fitcopula {SpatialExtremes}

Fit a copula-based model to spatial extremes

Description

This function fits various copula-based models to spatial extremes data sets.

Usage

fitcopula(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)

Arguments

data

A matrix representing the data. Each column corresponds to one location.

coord

A matrix that gives the coordinates of each location. Each row corresponds to one location.

copula

A character string. Must be one of "gaussian" and "student" for a Gaussian and Student copula.

cov.mod

A character string corresponding to the correlation function family used in the copula. Must be one of "whitmat", "cauchy", "powexp", "bessel" or "caugen" for the Whittle-Matern, the Cauchy, the Powered Exponential, the Bessel and the Generalized Cauchy correlation families.

loc.form, scale.form, shape.form

R formulas defining the spatial linear model for the GEV parameters. May be missing. See section Details of function fitmaxstab.

marg.cov

Matrix with named columns giving additional covariates for the GEV parameters. If NULL, no extra covariates are used.

temp.cov

Matrix with names columns giving additional *temporal* covariates for the GEV parameters. If NULL, no temporal trend are assume for the GEV parameters — see section Details of function fitmaxstab.

temp.form.loc, temp.form.scale, temp.form.shape

R formulas defining the temporal trends for the GEV parameters. May be missing. See section Details of function fitmaxstab.

...

Several arguments to be passed to the optim, nlm or nlminb functions.

start

A named list giving the initial values for the parameters over which the pairwise likelihood is to be minimized. If start is omitted the routine attempts to find good starting values - but might fail.

control

A list giving the control parameters to be passed to the optim function.

method

The method used for the numerical optimisation procedure. Must be one of BFGS, Nelder-Mead, CG, L-BFGS-B, SANN, nlm or nlminb. See optim for details. Please note that passing nlm or nlminb will use the nlm or nlminb functions instead of optim.

std.err

Logical. Should the standard errors be computed ? The default is to return the standard errors, i.e., std.err = TRUE.

warn

Logical. If TRUE (default), users are warned if the log-likelihood is infinite at starting values and/or problems arised while computing the standard errors.

corr

Logical. If TRUE (non default), the asymptotic correlation matrix is computed.

Value

This function returns a object of class copula.

Warning

This function does not use max-stable copula and the use of non max-stable copula for modelling spatial extreme is highly questionable. This function was mainly implemented for educational purposes and not for concrete modelling purposes.

Author(s)

Mathieu Ribatet

References

Davison, A.C., Padoan, S.A., Ribatet, M. (2010) Statistical Modelling of Spatial Extremes. Submitted to Statistical Science.

See Also

fitmaxstab, latent

Examples

## Not run: 
n.site <- 30
n.obs <- 50

coord <- matrix(runif(2 * n.site, -10, 10), ncol = 2)
colnames(coord) <- c("lon", "lat")

## Generate data from a Gaussian copula model
data <- rcopula(n.obs, coord, "gaussian", "powexp", nugget = 0, range = 4, smooth = 1.2)

## Transform the margins to GEV
locs <- -5 + coord[,"lon"] / 10
scales <- 10 + coord[,"lat"] / 2
shapes <- rep(0.2, n.site)

for (i in 1:n.site)
  data[,i] <- frech2gev(data[,i], locs[i], scales[i], shapes[i])

## Fit a Gaussian copula model

## 1. Define trend surfaces
loc.form <- y ~ lon
scale.form <- y ~ lat
shape.form <- y ~ 1

## 2. Fit
M0 <- fitcopula(data, coord, "gaussian", "powexp", loc.form, scale.form,
                shape.form, nugget = 0)

## End(Not run)