R: Method for profiling fitted max-stable objects

profile {SpatialExtremes} | R Documentation

## 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", ...)

### 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.

### Details

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

The Chandler and Bate approach adjusts the composite likelihood itself is such a way that the usual asymptotic χ^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.

### 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!

### Author(s)

Mathieu Ribatet

### 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

    ## 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(50, locations, cov.mod = "gauss", cov11 = 100, cov12 =
    25, cov22 = 220)

    ##Fit a max-stable process
    ##  1- using the Smith's model
    fitted <- fitmaxstab(data, locations, "gauss", fit.marge = FALSE)

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

    ## End(Not run)

[Package SpatialExtremes version 2.0-5 Index]