SpatialExtremes (version 1.2-0)

profile: Method for profiling fitted max-stable objects

Description

Computes profile traces for fitted max-stable models.

Usage

## S3 method for class 'maxstab':
profile(fitted, param, range, n = 10, plot = TRUE,
conf = 0.90, method = "RJ", square = "chol", \dots)

Arguments

fitted

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

param

A character string giving the model parameter that are to be profiled.

range

The range for the profiled model parameter that must be explored.

n

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

plot

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

conf

Numeric giving the confidence interval level.

method

Character string. Must be one of "CB", "RJ" or "none" for the Chandler and Bate or the Rotnitzky and Jewell approaches respectively. The "none" method simply plots the profile of the log-composite likelihood. See details.

square

The choice for the matrix square root. This is only useful for the 'CB' method. Must be one of 'chol' (Cholesky) or 'svd' (Singular Value Decomposition).

...

Extra options that must be passed to the plot function.

Value

• A matrix. The first column corresponds to the values for which the profiled model parameter is fixed. The second column gives the value of the pairwise log-likelihood. The remaining columns contain the constrained maximum likelihood estimates for the remaining model parameters.

Warnings

This function can be really time consuming!

Details

The Rotnitzky and Jewell approach consists in adjusting the distribution of the likelihood ratio statistics - which under misspecification is no longer $\chi^2$ distributed.

The Chandler and Bate approach adjusts the composite likelihood itself is such a way that the usual asymptotic $\chi^2$ null distribution is preserved. Note that in the current code, we use the singular value decomposition for the computation of matrix square roots to preserve asymmetry in the profile composite likelihood.

References

Chandler, R. E. and Bate, S. (2007) Inference for clustered data using the independence loglikelihood Biometrika, 94, 167--183.

Rotnitzky, A. and Jewell, N. (1990) Hypothesis testing of regression parameters in semiparametric generalized linear models for cluster correlated data. Biometrika 77, 485--97.

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
sigma <- matrix(c(100, 25, 25, 220),ncol = 2)
sigma.inv <- solve(sigma)
sqrtCinv <- t(chol(sigma.inv))
model <- list(list(model = "gauss", var = 1, aniso = sqrtCinv / 2))
ms0 <- MaxStableRF(locations[,1], locations[,2], grid=FALSE, model=model,
                   maxstable="Bool", n = 50)
ms0 <- t(ms0)
##Fit a max-stable process
##  1- using the Smith's model
fitted <- fitmaxstab(ms0, locations, "gauss", fit.marge = FALSE)

##Plot the profile pairwise log-likelihood for the ''cov11'' parameter
profile(fitted, "cov11", range = c(20, 180))