anova: Anova Tables

In SpatialExtremes: Modelling Spatial Extremes

Description

Computes analysis of deviance for objects of class 'maxstab' or 'spatgev'.

Usage

## S3 method for class 'maxstab'
anova(object, object2, method = "RJ", square = "chol", ...)
## S3 method for class 'spatgev'
anova(object, object2, method = "RJ", square = "chol", ...)

Arguments

object, object2	Two objects of class 'maxstab' or 'spatgev'.
method	Character string. Must be one of "CB" or "RJ" for the Chandler and Bate or the Rotnitzky and Jewell approaches respectively. See function profile.
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).
...	Other options to be passed to the anova function.

Details

As ”maxstab” objects are fitted using pairwise likelihood, the model is misspecified. As a consequence, the likelihood ratio statistic is no longer χ^2 distributed. To compute the anova table, we use the methodology proposed by Rotnitzky and Jewell to adjust the distribution of the likelihood ratio statistic.

Value

This function returns an object of class anova. These objects represent analysis-of-deviance tables.

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, 485–497.

See Also

fitmaxstab, fitspatgev, profile, TIC

Examples

##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)

##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 three models for the GEV margins to be fitted
loc.form <- loc ~ lat
scale.form <- scale ~ lon + I(lat^2)
shape.form <- shape ~ lon

M0 <- fitspatgev(data, locations, loc.form, scale.form, shape.form)
M1 <- fitspatgev(data, locations, loc.form, scale.form, shape.form,
shapeCoeff2 = 0)

##Model selection
anova(M0, M1)
anova(M0, M1, method = "CB", square = "svd")

Example output

Eigenvalue(s): 0.3 

Analysis of Variance Table
   MDf Deviance Df  Chisq Pr(> sum lambda Chisq)
M1   6    10203                                 
M0   7    10203  1 0.2917                 0.3272
Analysis of Variance Table
   MDf Deviance Df  Chisq Pr(> sum lambda Chisq)
M1   6   799.19                                 
M0   7   798.40  1 0.7889                 0.3744

SpatialExtremes documentation built on Sept. 1, 2020, 3:01 a.m.