profile2d.maxstab: Method for profiling (in 2d) fitted max-stable objects
In SpatialExtremes: Modelling Spatial Extremes

Description Usage Arguments Value Warnings Author(s) Examples

Computes profile surfaces for fitted max-stable models.

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

`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.

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.

This function can be really time consuming!

Mathieu Ribatet

## Not run: 
##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
data <- rmaxstab(30, locations, cov.mod = "whitmat", nugget = 0, range = 30,
smooth = 0.5)

##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)
  data[,i] <- frech2gev(data[,i], param.loc[i], param.scale[i],
param.shape[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(data, locations, "whitmat", 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)

## End(Not run)