Nothing
fitcopula <- function(data, coord, copula = "gaussian", cov.mod = "whitmat",
loc.form, scale.form, shape.form, marg.cov = NULL, temp.cov = NULL,
temp.form.loc = NULL, temp.form.scale = NULL,
temp.form.shape = NULL, ..., start,
control = list(maxit = 10000), method = "Nelder",
std.err = TRUE, warn = TRUE, corr = FALSE){
n.site <- ncol(data)
n.obs <- nrow(data)
dist.dim <- ncol(coord)
std.err2 <- std.err
dist <- t(as.matrix(dist(coord, diag = TRUE)))
dist <- dist[lower.tri(dist, diag = TRUE)]
if (!(cov.mod %in% c("whitmat","cauchy","powexp","bessel","caugen")))
stop("''cov.mod'' must be one of 'whitmat', 'cauchy', 'powexp', 'bessel', 'caugen'")
if (!(copula %in% c("gaussian", "student")))
stop("''copula'' must be one of 'gaussian' or 'student'")
if (cov.mod == "whitmat")
cov.mod.num <- 1
if (cov.mod == "cauchy")
cov.mod.num <- 2
if (cov.mod == "powexp")
cov.mod.num <- 3
if (cov.mod == "bessel")
cov.mod.num <- 4
if (cov.mod == "caugen")
cov.mod.num <- 5
if (copula == "gaussian")
copula.num <- 1
else
copula.num <- 2
if (missing(loc.form) && missing(scale.form) && missing(shape.form))
fit.marge <- FALSE
if (!missing(loc.form) && !missing(scale.form) && !missing(shape.form)){
fit.marge <- TRUE
if ((class(loc.form) != "formula") || (class(scale.form) != "formula") ||
(class(shape.form) != "formula"))
stop("''loc.form'', ''scale.form'' and ''shape.form'' must be valid R formulas")
}
flag <- missing(loc.form) + missing(scale.form) + missing(shape.form)
if (!(flag %in% c(0, 3)))
stop("if one formula is given for the GEV parameters, then it should
be given for *ALL* GEV parameters")
param <- c("nugget", "range", "smooth")
if (cov.mod == "caugen")
param <- c(param, "smooth2")
else
##Fix it to 0 as it won't be used anyway
smooth2 <- 0
if (copula == "student")
param <- c("DoF", param)
else
##Fix it to 0 as it won't be used anyway
DoF <- 0
if (n.site != nrow(coord))
stop("'data' and 'coord' doesn't match")
use.temp.cov <- c(!is.null(temp.form.loc), !is.null(temp.form.scale),
!is.null(temp.form.shape))
if (any(use.temp.cov) && (n.obs != nrow(temp.cov)))
stop("'data' and 'temp.cov' doesn't match")
if (any(use.temp.cov) && is.null(temp.cov))
stop("'temp.cov' must be supplied if at least one temporal formula is given")
if (fit.marge){
##With our notation, formula must be of the form y ~ xxxx
loc.form <- update(loc.form, y ~ .)
scale.form <- update(scale.form, y ~ .)
shape.form <- update(shape.form, y ~ .)
if (use.temp.cov[1])
temp.form.loc <- update(temp.form.loc, y ~. + 0)
if (use.temp.cov[2])
temp.form.scale <- update(temp.form.scale, y ~. + 0)
if (use.temp.cov[3])
temp.form.shape <- update(temp.form.shape, y ~. + 0)
if (is.null(marg.cov))
covariables <- data.frame(coord)
else
covariables <- data.frame(coord, marg.cov)
loc.model <- modeldef(covariables, loc.form)
scale.model <- modeldef(covariables, scale.form)
shape.model <- modeldef(covariables, shape.form)
loc.dsgn.mat <- loc.model$dsgn.mat
scale.dsgn.mat <- scale.model$dsgn.mat
shape.dsgn.mat <- shape.model$dsgn.mat
loc.pen.mat <- loc.model$pen.mat
scale.pen.mat <- scale.model$pen.mat
shape.pen.mat <- shape.model$pen.mat
loc.penalty <- loc.model$penalty.tot
scale.penalty <- scale.model$penalty.tot
shape.penalty <- shape.model$penalty.tot
##The total number of parameters to be estimated for each GEV
##parameter
n.loccoeff <- ncol(loc.dsgn.mat)
n.scalecoeff <- ncol(scale.dsgn.mat)
n.shapecoeff <- ncol(shape.dsgn.mat)
##The number of ``purely parametric'' parameters to estimate i.e. we
##do not consider the weigths given to each basis function
n.pparloc <- loc.model$n.ppar
n.pparscale <- scale.model$n.ppar
n.pparshape <- shape.model$n.ppar
loc.names <- paste("locCoeff", 1:n.loccoeff, sep="")
scale.names <- paste("scaleCoeff", 1:n.scalecoeff, sep="")
shape.names <- paste("shapeCoeff", 1:n.shapecoeff, sep="")
}
else {
loc.dsgn.mat <- scale.dsgn.mat <- shape.dsgn.mat <- loc.pen.mat <-
scale.pen.mat <- shape.pen.mat <- loc.names <- scale.names <-
shape.names <- loc.form <- scale.form <- shape.form <- NULL
n.loccoeff <- n.scalecoeff <- n.shapecoeff <- n.pparloc <-
n.pparscale <- n.pparshape <- loc.penalty <- scale.penalty <-
shape.penalty <- 0
}
##Do the same for the temporal regression coefficients
if (use.temp.cov[1]){
temp.model.loc <- modeldef(temp.cov, temp.form.loc)
temp.dsgn.mat.loc <- temp.model.loc$dsgn.mat
temp.pen.mat.loc <- temp.model.loc$pen.mat
temp.penalty.loc <- temp.model.loc$penalty.tot
n.tempcoeff.loc <- ncol(temp.dsgn.mat.loc)
n.ppartemp.loc <- temp.model.loc$n.ppar
temp.names.loc <- paste("tempCoeffLoc", 1:n.tempcoeff.loc, sep="")
}
else {
temp.model.loc <- temp.dsgn.mat.loc <- temp.pen.mat.loc <- temp.names.loc <- NULL
n.tempcoeff.loc <- n.ppartemp.loc <- temp.penalty.loc <- 0
}
if (use.temp.cov[2]){
temp.model.scale <- modeldef(temp.cov, temp.form.scale)
temp.dsgn.mat.scale <- temp.model.scale$dsgn.mat
temp.pen.mat.scale <- temp.model.scale$pen.mat
temp.penalty.scale <- temp.model.scale$penalty.tot
n.tempcoeff.scale <- ncol(temp.dsgn.mat.scale)
n.ppartemp.scale <- temp.model.scale$n.ppar
temp.names.scale <- paste("tempCoeffScale", 1:n.tempcoeff.scale, sep="")
}
else {
temp.model.scale <- temp.dsgn.mat.scale <- temp.pen.mat.scale <- temp.names.scale <- NULL
n.tempcoeff.scale <- n.ppartemp.scale <- temp.penalty.scale <- 0
}
if (use.temp.cov[3]){
temp.model.shape <- modeldef(temp.cov, temp.form.shape)
temp.dsgn.mat.shape <- temp.model.shape$dsgn.mat
temp.pen.mat.shape <- temp.model.shape$pen.mat
temp.penalty.shape <- temp.model.shape$penalty.tot
n.tempcoeff.shape <- ncol(temp.dsgn.mat.shape)
n.ppartemp.shape <- temp.model.shape$n.ppar
temp.names.shape <- paste("tempCoeffShape", 1:n.tempcoeff.shape, sep="")
}
else {
temp.model.shape <- temp.dsgn.mat.shape <- temp.pen.mat.shape <- temp.names.shape <- NULL
n.tempcoeff.shape <- n.ppartemp.shape <- temp.penalty.shape <- 0
}
param <- c(param, loc.names, scale.names, shape.names, temp.names.loc, temp.names.scale,
temp.names.shape)
nllik <- function(x) x
body(nllik) <- parse(text = paste("-.C(C_copula, as.integer(copula.num), as.integer(cov.mod.num),
as.double(dist), as.double(data), as.integer(n.site), as.integer(n.obs), as.integer(dist.dim), as.integer(fit.marge),
as.double(loc.dsgn.mat), as.double(loc.pen.mat), as.integer(n.loccoeff), as.integer(n.pparloc),
as.double(loc.penalty), as.double(scale.dsgn.mat), as.double(scale.pen.mat),
as.integer(n.scalecoeff), as.integer(n.pparscale), as.double(scale.penalty),
as.double(shape.dsgn.mat), as.double(shape.pen.mat), as.integer(n.shapecoeff),
as.integer(n.pparshape), as.double(shape.penalty), as.integer(use.temp.cov),
as.double(temp.dsgn.mat.loc), as.double(temp.pen.mat.loc), as.integer(n.tempcoeff.loc),
as.integer(n.ppartemp.loc), as.double(temp.penalty.loc), as.double(temp.dsgn.mat.scale),
as.double(temp.pen.mat.scale), as.integer(n.tempcoeff.scale), as.integer(n.ppartemp.scale),
as.double(temp.penalty.scale), as.double(temp.dsgn.mat.shape), as.double(temp.pen.mat.shape),
as.integer(n.tempcoeff.shape), as.integer(n.ppartemp.shape), as.double(temp.penalty.shape),",
paste("as.double(c(", paste(loc.names, collapse = ","), ")), "),
paste("as.double(c(", paste(scale.names, collapse = ","), ")), "),
paste("as.double(c(", paste(shape.names, collapse = ","), ")), "),
paste("as.double(c(", paste(temp.names.loc, collapse = ","), ")), "),
paste("as.double(c(", paste(temp.names.scale, collapse = ","), ")), "),
paste("as.double(c(", paste(temp.names.shape, collapse = ","), ")), "),
"as.double(DoF), as.double(nugget), as.double(range), as.double(smooth),
as.double(smooth2), dns = double(1))$dns"))
##Define the formal arguments of the function
form.nllik <- NULL
for (i in 1:length(param))
form.nllik <- c(form.nllik, alist(a=))
names(form.nllik) <- param
formals(nllik) <- form.nllik
if (missing(start)){
start <- list(nugget = 0, range = 0.25 * max(dist), smooth = 1)
if (copula == "student")
start <- c(list(DoF = 1), start)
if (fit.marge){
loc <- scale <- shape <- rep(0, n.site)
for (i in 1:n.site){
gev.param <- gevmle(data[,i])
loc[i] <- gev.param["loc"]
scale[i] <- gev.param["scale"]
shape[i] <- gev.param["shape"]
}
locCoeff <- loc.model$init.fun(loc)
scaleCoeff <- scale.model$init.fun(scale)
shapeCoeff <- shape.model$init.fun(shape)
locCoeff[is.na(locCoeff)] <- 0
scaleCoeff[is.na(scaleCoeff)] <- 0
shapeCoeff[is.na(shapeCoeff)] <- 0
##To be sure that the scale parameter is always positive at starting
##values
scales.hat <- scale.model$dsgn.mat %*% scaleCoeff
if (any(scales.hat <= 0))
scaleCoeff[1] <- scaleCoeff[1] - 1.001 * min(scales.hat)
names(locCoeff) <- loc.names
names(scaleCoeff) <- scale.names
names(shapeCoeff) <- shape.names
if (use.temp.cov[1]){
tempCoeff.loc <- rep(0, n.tempcoeff.loc)
names(tempCoeff.loc) <- temp.names.loc
}
else
tempCoeff.loc <- NULL
if (use.temp.cov[2]){
tempCoeff.scale <- rep(0, n.tempcoeff.scale)
names(tempCoeff.scale) <- temp.names.scale
}
else
tempCoeff.scale <- NULL
if (use.temp.cov[3]){
tempCoeff.shape <- rep(0, n.tempcoeff.shape)
names(tempCoeff.shape) <- temp.names.shape
}
else
tempCoeff.shape <- NULL
start <- c(start, as.list(c(locCoeff, scaleCoeff, shapeCoeff, tempCoeff.loc, tempCoeff.scale, tempCoeff.shape)))
}
start <- start[!(param %in% names(list(...)))]
}
if (!length(start))
stop("there are no parameters left to maximize over")
nm <- names(start)
l <- length(nm)
f <- formals(nllik)
names(f) <- param
m <- match(nm, param)
if(any(is.na(m)))
stop("'start' specifies unknown arguments")
formals(nllik) <- c(f[m], f[-m])
nllh <- function(p, ...) nllik(p, ...)
if(l > 1)
body(nllh) <- parse(text = paste("nllik(", paste("p[",1:l,
"]", collapse = ", "), ", ...)"))
fixed.param <- list(...)[names(list(...)) %in% param]
if(any(!(param %in% c(nm,names(fixed.param)))))
stop("unspecified parameters")
start.arg <- c(list(p = unlist(start)), fixed.param)
init.lik <- do.call("nllh", start.arg)
if (warn && (init.lik >= 1.0e6))
warning("negative log-likelihood is infinite at starting values")
if (method == "nlminb"){
start <- as.numeric(start)
opt <- nlminb(start, nllh, ..., control = control, hessian = std.err)
opt$counts <- opt$evaluations
opt$value <- opt$objective
names(opt$par) <- nm
}
else if (method == "nlm"){
start <- as.numeric(start)
opt <- nlm(nllh, start, ..., hessian = std.err)
opt$counts <- opt$iterations
names(opt$counts) <- "function"
opt$value <- opt$minimum
opt$par <- opt$estimate
names(opt$par) <- nm
if (opt$code <= 2){
opt$convergence <- 0
opt$message <- NULL
}
if (opt$code > 2){
opt$convergence <- 1
opt$message <- paste("nlm error code", opt$code)
}
}
else
opt <- optim(start, nllh, ..., method = method, control = control,
hessian = std.err)
if ((opt$convergence != 0) || (opt$value >= 1.0e6)){
if (warn)
warning("optimization may not have succeeded")
}
else
opt$convergence <- "successful"
param.names <- param
param <- c(opt$par, unlist(fixed.param))
param <- param[param.names]
if (std.err2){
ihessian <- try(solve(opt$hessian), silent = TRUE)
if(!is.matrix(ihessian)){
if (warn)
warning("observed information matrix is singular; std. err. won't be computed")
std.err2 <- FALSE
}
else{
std.err <- diag(ihessian)
std.idx <- which(std.err <= 0)
if(length(std.idx) > 0){
if (warn)
warning("Some (observed) standard errors are negative;\n passing them to NA")
std.err[std.idx] <- NA
}
std.err <- sqrt(std.err)
if(corr) {
.mat <- diag(1/std.err, nrow = length(std.err))
corr.mat <- structure(.mat %*% ihessian %*% .mat, dimnames = list(nm,nm))
diag(corr.mat) <- rep(1, length(std.err))
}
else
corr.mat <- NULL
colnames(ihessian) <- rownames(ihessian) <- names(std.err) <- nm
}
}
if (!std.err2)
std.err <- std.err.type <- corr.mat <- var.cov <- ihessian <-
var.score <- NULL
if (cov.mod == "caugen")
cov.fun <- covariance(nugget = param["nugget"], sill = 1 - param["nugget"], range = param["range"],
smooth = param["smooth"], smooth2 = param["smooth2"],
cov.mod = cov.mod, plot = FALSE)
else
cov.fun <- covariance(nugget = param["nugget"], sill = 1 - param["nugget"], range = param["range"],
smooth = param["smooth"], cov.mod = cov.mod, plot = FALSE)
if (copula == "gaussian")
ext.coeff <- function(h)
rep(2, length(h))
else
ext.coeff <- function(h)
2 * (1 - pt(-sqrt((param["DoF"] + 1) * (1 - cov.fun(h)) /
(1 + cov.fun(h))), param["DoF"] + 1))
ans <- list(fitted.values = opt$par, param = param, std.err = std.err,
counts = opt$counts, message = opt$message, coord = coord,
logLik = -opt$value, loc.form = loc.form, scale.form = scale.form,
shape.form = shape.form, convergence = opt$convergence,
nllh = nllh, deviance = 2 * opt$value, var.cov = ihessian,
data = data, fixed = unlist(fixed.param), hessian = opt$hessian,
marg.cov = marg.cov, use.temp.cov = use.temp.cov, corr = corr.mat,
copula = copula, ext.coeff = ext.coeff, cov.fun = cov.fun,
cov.mod = cov.mod, fit.marge = fit.marge, iso = TRUE)
class(ans) <- "copula"
return(ans)
}
rcopula <- function(n, coord, copula = "gaussian", cov.mod = "whitmat", grid = FALSE,
control = list(), nugget = 0, range = 1, smooth = 1, DoF = 1){
## This function simulates realizations from a copula with unit
## Frechet margins
if (!(cov.mod %in% c("whitmat","cauchy","powexp","bessel")))
stop("'cov.mod' must be one of 'gauss', 'whitmat', 'cauchy', 'powexp' or 'bessel'")
if ((nugget > 1) || (nugget < 0))
stop("'nugget' should lie in [0, 1]")
sill <- 1 - nugget
gp <- rgp(n, coord, cov.mod, grid = grid, control = list(), nugget = nugget,
sill = sill, range = range, smooth = smooth)
if (copula == "gaussian")
ans <- qgev(pnorm(gp), 1, 1, 1)
if (copula == "student"){
if (DoF <= 0)
stop("'DoF' has to be positive.")
scalings <- sqrt(DoF / rchisq(n, DoF))
if (!grid)
ans <- gp * scalings
else {
ans <- array(NA, dim = dim(gp))
for (i in 1:n)
ans[,,i] <- gp[,,i] * scalings[i]
}
ans <- qgev(pt(ans, DoF), 1, 1, 1)
}
return(ans)
}
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