SpatialExtremes (version 1.2-0)

profile2d: Method for profiling (in 2d) fitted max-stable objects

Description

Computes profile surfaces for fitted max-stable models.

Usage

## S3 method for class 'maxstab':
profile2d(fitted, params, ranges, n = 10, plot = TRUE,
\dots)

Arguments

fitted

An object of class ``maxstab''. Most often, it will be the output of the function fitmaxstab.

params

A character vector giving the two model parameters that are to be profiled.

ranges

A matrix corresponding to the ranges for the profiled model parameters that must be explored. Each row corresponds to one model parameter range.

n

Integer. The number of profiled model parameter that must be considered.

plot

Logical. If TRUE (default), the profile surface is plotted.

...

Extra options that must be passed to the plot function.

Value

• A list with two arguments: coord and llik. coord is a matrix representing the grid where the profiled model parameters are fixed. llik the corresponding pairwise log-likelihood.

Warnings

This function can be really time consuming!

Examples

require(RandomFields)

##Define the coordinates of each location
n.site <- 30
locations <- matrix(rnorm(2*n.site, sd = sqrt(.2)), ncol = 2)
colnames(locations) <- c("lon", "lat")

##Simulate a max-stable process - with unit Frechet margins
ms0 <- MaxStableRF(locations[,1], locations[,2], grid=FALSE, model="wh",
                   param=c(0,1,0,30, .5), maxstable="extr",
                   n = 30)
ms1 <- t(ms0)

##Now define the spatial model for the GEV parameters
param.loc <- -10 + 2 * locations[,2]
param.scale <- 5 + 2 * locations[,1] + locations[,2]^2
param.shape <- rep(0.2, n.site)
##Transform the unit Frechet margins to GEV 
for (i in 1:n.site)
  ms1[,i] <- param.scale[i] * (ms1[,i]^param.shape[i] - 1) /
  param.shape[i] + param.loc[i]

##Define a model for the GEV margins to be fitted
##shape ~ 1 stands for the GEV shape parameter is constant
##over the region
loc.form <- loc ~ lat
scale.form <- scale ~ lon + (lat^2)
shape.form <- shape ~ 1

##Fit a max-stable process
##  1- using the Schlather representation
fitted <- fitmaxstab(ms1, locations, "schlather", loc.form, scale.form,
                     shape.form)

##Plot the profile pairwise log-likelihood for the smooth parameter
ranges <- rbind(c(9,11), c(.3, .8))
profile2d(fitted, c("range", "smooth"), ranges = ranges)