacobian <- 0
}
else {
if(any(z <= 0))
stop("Transformation option not allowed when there are zeros or negative data")
if(any(z^(lambda - 1) <= 0))
log.jacobian <- log(prod(z^(lambda - 1)))
else log.jacobian <- sum(log(z^(lambda - 1)))
if(lambda == 0)
z <- log(z)
else z <- ((z^lambda) - 1)/lambda
}
kappa <- .temp.list$kappa
V <- varcov.spatial(dists.lowertri = .temp.list$dists.lowertri,
cov.model = .temp.list$cov.model, kappa = kappa,
nugget = tausq, cov.pars = c(sigmasq, phi),
det = TRUE)
xix <- crossprod(.temp.list$xmat,solve(V$varcov,.temp.list$xmat))
if(length(as.vector(xix)) == 1) choldet <- 0.5 * log(xix)
else choldet <- sum(log(diag(chol(xix))))
iz <- solve(V$varcov,z)
xiy <- crossprod(.temp.list$xmat,iz)
beta.hat <- drop(solve(xix,xiy))
yiy <- drop(crossprod(z,iz))
ssresmat <- as.vector(yiy - crossprod(beta.hat,xiy))
return(list(log.det.to.half = V$log.det.to.half,
ssresmat = ssresmat,
ixix = solve(xix), log.jacobian = log.jacobian))
}
".proflik.lambda" <-
function(lambda)
{
.temp.list <- get(".temp.list", envir=.geoR.env)
.temp.lower.lambda <- get(".temp.lower.lambda", envir=.geoR.env)
.temp.upper.lambda <- get(".temp.upper.lambda", envir=.geoR.env)
if (any(is.na(lambda)) | any(lambda==Inf) | any(is.nan(lambda)))
neglik <- 1e+32
else{
if(.temp.list$minimisation.function == "nlm"){
if (exists(".temp.lambda", envir=.geoR.env)) remove(".temp.lambda", envir=.geoR.env, inherits = TRUE)
lambda.minimiser <- lambda
penalty <- 1000 * (.temp.lower.lambda - min(lambda, .temp.lower.lambda))
lambda <- max(lambda, .temp.lower.lambda)
penalty <- penalty + 1000 * (.temp.upper.lambda - max(lambda, .temp.upper.lambda))
lambda <- min(lambda, .temp.upper.lambda)
if (round(1000 * lambda.minimiser) <= round(1000 * .temp.lower.lambda))
assign(".temp.lambda", lambda, envir=.geoR.env)
if (round(1000 * lambda.minimiser) >= round(1000 * .temp.upper.lambda))
assign(".temp.lambda", lambda, envir=.geoR.env)
}
z <- .temp.list$z
n <- .temp.list$n
if(lambda == 1) {
.temp.list$log.jacobian <- 0
}
else {
if(any(z < 0))
stop("Transformation option not allowed when there are zeros or negative data")
if(any(z^(lambda - 1) <= 0))
.temp.list$log.jacobian <- log(prod(z^(lambda - 1)))
else .temp.list$log.jacobian <- sum(log(z^(lambda - 1)))
if(lambda == 0)
z <- log(z)
else z <- ((z^lambda) - 1)/lambda
}
beta.size <- .temp.list$beta.size
kappa <- .temp.list$kappa
xmat <- .temp.list$xmat
txmat <- .temp.list$txmat
ixx <- solve(crossprod(xmat))
tausqhat <- (z %*% (diag(n) - xmat %*% ixx %*% txmat) %*% z)/n
if(.temp.list$method == "ML")
neglik <- ((n/2) * log(2 * pi) +
(n/2) * log(tausqhat) +
(n/2) -
.temp.list$log.jacobian
)
if(.temp.list$method == "RML") {
eigentrem <- eigen(ixx, symmetric = TRUE, only.values = TRUE)
neglik <- (((n - beta.size)/2) * log(2 * pi) +
((n - beta.size)/2) * log(tausqhat) +
(n/2) -
0.5 * sum(log(eigentrem$values)) -
.temp.list$log.jacobian
)
}
}
if(.temp.list$minimisation.function == "nlm")
return(as.vector(neglik + penalty))
else
return(as.vector(neglik))
}
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"proflik" <-
function(obj.likfit, geodata, coords = geodata$coords,
data = geodata$data,
sill.values,
range.values,
nugget.values,
nugget.rel.values,
lambda.values,
sillrange.values = TRUE,
sillnugget.values = TRUE,
rangenugget.values = TRUE,
sillnugget.rel.values = FALSE,
rangenugget.rel.values = FALSE,
silllambda.values = FALSE,
rangelambda.values = TRUE,
nuggetlambda.values = FALSE,
nugget.rellambda.values = FALSE,
uni.only = TRUE,
bi.only = FALSE,
messages,
...)
{
##
## 1. setting arguments
##
if(missing(messages))
messages.screen <- as.logical(ifelse(is.null(getOption("geoR.messages")), TRUE, getOption("geoR.messages")))
else messages.screen <- messages
if(missing(geodata))
geodata <- list(coords = coords, data = data)
# if(! "package:stats" %in% search()) require(mva)
call.fc <- match.call()
n.cov.pars <- obj.likfit$npars - length(obj.likfit$beta)
if(obj.likfit$transform.info$fix.lambda == FALSE)
n.cov.pars <- n.cov.pars - 1
if(missing(sill.values))
sill.values <- sillrange.values <- sillnugget.values <- FALSE
if(missing(range.values))
range.values <- sillrange.values <- rangenugget.values <- rangelambda.values <- FALSE
if(!is.null(obj.likfit$call$fix.nugget))
if(obj.likfit$call$fix.nugget == TRUE)
nugget.values <- nugget.rel.values <- FALSE
if(missing(nugget.values))
nugget.values <- sillnugget.values <- rangenugget.values <- nuggetlambda.values <- FALSE
if(missing(nugget.rel.values))
nugget.rel.values <- sillnugget.rel.values <- rangenugget.rel.values <- nugget.rellambda.values <- FALSE
if(missing(lambda.values) | obj.likfit$transform.info$fix.lambda) lambda.values <- FALSE
if(uni.only){
sillrange.values <- sillnugget.values <- rangenugget.values <-
sillnugget.rel.values <- rangenugget.rel.values <-
silllambda.values <- rangelambda.values <-
nugget.rellambda.values <- nuggetlambda.values <- FALSE
}
else{
if(all(sillrange.values == TRUE)){
if(all(sill.values == FALSE) | all(range.values == FALSE)){
sillrange.values <- FALSE
stop("if argument sillrange.values = TRUE sill.values and range.values must be provided. Alternatively a matrix can be provided in sillrange.values or set this to FALSE")
}
else
sillrange.values <- as.matrix(expand.grid(sill.values, range.values))
}
if(n.cov.pars == 2){
sillnugget.values <- rangenugget.values <-
sillnugget.rel.values <- rangenugget.rel.values <-
nugget.rellambda.values <- nuggetlambda.values <- FALSE
}
else{
if(all(sillnugget.values == TRUE)){
if(all(sill.values == FALSE) | all(nugget.values == FALSE)){
sillnugget.values <- FALSE
stop("if argument sillnugget.values = TRUE sill.values and nugget.values must be provided. Alternatively a matrix can be provided in sillnugget.values or set this to FALSE")
}
else
sillnugget.values <- as.matrix(expand.grid(sill.values, nugget.values))
}
if(all(rangenugget.values == TRUE)){
if(all(range.values == FALSE) | all(nugget.values == FALSE)){
rangenugget.values <- FALSE
stop("if argument rangenugget.values = TRUE range.values and nugget.values must be provided. Alternatively a matrix can be provided in rangenugget.values or set this to FALSE")
}
else
rangenugget.values <- as.matrix(expand.grid(range.values, nugget.values))
}
if(all(sillnugget.rel.values == TRUE)){
if(all(sill.values == FALSE) | all(nugget.rel.values == FALSE)){
sillnugget.rel.values <- FALSE
stop("if argument sillnugget.rel.values = TRUE sill.values and nugget.rel.values must be provided. Alternatively a matrix can be provided in sillnugget.rel.values or set this to FALSE")
}
else
sillnugget.rel.values <- as.matrix(expand.grid(sill.values, nugget.rel.values))
}
if(all(rangenugget.rel.values == TRUE)){
if(all(range.values == FALSE) | all(nugget.rel.values == FALSE)){
rangenugget.rel.values <- FALSE
stop("if argument rangenugget.rel.values = TRUE range.values and nugget.rel.values must be provided. Alternatively a matrix can be provided in rangenugget.rel.values or set this to FALSE")
}
else
rangenugget.rel.values <- as.matrix(expand.grid(range.values, nugget.rel.values))
}
if(obj.likfit$transform.info$fix.lambda == TRUE){
if(all(nuggetlambda.values == TRUE)){
if(all(lambda.values == FALSE) | all(nugget.values == FALSE)){
nuggetlambda.values <- FALSE
stop("if argument nuggetlambda.values = TRUE lambda.values and nugget.values must be provided. Alternatively a matrix can be provided in nuggetlambda.values or set this to FALSE")
}
else
nuggetlambda.values <- as.matrix(expand.grid(lambda.values, nugget.values))
}
if(all(nugget.rellambda.values == TRUE)){
if(all(lambda.values == FALSE) | all(nugget.rel.values == FALSE)){
nugget.rellambda.values <- FALSE
stop("if argument nugget.rellambda.values = TRUE lambda.values and nugget.rel.values must be provided. Alternatively a matrix can be provided in nugget.rellambda.values or set this to FALSE")
}
else
nugget.rellambda.values <- as.matrix(expand.grid(lambda.values, nugget.rel.values))
}
}
}
if(obj.likfit$transform.info$fix.lambda == TRUE)
silllambda.values <- rangelambda.values <- FALSE
else{
if(all(silllambda.values == TRUE)){
if(all(sill.values == FALSE) | all(lambda.values == FALSE)){
silllambda.values <- FALSE
stop("if argument silllambda.values = TRUE sill.values and lambda.values must be provided. Alternatively a matrix can be provided in silllambda.values or set this to FALSE")
}
else
silllambda.values <- as.matrix(expand.grid(sill.values, lambda.values))
}
if(all(rangelambda.values == TRUE)){
if(all(range.values == FALSE) | all(lambda.values == FALSE)){
rangelambda.values <- FALSE
stop("if argument rangelambda.values = TRUE range.values and lambda.values must be provided. Alternatively a matrix can be provided in rangelambda.values or set this to FALSE")
}
else
rangelambda.values <- as.matrix(expand.grid(range.values, lambda.values))
}
}
}
##
## 2. data preparation
##
trend <- unclass(trend.spatial(trend=obj.likfit$trend, geodata = geodata))
if (nrow(trend) != nrow(coords))
stop("coords and trend have incompatible sizes")
data <- as.vector(data)
dimnames(trend) <- list(NULL, NULL)
if(obj.likfit$transform.info$fix.lambda) {
if(obj.likfit$lambda != 1) {
if(any(data <= 0))
stop("Data transformation not allowed when there are zeros or negative data"
)
if(obj.likfit$lambda == 0)
data <- log(data)
else data <- ((data^obj.likfit$lambda) - 1)/obj.likfit$lambda
}
}
n <- length(data)
dists.vec <- as.vector(dist(coords))
d <- range(dists.vec)
min.dist <- d[1]
max.dist <- d[2]
tausq <- obj.likfit$nugget
sigmasq <- obj.likfit$cov.pars[1]
tausq.rel <- tausq/sigmasq
phi <- obj.likfit$cov.pars[2]
lambda <- obj.likfit$lambda
loglik <- obj.likfit$loglik
sill.total <- sigmasq + tausq
n.uni <- 0
n.bi <- 0
lower.phi <- 0.01 * (min.dist/max.dist)
upper.phi <- 1000 * max.dist
lower.sigmasq <- 0.01 * sill.total
result <- list()
assign(".temp.list", list(n = n,
z = data,
beta.size = dim(trend)[2],
kappa = obj.likfit$kappa,
xmat = trend,
## txmat = t(trend),
method.lik = obj.likfit$method.lik,
dists.lowertri = dists.vec,
cov.model = obj.likfit$cov.model,
fix.lambda = obj.likfit$transform.info$fix.lambda,
lambda = obj.likfit$lambda,
lower.phi = lower.phi,
upper.phi = upper.phi,
lower.sigmasq = lower.sigmasq,
phi.est = phi,
tausq.rel.est = tausq.rel,
tausq.est = tausq,
sigmasq.est = sigmasq), envir=.geoR.env)
if(obj.likfit$transform.info$fix.lambda == TRUE)
eval(substitute(.temp.list$log.jacobian <- xxx, list(xxx=obj.likfit$transform.info$log.jacobian)), envir=.geoR.env)
##
## 3. One-dimentional profile likelihoods
##
##
## 3.1 Profile for sigmasq
##
if(bi.only == FALSE) {
if(any(sill.values != FALSE)) {
n.uni <- n.uni + 1
if(messages.screen) cat("proflik: computing profile likelihood for the sill\n")
if(n.cov.pars == 2) {
if(tausq == 0) {
if(obj.likfit$transform.info$fix.lambda == FALSE) {
ini.grid <- as.matrix(expand.grid(seq(min(range.values),
max(range.values),
l = 5),
seq(-1,1,l = 5)))
}
else {
ini.grid <- as.matrix(seq(min(range.values),
max(range.values),
l = 10))
}
dimnames(ini.grid) <- list(NULL, NULL)
eval(substitute(.temp.list$ini.grid <- xxx, list(xxx= ini.grid)), envir=.geoR.env)
pl.sigmasq <- apply(matrix(sill.values,
ncol = 1), 1, .proflik.aux2, ...)
eval(expression(.temp.list$ini.grid <- NULL), envir=.geoR.env)
}
else {
stop("not yet implemented for fixed nugget != 0")
}
}
if(n.cov.pars == 3) {
if(any(lambda.values != FALSE)) {
ini.grid <- as.matrix(expand.grid(seq(min(range.values),
max(range.values), l = 6),
seq(0, 2 * tausq.rel, l = 4),
seq(-1, 1, l = 5)))
}
else {
ini.grid <- as.matrix(expand.grid(seq(min(range.values),
max(range.values), l = 10),
seq(0, 2 * tausq.rel, l = 4)))
}
dimnames(ini.grid) <- list(NULL, NULL)
eval(substitute(.temp.list$ini.grid <- xxx, list(xxx= ini.grid)), envir=.geoR.env)
pl.sigmasq <- apply(matrix(sill.values, ncol =
1), 1, .proflik.aux9, ...)
eval(expression(.temp.list$ini.grid <- NULL), envir=.geoR.env)
}
v.ord <- order(c(sigmasq, sill.values))
if(obj.likfit$transform.info$fix.lambda == TRUE)
pl.sigmasq <- pl.sigmasq + obj.likfit$transform.info$log.jacobian
result$sill <- list(sill = c(sigmasq, sill.values)[
v.ord], proflik.sill = c(loglik, pl.sigmasq)[
v.ord], est.sill = c(sigmasq, loglik))
}
##
## 3.2 Profile for phi
##
if(any(range.values != FALSE)) {
n.uni <- n.uni + 1
if(messages.screen) cat("proflik: computing profile likelihood for the range\n")
if(n.cov.pars == 2) {
if(tausq == 0) {
eval(expression(.temp.list$nugget <- 0), envir=.geoR.env)
pl.phi <- apply(matrix(range.values,
ncol = 1), 1, .proflik.aux0, ...)
eval(expression(.temp.list$nugget <- NULL), envir=.geoR.env)
}
else {
stop("not yet implemented for fixed nugget != 0"
)
}
}
if(n.cov.pars == 3) {
pl.phi <- apply(matrix(range.values, ncol = 1),
1, .proflik.aux7, ...)
}
v.ord <- order(c(phi, range.values))
if(obj.likfit$transform.info$fix.lambda == TRUE)
pl.phi <- pl.phi + obj.likfit$transform.info$log.jacobian
result$range <- list(range = c(phi, range.values)[
v.ord], proflik.range = c(loglik, pl.phi)[
v.ord], est.range = c(phi, loglik))
}
##
## 3.3 Profile for \tau^2
##
if(n.cov.pars == 3) {
if(any(nugget.values != FALSE)) {
n.uni <- n.uni + 1
if(messages.screen) cat("proflik: computing profile likelihood for the nugget\n"
)
pl.tausq <- apply(matrix(nugget.values, ncol =
1), 1, .proflik.aux11, ...)
v.ord <- order(c(tausq, nugget.values))
if(obj.likfit$transform.info$fix.lambda == TRUE)
pl.tausq <- pl.tausq + obj.likfit$transform.info$log.jacobian
result$nugget <- list(nugget = c(tausq,
nugget.values)[v.ord], proflik.nugget
= c(loglik, pl.tausq)[v.ord],
est.nugget = c(tausq, loglik))
}
##
## 3.4 Profile for relative \tau^2
##
if(any(nugget.rel.values != FALSE)) {
if(messages.screen) cat("proflik: computing profile likelihood for the relative nugget\n"
)
n.uni <- n.uni + 1
pl.tausq.rel <- apply(matrix(nugget.rel.values,
ncol = 1), 1, .proflik.aux5, ...)
v.ord <- order(c(tausq.rel, nugget.rel.values))
if(obj.likfit$transform.info$fix.lambda == TRUE)
pl.tausq.rel <- pl.tausq.rel + obj.likfit$transform.info$log.jacobian
result$nugget.rel <- list(nugget.rel = c(
tausq.rel, nugget.rel.values)[v.ord],
proflik.nugget = c(loglik, pl.tausq.rel
)[v.ord],
est.nugget.rel = c(tausq.rel,loglik))
}
}
##
## 3.5 Profile for \lambda
##
if(any(lambda.values != FALSE)) {
assign(".temp.temp.list", get(".temp.list", envir=.geoR.env))
eval(substitute(.temp.temp.list$coords <- xxx, list(xxx= coords)), envir=.geoR.env)
n.uni <- n.uni + 1
if(messages.screen) cat("proflik: computing profile likelihood for lambda\n"
)
if(n.cov.pars == 2) {
if(tausq == 0) {
eval(expression(.temp.temp.list$fixtau <- TRUE), envir=.geoR.env)
eval(substitute(.temp.temp.list$ini <- xxx, list(xxx= c(sigmasq,phi))), envir=.geoR.env)
pl.lambda <- apply(as.matrix(lambda.values), 1, .proflik.aux23, ...)
}
else {
stop("not yet implemented for fixed nugget != 0")
}
}
if(n.cov.pars == 3) {
eval(expression(.temp.temp.list$fixtau <- FALSE), envir=.geoR.env)
eval(substitute(.temp.temp.list$ini <- xxx, list(xxx= phi)), envir=.geoR.env)
pl.lambda <- apply(matrix(lambda.values,
ncol = 1), 1, .proflik.aux23, ...)
}
v.ord <- order(c(lambda, lambda.values))
result$lambda <- list(lambda = c(lambda,
lambda.values)[v.ord], proflik.lambda
= c(loglik, pl.lambda)[v.ord],
est.lambda = c(lambda, loglik))
remove(".temp.temp.list", inherits=TRUE, envir=.geoR.env)
}
}
##
## 4. Two-dimentional profile likelihoods
##
##
## 4.1 Profile for \sigma^2 and \phi
##
if(uni.only == FALSE){
if(any(sillrange.values != FALSE)) {
n.bi <- n.bi + 1
if(messages.screen) cat("proflik: computing 2-D profile likelihood for the sill and range parameters\n")
if(n.cov.pars == 2) {
if(tausq == 0) {
eval(expression(.temp.list$nugget <- 0), envir=.geoR.env)
if(get(".temp.list", envir=.geoR.env)$fix.lambda == TRUE) {
pl.sigmasqphi <- apply(cbind(0, sillrange.values, 1), 1, loglik.spatial, ...)
}
else {
pl.sigmasqphi <- apply(sillrange.values,
1, .proflik.aux28, ...)
}
eval(expression(.temp.list$nugget <- NULL), envir=.geoR.env)
}
else {
stop("not yet implemented for fixed nugget != 0"
)
}
}
if(n.cov.pars == 3) {
pl.sigmasqphi <- apply(sillrange.values, 1, .proflik.aux13, ...)
}
names(pl.sigmasqphi) <- NULL
if(obj.likfit$transform.info$fix.lambda == TRUE)
pl.sigmasqphi <- pl.sigmasqphi + obj.likfit$transform.info$log.jacobian
result$sillrange <- list(sill = as.numeric(levels(as.factor(sillrange.values[,1]))), range =
as.numeric(levels(as.factor(sillrange.values[,2]))), proflik.sillrange = pl.sigmasqphi,
est.sillrange = c(sigmasq, phi, loglik))
}
##
## 4.2 Profile for \sigma^2 and \tau^2
##
if(any(sillnugget.values != FALSE)) {
n.bi <- n.bi + 1
if(messages.screen) cat("proflik: computing 2-D profile likelihood for the sill and nugget\n")
if(obj.likfit$transform.info$fix.lambda == FALSE)
ini.grid <- as.matrix(expand.grid(seq(min(range.values),
max(range.values), l =
10), seq(-1, 1, l = 5)))
else
ini.grid <- as.matrix(seq(min(range.values),
max(range.values), l = 10))
dimnames(ini.grid) <- list(NULL, NULL)
eval(substitute(.temp.list$ini.grid <- xxx, list(xxx=ini.grid)), envir=.geoR.env)
pl.sigmasqtausq <- apply(sillnugget.values, 1, .proflik.aux15, ...)
eval(expression(.temp.list$ini.grid <- NULL), envir=.geoR.env)
names(pl.sigmasqtausq) <- NULL
if(obj.likfit$transform.info$fix.lambda == TRUE)
pl.sigmasqtausq <- pl.sigmasqtausq + obj.likfit$transform.info$log.jacobian
result$sillnugget <- list(sill = as.numeric(levels(as.factor(sillnugget.values[,1]))), nugget = as.numeric(levels(as.factor(sillnugget.values[,2]))), proflik.sillnugget =
pl.sigmasqtausq, est.sillrange = c(sigmasq,
tausq, loglik))
}
##
## 4.3 Profile for \phi and \tau^2
##
if(any(rangenugget.values != FALSE)) {
n.bi <- n.bi + 1
if(messages.screen) cat("proflik: computing 2-D profile likelihood for the range and nugget\n"
)
eval(substitute(.temp.list$ini.grid <- xxx, list(xxx= as.matrix(seq(sigmasq/4, 5 *
sigmasq, l = 15)))), envir=.geoR.env)
pl.phitausq <- apply(rangenugget.values, 1, .proflik.aux17, ...)
eval(expression(.temp.list$ini.grid <- NULL), envir=.geoR.env)
names(pl.phitausq) <- NULL
if(obj.likfit$transform.info$fix.lambda == TRUE)
pl.phitausq <- pl.phitausq + obj.likfit$transform.info$log.jacobian
result$rangenugget <- list(range = as.numeric(levels(as.factor(rangenugget.values[,1]))), nugget
= as.numeric(levels(as.factor(rangenugget.values[,1]))), proflik.rangenugget =
pl.phitausq, est.rangenugget = c(phi, tausq,
loglik))
}
##
## 4.4 Profile for \sigma^2 and \tau^2_{rel}
##
if(any(sillnugget.rel.values != FALSE)) {
n.bi <- n.bi + 1
if(messages.screen) cat("proflik: computing 2-D profile likelihood for the sill and relative nugget parameters\n"
)
if(get(".temp.list", envir=.geoR.env)$fix.lambda == FALSE)
ini.grid <- as.matrix(expand.grid(seq(min(range.values), max(range.values), l =
10), seq(-1, 1, l = 5)))
else
ini.grid <- as.matrix(seq(min(range.values),
max(range.values), l = 10))
dimnames(ini.grid) <- list(NULL, NULL)
eval(substitute(.temp.list$ini.grid <- xxx, list(xxx= ini.grid)), envir=.geoR.env)
pl.sigmasqtausq.rel <- apply(sillnugget.rel.values, 1,
.proflik.aux19, ...)
eval(expression(.temp.list$ini.grid <- NULL), envir=.geoR.env)
names(pl.sigmasqtausq.rel) <- NULL
if(obj.likfit$transform.info$fix.lambda == TRUE)
pl.sigmasqtausq.rel <- pl.sigmasqtausq.rel + obj.likfit$transform.info$log.jacobian
result$sillnugget.rel <- list(sill = as.numeric(levels(as.factor(sillnugget.rel.values[,1]))),
nugget.rel = as.numeric(levels(as.factor(sillnugget.rel.values[,2]))),
proflik.sillnugget.rel = pl.sigmasqtausq.rel,
est.sillrange.rel = c(sigmasq, tausq.rel,
loglik))
}
##
## 4.5 Profile for \phi and \tau^2_{rel}
##
if(any(rangenugget.rel.values != FALSE)) {
n.bi <- n.bi + 1
if(messages.screen) cat("proflik: computing 2-D profile likelihood for the range and relative nugget parameters\n"
)
pl.phitausq.rel <- apply(rangenugget.rel.values, 1, .proflik.aux30, ...)
names(pl.phitausq.rel) <- NULL
if(obj.likfit$transform.info$fix.lambda == TRUE)
pl.phitausq.rel <- pl.phitausq.rel + obj.likfit$transform.info$log.jacobian
result$rangenugget.rel <- list(range = as.numeric(levels(as.factor(rangenugget.rel.values[,1]))),
nugget.rel = as.numeric(levels(as.factor(rangenugget.rel.values[,2]))),
proflik.rangenugget.rel = pl.phitausq.rel,
"est.rangenugget.rel" = c(phi, tausq.rel,
loglik))
}
}
##
## 4.6 Profile for \sigma^2 and \lambda
##
if(any(silllambda.values != FALSE)) {
n.bi <- n.bi + 1
if(messages.screen) cat("proflik: computing 2-D profile likelihood for the sill and transformation parameters\n"
)
if(n.cov.pars == 2) {
ini.grid <- as.matrix(seq(min(range.values), max(
range.values), l = 10))
dimnames(ini.grid) <- list(NULL, NULL)
eval(substitute(.temp.list$ini.grid <- xxx, list(xxx= ini.grid)), envir=.geoR.env)
if(tausq == 0) {
eval(expression(.temp.list$nugget <- 0), envir=.geoR.env)
pl.sigmasqlambda <- apply(silllambda.values, 1, .proflik.aux24, ...)
eval(expression(.temp.list$ini.grid <- NULL), envir=.geoR.env)
eval(expression(.temp.list$nugget <- NULL), envir=.geoR.env)
}
else {
stop("not yet implemented for fixed nugget != 0"
)
}
}
if(n.cov.pars == 3) {
ini.grid <- as.matrix(expand.grid(seq(min(range.values),
max(range.values), l = 10), seq(0, 1, l = 5)))
dimnames(ini.grid) <- list(NULL, NULL)
eval(substitute(.temp.list$ini.grid <- xxx, list(xxx=ini.grid)), envir=.geoR.env)
pl.sigmasqlambda <- apply(silllambda.values, 1, .proflik.aux27, ...)
eval(expression(.temp.list$ini.grid <- NULL), envir=.geoR.env)
}
names(pl.sigmasqlambda) <- NULL
result$silllambda <- list(sill = as.numeric(levels(as.factor(silllambda.values[,1]))), lambda = as.numeric(levels(as.factor(silllambda.values[,2]))), proflik.silllambda = pl.sigmasqlambda,
est.silllambda = c(sigmasq, lambda, loglik))
}
##
## 4.7 Profile for \phi and \lambda
##
if(any(rangelambda.values != FALSE)) {
eval(substitute(.temp.list$data <- xxx, list(xxx=.temp.list$z)), envir=.geoR.env)
n.bi <- n.bi + 1
cat("proflik: computing 2-D profile likelihood for the range and transformation parameters\n"
)
if(n.cov.pars == 2) {
if(tausq == 0) {
eval(expression(.temp.list$nugget <- 0), envir=.geoR.env)
pl.philambda <- apply(rangelambda.values, 1,
.proflik.aux1, ...)
eval(expression(.temp.list$nugget <- NULL), envir=.geoR.env)
}
else {
stop("not yet implemented for fixed nugget != 0"
)
}
}
if(n.cov.pars == 3) {
pl.philambda <- apply(rangelambda.values, 1, .proflik.aux31, ...)
}
names(pl.philambda) <- NULL
result$rangelambda <- list(range = as.numeric(levels(as.factor(rangelambda.values[,1]))), lambda = as.numeric(levels(as.factor(rangelambda.values[,2]))), proflik.rangelambda = pl.philambda,
est.rangelambda = c(phi, lambda, loglik))
}
##
## 4.8 Profile for \tau^2 and \lambda
##
if(any(nuggetlambda.values != FALSE)) {
n.bi <- n.bi + 1
cat("proflik: computing 2-D profile likelihood for the nugget and transformation parameters\n"
)
pl.nuggetlambda <- apply(nuggetlambda.values, 1, .proflik.aux32, ...)
names(pl.nuggetlambda) <- NULL
result$nuggetlambda <- list(nugget = as.numeric(levels(as.factor(nuggetlambda.values[,1]))), lambda = as.numeric(levels(as.factor(nuggetlambda.values[,2])))
, proflik.nuggetlambda = pl.nuggetlambda,
est.nuggetlambda = c(tausq, lambda, loglik))
}
##
## 4.9 2-D Profile for \tau^2_{rel} and \lambda
##
if(any(nugget.rellambda.values != FALSE)) {
n.bi <- n.bi + 1
pl.nugget.rellambda <- apply(nugget.rellambda.values, 1, .proflik.aux33, ...)
names(pl.nugget.rellambda) <- NULL
result$nugget.rellambda <- list(nugget.rel = as.numeric(levels(as.factor(nugget.rellambda.values[,1]))),
lambda = as.numeric(levels(as.factor(nugget.rellambda.values[,2]))), proflik.nugget.rellambda =
pl.nugget.rellambda, est.nugget.rellambda = c(tausq.rel,
lambda, loglik))
}
result$n.uni <- n.uni
result$n.bi <- n.bi
result$method.lik <- obj.likfit$method.lik
result$call <- call.fc
oldClass(result) <- "proflik"
return(result)
}
".proflik.aux0" <-
function(phi, ...)
{
## This function computes the value of the profile likelihood for the correlation parameter \phi when nugget effect is not included in the model.
## It requires the minimisation of the function wrt \phi for each value of \lambda, if this transformation parameter is included in the model
## This is an auxiliary function called by likfit.proflik
##
if(get(".temp.list", envir=.geoR.env)$fix.lambda == TRUE)
proflik <- .proflik.aux1(philambda = phi)
else {
eval(substitute(.temp.list$phi <- xxx, list(xxx=phi)), envir=.geoR.env)
# proflik <- - (optim(.temp.list$lambda, .proflik.aux1.1, method="L-BFGS-B", lower
# = -2, upper = 2, ...)$value)
proflik <- - (optimise(.proflik.aux1.1, lower = -5, upper = 5, ...)$objective)
return(proflik)
}
}
".proflik.aux1" <-
function(philambda, ...)
{
## This function computes the value of the profile likelihood for the correlation function scale parameter \phi when nugget effect = 0
.temp.list <- get(".temp.list", envir=.geoR.env)
if(length(philambda) == 2) lambda <- philambda[2]
else lambda <- 1
n <- .temp.list$n
main <- .proflik.main(tausq=.temp.list$nugget, sigmasq=1, phi=philambda[1], lambda = lambda)
if(.temp.list$method.lik == "ML") {
proflik <- - (n/2) * log(2 * pi) - main$log.det.to.half -
(n/2) * log(main$ssresmat/n) - (n/2) + main$
log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
proflik <- - ((n - .temp.list$beta.size)/2) * log(2 * pi) - main$
log.det.to.half - ((n - .temp.list$beta.size)/2) * log(main$ssresmat/
n) - (n/2) + 0.5 * sum(log(eigentrem$values)) +
main$log.jacobian
}
return(proflik)
}
".proflik.aux10" <-
function(phitausq.rel.lambda, ...)
{
.temp.list <- get(".temp.list", envir=.geoR.env)
if(length(phitausq.rel.lambda) == 3)
lambda <- phitausq.rel.lambda[3]
else lambda <- 1
phitausq.rel.lambda <- as.vector(phitausq.rel.lambda)
n <- .temp.list$n
phi <- phitausq.rel.lambda[1]
tausq <- phitausq.rel.lambda[2]
sigmasq <- .temp.list$sigmasq
main <- .proflik.main(tausq=tausq, sigmasq=1, phi=phi, lambda = lambda)
if(.temp.list$method.lik == "ML") {
neglik <- (n/2) * log(2 * pi) + main$log.det.to.half +
(n/2) * log(sigmasq) + (0.5/sigmasq) * main$ssresmat -
main$log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
neglik <- ((n - .temp.list$beta.size)/2) * log(2 * pi) + main$
log.det.to.half + ((n - .temp.list$beta.size)/2) * log(sigmasq) +
(0.5/sigmasq) * main$ssresmat - 0.5 * sum(log(eigentrem$
values)) - main$log.jacobian
}
return(as.vector(round(neglik, digits=8)))
}
".proflik.aux11" <-
function(tausq, ...)
{
## This function computes the value of the profile likelihood for the parameter \tau^2.
## It requires the minimisation of the function wrt \sigma^2, \phi and \lambda (if the case) for each value of \tau^2.
## This is an auxiliary function called by proflik.
eval(substitute(.temp.list$nugget <- xxx, list(xxx=as.vector(tausq))), envir=.geoR.env)
.temp.list <- get(".temp.list", envir=.geoR.env)
if(.temp.list$fix.lambda == TRUE) {
sigmasqphi.res <- optim(c(.temp.list$sigmasq.est, .temp.list$phi.est),
.proflik.aux12, method="L-BFGS-B",
lower = c(.temp.list$lower.sigmasq,
.temp.list$lower.phi),
upper=c(+Inf, .temp.list$upper.phi), ...)$value
}
else {
sigmasqphi.res <- optim(c(.temp.list$sigmasq.est, .temp.list$phi.est,
.temp.list$lambda), .proflik.aux12,method="L-BFGS-B",
lower = c(.temp.list$lower.sigmasq, .temp.list$lower.phi, -2),
upper = c( + Inf, .temp.list$upper.phi, 2), ...)$value
}
eval(expression(.temp.list$nugget <- NULL), envir=.geoR.env)
return( - sigmasqphi.res)
}
".proflik.aux1.1" <-
function(lambda, ...)
{
## This function computes the value of the profile likelihood for the correlation function scale parameter \phi when nugget effect = 0
.temp.list <- get(".temp.list", envir=.geoR.env)
phi <- .temp.list$phi
n <- .temp.list$n
main <- .proflik.main(tausq=.temp.list$nugget, sigmasq=1, phi=phi, lambda = lambda)
if(.temp.list$method.lik == "ML") {
neglik <- (n/2) * log(2 * pi) + main$log.det.to.half +
(n/2) * log(main$ssresmat/n) + (n/2) - main$log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
neglik <- ((n - .temp.list$beta.size)/2) * log(2 * pi) + main$
log.det.to.half + ((n - .temp.list$beta.size)/2) * log(main$ssresmat/n) +
(n/2) - 0.5 * sum(log(eigentrem$values)) -
main$log.jacobian
}
return(as.vector(round(neglik, digits=8)))
}
".proflik.aux12" <-
function(sigmasqphi.lambda, ...)
{
## This function computes the value of the profile likelihood for the nugget parameter \tau^2, minimizing the likelihood wrt correlation function scale parameter \phi (range), the random field scale parameter \sigma^2 (sill) and the transformation parameter \lambda.
.temp.list <- get(".temp.list", envir=.geoR.env)
if(length(sigmasqphi.lambda) == 3) lambda <- sigmasqphi.lambda[3]
else lambda <- 1
sigmasqphi.lambda <- as.vector(sigmasqphi.lambda)
n <- .temp.list$n
sigmasq <- sigmasqphi.lambda[1]
phi <- sigmasqphi.lambda[2]
main <- .proflik.main(tausq=.temp.list$nugget, sigmasq=sigmasq, phi=phi, lambda = lambda)
if(.temp.list$method.lik == "ML") {
neglik <- (n/2) * log(2 * pi) +
main$log.det.to.half +
0.5 * (main$ssresmat) -
main$log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
neglik <- ((n - .temp.list$beta.size)/2) * log(2 * pi) +
main$log.det.to.half +
0.5 * (main$ssresmat) -
0.5 * sum(log(eigentrem$values)) -
main$log.jacobian
}
return(as.vector(round(neglik, digits=8)))
}
".proflik.aux13" <-
function(sigmasqphi, ...)
{
## This function computes the value of the 2-D profile likelihood for the parameters \sigma^2 and \phi when the nugget is included.
## It requires the minimisation of the function wrt \tau^2 and \lambda (if the case) for each value of (\sigma^2, \phi)
## This is an auxiliary function called by likfit.proflik
eval(substitute(.temp.list$sigmasqphi <- xxx, list(xxx=as.vector(sigmasqphi))), envir=.geoR.env)
.temp.list <- get(".temp.list", envir=.geoR.env)
if(.temp.list$fix.lambda == TRUE) {
## tausq.res <- optim(.temp.list$tausq.est, .proflik.aux14, method="L-BFGS-B", lower
## = 0, ...)$value
tausq.res <- optimise(.proflik.aux14, lower = 0, upper = .Machine$double.xmax^0.25, ...)$objective
}
else {
tausq.res <- optim(
c(.temp.list$tausq.est, .temp.list$lambda),
.proflik.aux14, method="L-BFGS-B",lower = c(0, -2),
upper = c( +Inf, 2), ...)$value
}
eval(expression(.temp.list$sigmasqphi <- NULL), envir=.geoR.env)
return( - tausq.res)
}
".proflik.aux14" <-
function(tausq.lambda, ...)
{
## This function computes the value of the 2-D profile likelihood for the parameters (\sigma^2, \phi), minimizing the likelihood wrt the nugget parameter \tau^2.
## This functions is called by the auxiliary function .proflik.aux13
.temp.list <- get(".temp.list", envir=.geoR.env)
if(length(tausq.lambda) == 2) lambda <- tausq.lambda[2]
else lambda <- 1
n <- .temp.list$n
tausq <- tausq.lambda[1]
main <- .proflik.main(tausq=tausq, .temp.list$sigmasqphi[1], phi=.temp.list$sigmasqphi[2], lambda = lambda)
if(.temp.list$method.lik == "ML") {
neglik <- (n/2) * log(2 * pi) + main$log.det.to.half + 0.5 *
main$ssresmat - main$log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
neglik <- ((n - .temp.list$beta.size)/2) * log(2 * pi) + main$
log.det.to.half + 0.5 * main$ssresmat - 0.5 * sum(log(
eigentrem$values)) - main$log.jacobian
}
return(as.vector(round(neglik, digits=8)))
}
".proflik.aux15" <-
function(sigmasqtausq, ...)
{
## This function computes the value of the 2-D profile likelihood for the parameters \sigma^2 and \tau^2
## It requires the minimisation of the function wrt \phi and also \lambda (if the case) for each value of (\sigma^2, \tau^2)
## This is an auxiliary function called by likfit.proflik
eval(substitute(.temp.list$sigmasqtausq <- xxx, list(xxx=as.vector(sigmasqtausq))), envir=.geoR.env)
.temp.list <- get(".temp.list", envir=.geoR.env)
ini.lik <- round(100000000. * apply(.temp.list$ini.grid, 1,
.proflik.aux16))
ini <- as.vector(.temp.list$ini.grid[which(ini.lik == min(ini.lik, na.rm = TRUE)),,drop=FALSE][1,])
if(.temp.list$fix.lambda == TRUE) {
# phi.res <- optim(ini, .proflik.aux16, method="L-BFGS-B", lower =
# .temp.list$lower.phi, upper=.temp.list$upper.phi, ...)$value
phi.res <- optimise(.proflik.aux16, lower = .temp.list$lower.phi, upper=.temp.list$upper.phi, ...)$objective
}
else {
phi.res <- optim(ini, .proflik.aux16, method="L-BFGS-B",
lower = c(.temp.list$lower.phi, -2),
upper = c(.temp.list$upper.phi, 2), ...)$value
}
eval(expression(.temp.list$sigmasqtausq <- NULL), envir=.geoR.env)
return( - phi.res)
}
".proflik.aux16" <-
function(phi.lambda, ...)
{
## This function computes the value of the 2-D profile likelihood for the sill and nugget parameters (\sigma^2,\tau^2), minimising the profile likelihood wrt correlation function scale parameter \phi (and the transformation parameter \lambda
## This is an auxiliary function called by likfit.aux15
.temp.list <- get(".temp.list", envir=.geoR.env)
if(length(phi.lambda) == 2) lambda <- phi.lambda[2]
else lambda <- 1
n <- .temp.list$n
phi <- phi.lambda[1]
main <- .proflik.main(tausq=.temp.list$sigmasqtausq[2], sigmasq=.temp.list$sigmasqtausq[1], phi=phi, lambda = lambda)
if(.temp.list$method.lik == "ML") {
neglik <- (n/2) * log(2 * pi) + main$log.det.to.half + 0.5 *
main$ssresmat - main$log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
neglik <- ((n - .temp.list$beta.size)/2) * log(2 * pi) + main$
log.det.to.half + 0.5 * main$ssresmat - 0.5 * sum(log(
eigentrem$values)) -
main$log.jacobian
}
return(as.vector(round(neglik, digits=8)))
}
".proflik.aux17" <-
function(phitausq, ...)
{
## This function computes the value of the 2-D profile likelihood for the parameters (\phi, \tau^2)
## It requires the minimisation of the function wrt \sigma^2 and \lambda (if the case) for each value of (\phi, \tau^2)
## This is an auxiliary function called by likfit.proflik
eval(substitute(.temp.list$phitausq <- xxx, list(xxx=as.vector(phitausq))), envir=.geoR.env)
.temp.list <- get(".temp.list", envir=.geoR.env)
if(.temp.list$fix.lambda == TRUE) {
## ini.lik <- round(100000000. * apply(.temp.list$ini.grid, 1,
## .proflik.aux18))
## ini <- as.vector(.temp.list$ini.grid[which(ini.lik == min(ini.lik, na.rm = TRUE)),,drop=FALSE][1,])
## sigmasq.res <- optim(ini, .proflik.aux18, method="L-BFGS-B",
## lower = .temp.list$lower.sigmasq, ...)$value
sigmasq.res <- optimise(.proflik.aux18, lower = .temp.list$lower.sigmasq, upper = .Machine$double.xmax^0.25, ...)$objective
}
else {
sigmasq.res <- optim(c(.temp.list$sigmasq.est, .temp.list$lambda),
.proflik.aux18, method="L-BFGS-B",
lower = c(.temp.list$lower.sigmasq, -2),
upper = c( + Inf, 2), ...)$value
}
eval(expression(.temp.list$phitausq <- NULL), envir=.geoR.env)
return( - sigmasq.res)
}
".proflik.aux18" <-
function(sigmasq.lambda, ...)
{
## This function computes the value of the 2-D profile likelihood for the range and nugget parameters (\phi, \tau^2), minimising the likelihood wrt the random field scale parameter \sigma^2 (sill) ant the transformation parameter \lambda.
## This is an auxiliary function called by likfit.aux17.
.temp.list <- get(".temp.list", envir=.geoR.env)
if(length(sigmasq.lambda) == 2) lambda <- sigmasq.lambda[2]
else lambda <- 1
n <- .temp.list$n
sigmasq <- sigmasq.lambda[1]
main <- .proflik.main(tausq=.temp.list$phitausq[2], sigmasq=sigmasq, phi=.temp.list$phitausq[1], lambda = lambda)
if(.temp.list$method.lik == "ML") {
neglik <- (n/2) * log(2 * pi) + main$log.det.to.half + 0.5 *
main$ssresmat - main$log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
neglik <- ((n - .temp.list$beta.size)/2) * log(2 * pi) + main$
log.det.to.half + 0.5 * main$ssresmat - 0.5 * sum(log(
eigentrem$values)) -
main$log.jacobian
}
return(as.vector(round(neglik, digits=8)))
}
".proflik.aux19" <-
function(sigmasqtausq.rel, ...)
{
## This function computes the value of the 2-D profile likelihood for the parameters (\sigma^2, \tau^2_{rel})
## It requires the minimisation of the function wrt \phi and \lambda (if the case) for each value of (\sigma^2, \tau^2_{rel})
## This is an auxiliary function called by likfit.proflik
eval(substitute(.temp.list$sigmasqtausq.rel <- xxx, list(xxx=as.vector(sigmasqtausq.rel))), envir=.geoR.env)
.temp.list <- get(".temp.list", envir=.geoR.env)
if(.temp.list$fix.lambda == TRUE) {
## phi.res <- optim(.temp.list$phi.est, .proflik.aux20, method="L-BFGS-B", lower =
## .temp.list$lower.phi, upper=.temp.list$upper.phi, ...)$value
phi.res <- optimise(.proflik.aux20, lower =
.temp.list$lower.phi, upper=.temp.list$upper.phi, ...)$objective
}
else {
phi.res <- optim(c(.temp.list$phi.est, .temp.list$lambda, ...), .proflik.aux20, method="L-BFGS-B",
lower = c(.temp.list$lower.phi, -2),
upper = c(.temp.list$upper.phi, 2), ...)$value
}
eval(expression( .temp.list$sigmasqtausq.rel <- NULL), envir=.geoR.env)
return( - phi.res)
}
".proflik.aux2" <-
function(sigmasq, ...)
{
## This function computes the value of the profile likelihood for the random field scale (variance) parameter \sigma^2 when nugget effect is not included in the model.
## It requires the minimisation of the function wrt \phi and maybe \lambda for each value of \sigma^2
## This is an auxiliary function called by likfit.proflik
##
eval(substitute(.temp.list$sigmasq <- xxx, list(xxx=as.vector(sigmasq))), envir=.geoR.env)
.temp.list <- get(".temp.list", envir=.geoR.env)
ini.lik <- round(100000000. * apply(.temp.list$ini.grid, 1,
.proflik.aux3))
ini <- as.vector(.temp.list$ini.grid[which(ini.lik == min(ini.lik, na.rm = TRUE)),,drop=FALSE][1,])
if(.temp.list$fix.lambda == TRUE) {
## phi.res <- optim(ini , .proflik.aux3, method="L-BFGS-B",
## lower = .temp.list$lower.phi,
## upper=.temp.list$upper.phi, ...)$value
phi.res <- optimise(.proflik.aux3,
lower = .temp.list$lower.phi,
upper=.temp.list$upper.phi, ...)$objective
}
else {
phi.res <- optim(ini, .proflik.aux3, method="L-BFGS-B",
lower = c(.temp.list$lower.phi, -2),
upper = c(.temp.list$upper.phi, 2), ...)$value
}
eval(expression(.temp.list$sigmasq <- NULL), envir=.geoR.env)
return( - phi.res)
}
".proflik.aux20" <-
function(phi.lambda, ...)
{
## This function computes the value of the 2-D profile likelihood for the sill and relative nugget parameters (\sigma^2, \tau^2_{rel}), minimising the likelihood wrt the correlation function scale parameter \phi and the transformation parameter \lambda.
## This is an auxiliary function called by likfit.aux19.
.temp.list <- get(".temp.list", envir=.geoR.env)
phi.lambda <- as.vector(phi.lambda)
if(length(phi.lambda) == 2) lambda <- phi.lambda[2]
else lambda <- 1
sigmasqtausq.rel <- as.vector(.temp.list$sigmasqtausq.rel)
sigmasq <- sigmasqtausq.rel[1]
tausq.rel <- sigmasqtausq.rel[2]
phi <- phi.lambda[1]
n <- .temp.list$n
main <- .proflik.main(tausq=tausq.rel, sigmasq=1, phi=phi, lambda = lambda)
if(.temp.list$method.lik == "ML") {
neglik <- (n/2) * log(2 * pi) +
main$log.det.to.half +
(n/2) * log(sigmasq) +
(0.5/sigmasq) * main$ssresmat -
main$log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
neglik <- ((n - .temp.list$beta.size)/2) * log(2 * pi) +
main$log.det.to.half +
(n/2) * log(sigmasq) +
(0.5/sigmasq) * main$ssresmat -
0.5 * sum(log(eigentrem$values)) -
main$log.jacobian
}
return(as.vector(round(neglik, digits=8)))
}
".proflik.aux21" <-
function(phitausq.rel, ...)
{
## This function computes the value of the 2-D profile likelihood for the parameters (\phi, \tau^2_{rel})
## This is an auxiliary function called by likfit.proflik
.temp.list <- get(".temp.list", envir=.geoR.env)
phitausq.rel <- as.vector(phitausq.rel)
phi <- phitausq.rel[1]
tausq.rel <- phitausq.rel[2]
n <- .temp.list$n
main <- .proflik.main(tausq=tausq.rel, sigmasq=1, phi=phi, lambda = 1)
sigmasq.hat <- main$ssresmat/n
if(.temp.list$method.lik == "ML") {
proflik <- - (n/2) * log(2 * pi) -
main$log.det.to.half -
(n/2) * log(sigmasq.hat) -
(n/2) -
main$log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
proflik <- - ((n - .temp.list$beta.size)/2) * log(2 * pi) -
main$log.det.to.half -
(n/2) * log(sigmasq.hat) -
(n/2) +
0.5 * sum(log(eigentrem$values)) -
main$log.jacobian
}
return(proflik)
}
".proflik.aux21.1" <-
function(lambda, ...)
{
## This function computes the value of the 2-D profile likelihood for the parameters (\phi, \tau^2_{rel})
## This requires minimasation wrt to the transformation parameter \lambda
## This is an auxiliary function called by likfit.proflik
.temp.list <- get(".temp.list", envir=.geoR.env)
n <- .temp.list$n
main <- .proflik.main(tausq = .temp.list$phitausq.rel[2], sigmasq = 1,
phi = .temp.list$phitausq.rel[1], lambda = lambda)
sigmasq.hat <- main$ssresmat/n
if(.temp.list$method.lik == "ML") {
neglik <- (n/2) * log(2 * pi) +
main$log.det.to.half + (n/2) * log(sigmasq.hat) +
(n/2) -
main$log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
neglik <- ((n - .temp.list$beta.size)/2) * log(2 * pi) +
main$log.det.to.half +
(n/2) * log(sigmasq.hat) +
(n/2) -
0.5 * sum(log(eigentrem$values)) -
main$log.jacobian
}
return(as.vector(round(neglik, digits=8)))
}
".proflik.aux22" <-
function(sigmasq, ...)
{
## This function computes the value of the 2-D profile likelihood for the range and nugget parameters (\phi, \tau^2), minimising the likelihood wrt the random field scale parameter \sigma^2 (sill)
## This is an auxiliary function called by likfit.aux17
.temp.list <- get(".temp.list", envir=.geoR.env)
n <- .temp.list$n
main <- .proflik.main(tausq=.temp.list$phitausq[2], sigmasq=sigmasq, phi= .temp.list$phitausq[1], lambda = 1)
if(.temp.list$method.lik == "ML") {
neglik <- (n/2) * log(2 * pi) +
main$log.det.to.half +
0.5 * main$ssresmat -
main$log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
neglik <- ((n - .temp.list$beta.size)/2) * log(2 * pi) +
main$log.det.to.half +
0.5 * main$ssresmat -
0.5 * sum(log(eigentrem$values)) -
main$log.jacobian
}
return(as.vector(round(neglik, digits=8)))
}
".proflik.aux23" <-
function(lambda, ...)
{
## This function computes the value of the profile likelihood for the transformation parameter \lambda
## It requires the minimisation of the function wrt \phi and \tau^2 and sigma^2 for each value of \lambda
## This is an auxiliary function called by proflik
.temp.list <- get(".temp.list", envir=.geoR.env)
.temp.temp.list <- get(".temp.temp.list", envir=.geoR.env)
lambda <- as.vector(lambda)
if(.temp.temp.list$fixtau == FALSE) {
if(lambda == 0)
data.l <- log(.temp.list$z)
else data.l <- ((.temp.list$z^lambda) - 1)/lambda
var.l <- var(data.l)
ini.cov <- c(var.l, .temp.temp.list$ini)
}
else
ini.cov <- .temp.temp.list$ini
if(dim(.temp.list$xmat)[2] == 1 & all(.temp.list$xmat == 1))
trend.mat <- "cte"
else
trend.mat <- ~ (.temp.list$xmat[,-1])
lambda.res <- likfit(coords = .temp.temp.list$coords,
data = .temp.list$z,
ini.cov.pars = ini.cov, trend = trend.mat,
fix.nugget = .temp.temp.list$fixtau,
lik.method = .temp.list$method.lik,
cov.model = .temp.list$cov.model,
kappa = .temp.list$kappa, fix.lambda = TRUE,
lambda = lambda,
messages = FALSE)$loglik
assign(".temp.list", .temp.temp.list, envir=.geoR.env)
return(lambda.res)
}
".proflik.aux24" <-
function(sigmasqlambda, ...)
{
## This function computes the value of the 2-D profile likelihood for the parameters (\sigma^2, \lambda) when there is no nugget effect (\tau^2 = 0, fixed)
## It requires the minimisation of the function wrt \phi for each value of (\sigma^2, \lambda)
## This is an auxiliary function called by proflik
sigmasqlambda <- as.vector(sigmasqlambda)
eval(substitute(.temp.list$sigmasq <- xxx, list(xxx=sigmasqlambda[1])), envir=.geoR.env)
.temp.list <- get(".temp.list", envir=.geoR.env)
lambda <- sigmasqlambda[2]
if(lambda == 1) {
eval(expression(.temp.list$log.jacobian <- 0), envir=.geoR.env)
}
else {
if(any(.temp.list$z <= 0))
stop("Transformation option not allowed when there are zeros or negative data"
)
eval(substitute(.temp.list$log.jacobian <- xxx, list(xxx=sum(log(.temp.list$z^(lambda - 1))))), envir=.geoR.env)
if(lambda == 0)
eval(substitute(.temp.list$z <- xxx, list(xxx=log(.temp.list$z))), envir=.geoR.env)
else eval(substitute(.temp.list$z <- xxx, list(xxx= ((.temp.list$z^lambda) - 1)/lambda)), envir=.geoR.env)
}
ini.lik <- round(100000000. * apply(.temp.list$ini.grid, 1,
.proflik.aux3))
ini <- as.vector(.temp.list$ini.grid[which(ini.lik == min(ini.lik, na.rm = TRUE)),,drop=FALSE][1,])
## phi.res <- optim(ini, .proflik.aux3, method="L-BFGS-B", lower = .temp.list$
## lower.phi, upper = .temp.list$upper.phi, ...)$value
phi.res <- optimise(.proflik.aux3, lower = .temp.list$lower.phi, upper = .temp.list$upper.phi, ...)$objective
eval(expression(.temp.list$log.jacobian <- NULL), envir=.geoR.env)
eval(expression(.temp.list$sigmasq <- NULL), envir=.geoR.env)
eval(substitute(.temp.list$z <- xxx, list(xxx=.temp.list$data)), envir=.geoR.env)
return( - phi.res)
}
".proflik.aux27" <-
function(sigmasqlambda, ...)
{
## This function computes the value of the 2-D profile likelihood for sill \sigma^2 and the transformation parameter \lambda
## It requires the minimisation of the function wrt \phi and \tau^2 and for each value of (\sigma^2,\lambda)
## This is an auxiliary function called by .proflik.
sigmasqlambda <- as.vector(sigmasqlambda)
eval(substitute(.temp.list$sigmasq <- xxx, list(xxx=sigmasqlambda[1])), envir=.geoR.env)
.temp.list <- get(".temp.list", envir=.geoR.env)
lambda <- sigmasqlambda[2]
if(lambda == 1) {
eval(expression(.temp.list$log.jacobian <- 0), envir=.geoR.env)
}
else {
eval(expression(.temp.list$fix.lambda <- TRUE), , envir=.geoR.env)
if(any(.temp.list$z^(lambda - 1) <= 0))
eval(substitute(.temp.list$log.jacobian <- xxx, list(xxx=log(prod(.temp.list$z^(lambda -
1))))), envir=.geoR.env)
else eval(substitute(.temp.list$log.jacobian <- xxx, list(xxx=sum(log(.temp.list$z^(lambda -
1))))), envir=.geoR.env)
if(lambda == 0)
eval(substitute(.temp.list$z <- xxx, list(xxx=log(.temp.list$z))), envir=.geoR.env)
else eval(substitute(.temp.list$z <- xxx, list(xxx=((.temp.list$z^lambda) - 1)/lambda)), envir=.geoR.env)
}
ini.lik <- round(100000000. * apply(.temp.list$ini.grid, 1,
.proflik.aux10))
ini <- as.vector(.temp.list$ini.grid[which(ini.lik == min(ini.lik, na.rm = TRUE)),,drop=FALSE][1,])
phitausq.rel.res <- optim(ini, .proflik.aux10, method="L-BFGS-B",
lower = c(.temp.list$lower.phi,
0), upper=c(.temp.list$upper.phi, 100), ...)$value
eval(expression(.temp.list$log.jacobian <- NULL), envir=.geoR.env)
eval(expression(.temp.list$sigmasq <- NULL), envir=.geoR.env)
eval(substitute(.temp.list$z <- xxx, list(xxx=.temp.list$data)), envir=.geoR.env)
return( - phitausq.rel.res)
}
".proflik.aux28" <-
function(sigmasqphi, ...)
{
## This function computes the value of the 2-D profile likelihood for the random field scale (variance) parameter \sigma^2 and the correlation function parameter \phi when nugget effect is not included in the model.
## It requires the minimisation of the function wrt \lambda for each value of (\sigma^2, \phi)
## This is an auxiliary function called by likfit.proflik
##
## ini.seq <- seq(-1.5, 1.5, l=7)
## .temp.list$sigmasqphi <<- as.vector(sigmasqphi)
## lambda.lik <- apply(as.matrix(ini.seq), 1, .proflik.aux4)
## ini <- ini.seq[lambda.lik == max(lambda.lik)]
## lambda.res <- optim(ini, .proflik.aux4, method="L-BFGS-B", lower = -2.5, upper = 2.5, ...)$value
lambda.res <- optimise(.proflik.aux4, lower = -5, upper = 5, ...)$objective
eval(expression(.temp.list$sigmasqphi <- NULL), envir=.geoR.env)
return( - lambda.res)
}
".proflik.aux30" <-
function(phitausq.rel, ...)
{
## This function computes the value of the profile likelihood for the correlation parameter \phi when nugget effect is not included in the model.
## It requires the minimisation of the function wrt \phi for each value of \lambda, if this transformation parameter is included in the model
## This is an auxiliary function called by likfit.proflik
##
.temp.list <- get(".temp.list", envir=.geoR.env)
if(.temp.list$fix.lambda == TRUE)
proflik <- .proflik.aux21(phitausq.rel = phitausq.rel)
else {
eval(substitute(.temp.list$phitausq.rel <- xxx, list(xxx=phitausq.rel)), envir=.geoR.env)
## proflik <- - (optim(.temp.list$lambda, .proflik.aux21.1, method="L-BFGS-B", lower =
## -2, upper = 2, ...)$value)
proflik <- - (optimise(.proflik.aux21.1, lower = -5, upper = 5, ...)$objective)
eval(expression(.temp.list$phitausq.rel <- NULL), envir=.geoR.env)
}
return(proflik)
}
".proflik.aux3" <-
function(phi.lambda, ...)
{
## This function computer the negative of the likelihood function for the correlation function scale parameter \phi (and maybe the transformation parameter \lambda) only for models with fixed nugget effect (i.e., when it is not a parameter to be estimated)
## This function is used when computing the profile likelihood for \sigma^2
## This is an auxiliary function called by .proflik.aux2
## phi <- pmax(phi, .temp.list$lower.phi)
.temp.list <- get(".temp.list", envir=.geoR.env)
if(length(phi.lambda) == 2)
lambda <- phi.lambda[2]
else lambda <- 1
sigmasq <- .temp.list$sigmasq
phi <- phi.lambda[1]
n <- .temp.list$n
main <- .proflik.main(tausq=0, sigmasq=1, phi=phi, lambda = lambda)
if(.temp.list$method.lik == "ML") {
neglik <- (n/2) * log(2 * pi) +
main$log.det.to.half +
(n/2) * log(sigmasq) + (0.5/sigmasq) * main$ssresmat -
main$log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
neglik <- ((n - .temp.list$beta.size)/2) * log(2 * pi) +
main$log.det.to.half +
((n - .temp.list$beta.size)/2) * log(sigmasq) +
(0.5/sigmasq) * main$ssresmat -
0.5 * sum(log(eigentrem$values)) -
main$log.jacobian
}
return(as.vector(round(neglik, digits=8)))
}
".proflik.aux31" <-
function(philambda, ...)
{
## This function computes the value of the 2-D profile likelihood for range \phi and the transformation parameter \lambda.
## It requires the minimisation of the function wrt \tau^2_{rel} and for each value of (\phi,\lambda).
## This is an auxiliary function called by .proflik.
.temp.list <- get(".temp.list", envir=.geoR.env)
philambda <- as.vector(philambda)
eval(substitute(.temp.list$phi <- xxx, list(xxx= philambda[1])), envir=.geoR.env)
.temp.list$lambda <- philambda[2]
## tausq.rel.res <- optim(.temp.list$tausq.rel.est, .proflik.aux8, method="L-BFGS-B", lower =
## 0, upper=100, ...)$value
tausq.rel.res <- optimise(.proflik.aux8, lower = 0, upper=1000, ...)$objective
eval(expression(.temp.list$phi <- NULL), envir=.geoR.env)
return( - tausq.rel.res)
}
".proflik.aux32" <-
function(tausqlambda, ...)
{
## This function computes the value of the 2-D profile likelihood for nugget \tau^2 and the transformation parameter \lambda.
# It requires the minimisation of the function wrt \phi and \sigma^2 and for each value of (\tau^2,\lambda).
# This is an auxiliary function called by .proflik.
tausqlambda <- as.vector(tausqlambda)
eval(substitute(.temp.list$nugget <- xxx, list(xxx=tausqlambda[1])), envir=.geoR.env)
.temp.list <- get(".temp.list", envir=.geoR.env)
lambda <- tausqlambda[2]
if(lambda == 1) {
eval(expression(.temp.list$log.jacobian <- 0), envir=.geoR.env)
}
else {
if(any(.temp.list$z^(lambda - 1) <= 0))
eval(substitute(.temp.list$log.jacobian <- xxx, list(xxx=log(prod(.temp.list$z^(lambda -
1))))), envir=.geoR.env)
else eval(substitute(.temp.list$log.jacobian <- xxx, list(xxx=sum(log(.temp.list$z^(lambda - 1))))), envir=.geoR.env)
if(lambda == 0)
eval(substitute(.temp.list$z <- xxx, list(xxx=log(.temp.list$z))), envir=.geoR.env)
else eval(substitute(.temp.list$z <- xxx, list(xxx=((.temp.list$z^lambda) - 1)/lambda)), envir=.geoR.env)
}
sigmasqphi.res <- optim(c(.temp.list$sigmasq.est, .temp.list$phi.est), .proflik.aux12, method="L-BFGS-B",
lower = c(.temp.list$lower.sigmasq, .temp.list$
lower.phi), upper=c(+Inf, .temp.list$upper.phi), ...)$value
eval(expression(.temp.list$log.jacobian <- NULL), envir=.geoR.env)
eval(substitute(.temp.list$z <- xxx, list(xxx=.temp.list$data)), envir=.geoR.env)
eval(expression(.temp.list$nugget <- NULL), envir=.geoR.env)
return( - sigmasqphi.res)
}
".proflik.aux33" <-
function(tausq.rellambda, ...)
{
## This function computes the value of the 2-D profile likelihood for nugget \tau^2 and the transformation parameter \lambda.
## It requires the minimisation of the function wrt \phi for each value of (\tau^2,\lambda).
## This is an auxiliary function called by .proflik.
tausq.rellambda <- as.vector(tausq.rellambda)
eval(substitute(.temp.list$nugget.rel <- xxx, list(xxx=tausq.rellambda[1])), envir=.geoR.env)
.temp.list <- get(".temp.list", envir=.geoR.env)
lambda <- tausq.rellambda[2]
if(lambda == 1) {
eval(expression(.temp.list$log.jacobian <- 0), envir=.geoR.env)
}
else {
if(any(.temp.list$z^(lambda - 1) <= 0))
eval(substitute(.temp.list$log.jacobian <- xxx, list(xxx=log(prod(.temp.list$z^(lambda -
1))))), envir=.geoR.env)
else eval(substitute(.temp.list$log.jacobian <- xxx, list(xxx=sum(log(.temp.list$z^(lambda -
1))))), envir=.geoR.env)
if(lambda == 0)
eval(substitute(.temp.list$z <- xxx, list(xxx=log(.temp.list$z))), envir=.geoR.env)
else eval(substitute(.temp.list$z <- xxx, list(xxx=((.temp.list$z^lambda) - 1)/lambda)), envir=.geoR.env)
}
## phi.res <- optim(.temp.list$phi.est, .proflik.aux6, method="L-BFGS-B", lower = .temp.list$
## lower.phi, upper=.temp.list$upper.phi, ...)$value
phi.res <- optimise(.proflik.aux6, lower = .temp.list$lower.phi, upper=.temp.list$upper.phi, ...)$objective
eval(expression(.temp.list$log.jacobian <- NULL), envir=.geoR.env)
eval(expression(.temp.list$nugget.rel <- NULL), envir=.geoR.env)
eval(substitute(.temp.list$z <- xxx, list(xxx=.temp.list$data)), envir=.geoR.env)
return( - phi.res)
}
".proflik.aux4" <-
function(lambda, ...)
{
## This function computer the values of the profile likelihood function for the parameters \phi and \sigma^2 for models with nugget effect = 0, including the tranformation parameter \lambda
## This is an auxiliary function called by .proflik.aux28
##
.temp.list <- get(".temp.list", envir=.geoR.env)
sigmasqphi <- as.vector(.temp.list$sigmasqphi)
sigmasq <- sigmasqphi[1]
phi <- sigmasqphi[2]
n <- .temp.list$n
if(lambda > 0.999 & lambda < 1.001)
lambda <- 1
main <- .proflik.main(tausq=.temp.list$nugget, sigmasq = sigmasq, phi=phi, lambda = lambda)
if(.temp.list$method.lik == "ML") {
neglik <- ((n/2) * log(2 * pi) +
main$log.det.to.half +
0.5 * main$ssresmat -
main$log.jacobian)
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
xx.eigen <- eigen(crossprod(.temp.list$xmat), symmetric = TRUE,
only.values = TRUE)
neglik <- (((n - .temp.list$beta.size)/2) * log(2 * pi) -
0.5 * sum(log(xx.eigen$values)) + main$log.det.to.half +
(0.5) * main$ssresmat + 0.5 * sum(log(eigentrem$values)) + main$log.jacobian)
}
return(as.vector(round(neglik, digits=8)))
}
".proflik.aux5" <-
function(tausq.rel, ...)
{
## This function computes the value of the profile likelihood for the parameter \tau^2_{rel}.
## It requires the minimisation of the function wrt \phi and \lambda (if the case) for each value of \tau^2_{rel}.
## This is an auxiliary function called by .proflik.
eval(substitute(.temp.list$nugget.rel <- xxx, list(xxx=as.vector(tausq.rel))), envir=.geoR.env)
.temp.list <- get(".temp.list", envir=.geoR.env)
if(.temp.list$fix.lambda == TRUE) {
## phi.res <- optim(.temp.list$phi.est, .proflik.aux6, method="L-BFGS-B", lower =
## .temp.list$lower.phi, upper=.temp.list$upper.phi, ...)$value
phi.res <- optimise(.proflik.aux6, lower =
.temp.list$lower.phi, upper=.temp.list$upper.phi, ...)$objective
}
else {
phi.res <- optim(c(.temp.list$phi.est, .temp.list$lambda), .proflik.aux6, method="L-BFGS-B",
lower = c(.temp.list$lower.phi, -2),
upper = c(.temp.list$upper.phi, 2), ...)$value
}
eval(expression(.temp.list$nugget.rel <- NULL), envir=.geoR.env)
return( - phi.res)
}
".proflik.aux6" <-
function(phi.lambda, ...)
{
## This function computes the value of the profile likelihood for the relative nugget parameter \tau^2_{rel}, minimizing the likelihood wrt correlation function scale parameter \phi (range) and the transformation parameter \lambda.
.temp.list <- get(".temp.list", envir=.geoR.env)
if(length(phi.lambda) == 2) lambda <- phi.lambda[2] else lambda <- 1
phi.lambda <- as.vector(phi.lambda)
phi <- phi.lambda[1]
n <- .temp.list$n
main <- .proflik.main(tausq=.temp.list$nugget.rel, sigmasq=1, phi=phi, lambda = lambda)
if(.temp.list$method.lik == "ML") {
neglik <- (n/2) * log(2 * pi) +
main$log.det.to.half +
(n/2) * log(main$ssresmat/n) +
(n/2) -
main$log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
neglik <- ((n - .temp.list$beta.size)/2) * log(2 * pi) +
main$log.det.to.half +
((n - .temp.list$beta.size)/2) * log(main$ssresmat/n) +
(n/2) -
0.5 * sum(log(eigentrem$values)) -
main$log.jacobian
}
return(as.vector(round(neglik, digits=8)))
}
".proflik.aux7" <-
function(phi, ...)
{
## This function computes the value of the profile likelihood for the parameter \phi when the nugget \tau^2 is included in the model
## It requires the minimisation of the function wrt relative \tau^2_{rel} for each value of \phi
## This is an auxiliary function called by .proflik.
eval(substitute(.temp.list$phi <- xxx, list(xxx=as.vector(phi))), envir=.geoR.env)
.temp.list <- get(".temp.list", envir=.geoR.env)
if(.temp.list$fix.lambda) {
eval(expression(.temp.list$lambda <- 1), envir=.geoR.env)
## tausq.rel.res <- optim(.temp.list$tausq.rel.est, .proflik.aux8, method="L-BFGS-B",
## lower = 0, upper=100, ...)$value
tausq.rel.res <- optimise(.proflik.aux8, lower = 0, upper=1000, ...)$objective
eval(expression(.temp.list$lambda <- NULL), envir=.geoR.env)
}
else {
tausq.rel.res <- optim(c(.temp.list$tausq.rel.est, .temp.list$lambda), .proflik.aux8,
method="L-BFGS-B", lower = c(0, -2), upper = c(100, 2), ...)$value
}
eval(expression(.temp.list$phi <- NULL), envir=.geoR.env)
return( - tausq.rel.res)
}
".proflik.aux8" <-
function(tausq.rel.lambda, ...)
{
## This function computes the value of the profile likelihood for the correlation function scale parameter \phi (and lambda), minimizing the likelihood wrt relative nugget parameter \tau^2_{rel}
.temp.list <- get(".temp.list", envir=.geoR.env)
if(length(tausq.rel.lambda) == 2)
lambda <- tausq.rel.lambda[2]
else lambda <- .temp.list$lambda
n <- .temp.list$n
phi <- .temp.list$phi
tausq.rel <- tausq.rel.lambda[1]
main <- .proflik.main(tausq=tausq.rel, sigmasq=1, phi=phi, lambda = lambda)
if(.temp.list$method.lik == "ML") {
neglik <- (n/2) * log(2 * pi) + main$log.det.to.half + (
n/2) * log(main$ssresmat/n) + (n/2) - main$log.jacobian
}
if(.temp.list$method.lik == "RML") {
eigentrem <- eigen(main$ixix, symmetric = TRUE, only.values = TRUE)
neglik <- (((n - .temp.list$beta.size)/2) * log(2 * pi) + main$
log.det.to.half + ((n - .temp.list$beta.size)/2) * log(main$ssresmat/
n) + (n/2) - 0.5 * sum(log(eigentrem$values))) -
main$log.jacobian
}
return(as.vector(round(neglik, digits=8)))
}
".proflik.aux9" <-
function(sigmasq, ...)
{
## This function computes the value of the profile likelihood for the parameter \sigma^2 when \tau^2 is included in the model
## It requires the minimisation of the function wrt \phi and \tau^2 for each value of \sigma^2
## This is an auxiliary function called by likfit.proflik
eval(substitute(.temp.list$sigmasq <- xxx, list(xxx=as.vector(sigmasq))), envir=.geoR.env)
.temp.list <- get(".temp.list", envir=.geoR.env)
ini.lik <- round(100000000. * apply(.temp.list$ini.grid, 1,
.proflik.aux10))
ini <- as.vector(.temp.list$ini.grid[which(ini.lik == min(ini.lik, na.rm = TRUE)),,drop=FALSE][1,])
if(.temp.list$fix.lambda == TRUE) {
phitausq.rel.res <- optim(ini, .proflik.aux10, method="L-BFGS-B",
lower = c(.temp.list$
lower.phi, 0),
upper=c(.temp.list$upper.phi, 100), ...)$value
}
else {
if(ini[2] == 0) ini[2] <- 0.01
phitausq.rel.res <- optim(ini, .proflik.aux10, method="L-BFGS-B",
lower = c(.temp.list$lower.phi, 0,-2),
upper = c(.temp.list$upper.phi, 100, 2), ...)$value
}
eval(expression(.temp.list$sigmasq <- NULL), envir=.geoR.env)
return( - phitausq.rel.res)
}
"plot.proflik" <-
function(x, pages = c("user", "one", "two"),
uni.only, bi.only, type.bi = c("contour", "persp"),
conf.int = c(0.90,0.95),
yaxis.lims = c("conf.int", "as.computed"),
by.col = TRUE, log.scale = FALSE, use.splines = TRUE,
par.mar.persp = c(0, 0, 0, 0), ask = FALSE,
...)
{
##
## Saving original par() parameters
##
## par.ori <- par(no.readonly = TRUE)
## on.exit(par(par.ori))
##
parask <- par()$ask
par(ask = ask)
on.exit(par(ask = parask))
##
## Checking whether to plot 1D and/or 2D profiles
##
if(missing(uni.only)){
if(x$n.bi == 0) uni.only <- TRUE
else uni.only <- FALSE
}
if(missing(bi.only)){
if(x$n.uni == 0) bi.only <- TRUE
else bi.only <- FALSE
}
if(!is.logical(uni.only))
stop("argument uni.only must be logical (TRUE or FALSE)")
if(!is.logical(bi.only))
stop("argument bi.only must be logical (TRUE or FALSE)")
n.uni <- x$n.uni
n.bi <- x$n.bi
if((uni.only == FALSE) & (bi.only == FALSE))
np <- n.uni + n.bi
if((uni.only == TRUE) & (bi.only == FALSE))
np <- n.uni
if((uni.only == FALSE) & (bi.only == TRUE))
np <- n.bi
if(n.uni == 0 & np > 0) bi.only <- TRUE
if(n.bi == 0 & np > 0) uni.only <- TRUE
##
##
##
if(mode(yaxis.lims) == "character")
yaxis.lims <- match.arg(yaxis.lims)
type.bi <- match.arg(type.bi)
##
## Definig number of pages to place the plots
##
pages <- match.arg(pages)
if(pages == "one") {
if(np >= 1 & np < 4)
par(mfrow = c(np, 1))
if(np >= 4) {
if(by.col == TRUE)
par(mfcol = c(ceiling(np/2), 2))
else par(mfrow = c(ceiling(np/2), 2))
}
}
if(pages == "two") {
if(n.uni > 1 & n.uni < 4)
par(mfrow = c(n.uni, 1))
if(n.uni >= 4)
par(mfrow = c(ceiling(n.uni/2), 2))
}
##
##
##
if(bi.only == FALSE) {
for(i in 1:n.uni) {
if(x$method.lik == "ML")
ylabm <- "profile log-likelihood"
else ylabm <- "profile log-(restricted) likelihood"
if(!is.logical(conf.int) || all(conf.int) != FALSE) {
if(mode(conf.int) != "numeric"| any(conf.int > 1))
stop("argument conf.int must be numerical (scalar or vector) with values between 0 and 1")
conf.int.drop <- x[[i]][[3]][2] - 0.5 * qchisq(conf.int,1)
}
if(all(is.character(yaxis.lims))){
if(yaxis.lims == "conf.int")
lik.lims <- c(min(conf.int.drop),
x[[i]][[3]][2])
else lik.lims <- c(min(x[[i]][[2]]),
x[[i]][[3]][2])
}
else
lik.lims <- yaxis.lims
if(log.scale == TRUE) {
if(use.splines){
nxpoints <- 5*length(x[[i]][[1]])
nodups <- which(duplicated(x[[i]][[1]]) == FALSE)
plot(spline(x = log(x[[i]][[1]][nodups]),
y = x[[i]][[2]][nodups],
n = nxpoints,
method="natural"), type = "l",
xlab = paste("log-",
.proflik.plot.aux1(names(x[[i]])[1])),
ylab = ylabm, ylim = lik.lims)
}
else{
plot(log(x[[i]][[1]]),
x[[i]][[2]],
type = "l",
xlab = paste("log-",
.proflik.plot.aux1(names(x[[i]])[1])),
ylab = ylabm, ylim = lik.lims)
}
lines(log(c(x[[i]][[3]][1], x[[i]][[3]][1])),
c(min(lik.lims), x[[i]][[3]][2]), lty = 2)
}
else {
if(use.splines){
nxpoints <- 5*length(x[[i]][[1]])
nodups <- which(duplicated(x[[i]][[1]]) == FALSE)
plot(spline(x = x[[i]][[1]][nodups],
y = x[[i]][[2]][nodups],
n = nxpoints,
method="natural"),
type = "l",
xlab = .proflik.plot.aux1(names(x[[i]])[1]),
ylab = ylabm, ylim = lik.lims)
}
else{
plot(x[[i]][[1]],
x[[i]][[2]],
type = "l", xlab =
.proflik.plot.aux1(names(x[[i]])[1]),
ylab = ylabm, ylim = lik.lims)
}
lines(c(x[[i]][[3]][1],
x[[i]][[3]][1]),
c(min(lik.lims), x[[
i]][[3]][2]), lty = 2)
}
abline(h = conf.int.drop, lty = 3)
}
}
if(uni.only == FALSE) {
if(pages == "two") {
if(n.bi >= 1 & n.bi < 4)
par(mfrow = c(n.bi, 1))
if(n.bi >= 4)
par(mfrow = c(ceiling(n.bi/2), 2))
}
for(i in 1:n.bi) {
if(type.bi == "contour") {
if(log.scale == TRUE) {
contour(log(x[[(n.uni + i)]][[1]]),
log(x[[(n.uni + i)]][[2]]),
matrix(x[[(n.uni + i)]][[3]],
ncol = length(x[[(n.uni +i)]][[2]])),
xlab = paste("log-", .proflik.plot.aux1(names(x[[(n.uni + i)]][1]))),
ylab = paste("log-", .proflik.plot.aux1(names(x[[(n.uni + i)]][2]))),
...)
points(log(t(x[[(n.uni + i)]][[4]][1:2])))
}
else {
contour(x[[(n.uni + i)]][[1]],
x[[(n.uni + i)]][[2]],
matrix(x[[(n.uni + i)]][[3]],
ncol = length(x[[(n.uni + i)]][[2]])),
xlab = .proflik.plot.aux1(names(x[[(n.uni + i)]][1])),
ylab = .proflik.plot.aux1(names(x[[(n.uni + i)]][2])),
...)
points(t(x[[(n.uni + i)]][[4]][1:2]))
}
}
if(type.bi == "persp") {
cat("For better visualisation arguments for the funtion `persp` can be passed.\nSome relevant argments are: theta, phi, r, d, among others.\n Type help(persp) for a description of the options\n")
if(x$method.lik == "ML")
zlabm <-
"profile log-likelihood"
else zlabm <- "profile log-(restricted) likelihood"
zlimm <- range(x[[(n.uni +
i)]][[3]])
zlimm[1] <- 1.01 * zlimm[1]
minlik <- min(x[[(n.uni + i)]][[3]])
if(log.scale == TRUE) {
persp(log(x[[(n.uni + i)]][[1]]),
log(x[[(n.uni + i)]][[2]]),
matrix(x[[(n.uni + i)]][[3]],
ncol = length(x[[(n.uni + i)]][[2]])),
xlab = .proflik.plot.aux1(paste("log-", names(x[[(n.uni + i)]][1]))),
ylab = paste("log-", .proflik.plot.aux1(names(x[[(n.uni + i)]][2]))),
zlab = zlabm, box = TRUE, ...)
# pp1 <- perspp(x = log(c(x[[(n.uni + i)]][[4]][1],
# min( x[[(n.uni + i)]][[1]]))[c(1, 1, 1, 2)]),
# y = log(c(x[[(n.uni + i)]][[4]][2],
# min(x[[(n.uni + i)]][[2]]))[c(1, 1, 2, 1)]),
# z = c(minlik, x[[(n.uni + i)]][[4]][3])[c(1, 2, 1, 1)], pp)
# segments(log(pp1$x[1]), log(pp1$y[1]), log(pp1$x[2]), log(pp1$y[2]),
# lwd = 2)
}
else {
persp(x = x[[(n.uni + i)]][[1]],
y = x[[(n.uni + i)]][[2]],
z = matrix(x[[(n.uni + i)]][[3]],
ncol = length(x[[(n.uni + i)]][[2]])),
xlab = .proflik.plot.aux1(names(x[[(n.uni + i)]][1])),
ylab = .proflik.plot.aux1(names(x[[(n.uni + i)]][2])),
zlab = zlabm, box = TRUE, ...)
# pp1 <- perspp(x = c(x[[(n.uni + i)]][[4]][1],
# min(x[[(n.uni + i)]][[1]]))[c(1, 1, 1, 2)],
# y = c(x[[(n.uni + i)]][[4]][2],
# min(x[[(n.uni + i)]][[2]]))[c(1, 1,2, 1)],
# z = c(minlik, x[[(n.uni + i)]][[4]][3])[c(1, 2, 1, 1)], pp)
# segments(pp1$x[1], pp1$y[1], pp1$x[2], pp1$y[2], lwd = 2)
}
}
}
}
return(invisible())
}
".proflik.plot.aux1" <-
function(parameter.name)
{
switch(parameter.name,
range = expression(phi),
sill = expression(sigma^2),
lambda = expression(lambda),
nugget = expression(tau^2),
nugget.rel = expression(tau[rel]^2))
}
".proflik.main" <-
function(tausq, sigmasq, phi, lambda)
{
.temp.list <- get(".temp.list", envir=.geoR.env)
z <- .temp.list$z
n <- .temp.list$n
if(lambda == 1){
## log.jacobian <- .temp.list$log.jacobian
log.jacobian <- 0
}
else {
if(any(z <= 0))
stop("Transformation option not allowed when there are zeros or negative data")
if(any(z^(lambda - 1) <= 0))
log.jacobian <- log(prod(z^(lambda - 1)))
else log.jacobian <- sum(log(z^(lambda - 1)))
if(lambda == 0)
z <- log(z)
else z <- ((z^lambda) - 1)/lambda
}
kappa <- .temp.list$kappa
V <- varcov.spatial(dists.lowertri = .temp.list$dists.lowertri,
cov.model = .temp.list$cov.model, kappa = kappa,
nugget = tausq, cov.pars = c(sigmasq, phi),
det = TRUE)
xix <- crossprod(.temp.list$xmat,solve(V$varcov,.temp.list$xmat))
if(length(as.vector(xix)) == 1) choldet <- 0.5 * log(xix)
else choldet <- sum(log(diag(chol(xix))))
iz <- solve(V$varcov,z)
xiy <- crossprod(.temp.list$xmat,iz)
beta.hat <- drop(solve(xix,xiy))
yiy <- drop(crossprod(z,iz))
ssresmat <- as.vector(yiy - crossprod(beta.hat,xiy))
return(list(log.det.to.half = V$log.det.to.half,
ssresmat = ssresmat,
ixix = solve(xix), log.jacobian = log.jacobian))
}
".proflik.lambda" <-
function(lambda)
{
.temp.list <- get(".temp.list", envir=.geoR.env)
.temp.lower.lambda <- get(".temp.lower.lambda", envir=.geoR.env)
.temp.upper.lambda <- get(".temp.upper.lambda", envir=.geoR.env)
if (any(is.na(lambda)) | any(lambda==Inf) | any(is.nan(lambda)))
neglik <- 1e+32
else{
if(.temp.list$minimisation.function == "nlm"){
if (exists(".temp.lambda", envir=.geoR.env)) remove(".temp.lambda", envir=.geoR.env, inherits = TRUE)
lambda.minimiser <- lambda
penalty <- 1000 * (.temp.lower.lambda - min(lambda, .temp.lower.lambda))
lambda <- max(lambda, .temp.lower.lambda)
penalty <- penalty + 1000 * (.temp.upper.lambda - max(lambda, .temp.upper.lambda))
lambda <- min(lambda, .temp.upper.lambda)
if (round(1000 * lambda.minimiser) <= round(1000 * .temp.lower.lambda))
assign(".temp.lambda", lambda, envir=.geoR.env)
if (round(1000 * lambda.minimiser) >= round(1000 * .temp.upper.lambda))
assign(".temp.lambda", lambda, envir=.geoR.env)
}
z <- .temp.list$z
n <- .temp.list$n
if(lambda == 1) {
.temp.list$log.jacobian <- 0
}
else {
if(any(z < 0))
stop("Transformation option not allowed when there are zeros or negative data")
if(any(z^(lambda - 1) <= 0))
.temp.list$log.jacobian <- log(prod(z^(lambda - 1)))
else .temp.list$log.jacobian <- sum(log(z^(lambda - 1)))
if(lambda == 0)
z <- log(z)
else z <- ((z^lambda) - 1)/lambda
}
beta.size <- .temp.list$beta.size
kappa <- .temp.list$kappa
xmat <- .temp.list$xmat
txmat <- .temp.list$txmat
ixx <- solve(crossprod(xmat))
tausqhat <- (z %*% (diag(n) - xmat %*% ixx %*% txmat) %*% z)/n
if(.temp.list$method == "ML")
neglik <- ((n/2) * log(2 * pi) +
(n/2) * log(tausqhat) +
(n/2) -
.temp.list$log.jacobian
)
if(.temp.list$method == "RML") {
eigentrem <- eigen(ixx, symmetric = TRUE, only.values = TRUE)
neglik <- (((n - beta.size)/2) * log(2 * pi) +
((n - beta.size)/2) * log(tausqhat) +
(n/2) -
0.5 * sum(log(eigentrem$values)) -
.temp.list$log.jacobian
)
}
}
if(.temp.list$minimisation.function == "nlm")
return(as.vector(neglik + penalty))
else
return(as.vector(neglik))
}
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