SpatialExtremes (version 1.0-0)

anova: Anova Tables

Description

Computes analysis of deviance for objects of class ''maxstab''

Usage

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

Arguments

object, object2

Two objects of class 'maxstab'.

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.

Value

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

Details

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

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.

See Also

fitmaxstab, profile, TIC

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 three nested models
M0 <- fitmaxstab(ms0, locations, "gauss", fit.marge = FALSE)
M1 <- fitmaxstab(ms0, locations, "gauss", fit.marge = FALSE, cov11 =
100)
M2 <- fitmaxstab(ms0, locations, "gauss", fit.marge = FALSE, cov11 =
100, cov22 = 500, method = "BFGS")
anova(M0, M1) ## <- M1 seems better
anova(M0, M2) ## <- M0 is better
anova(M1, M2) ## <- M1 is clearly better

##To use the Chandler and Bate methodology:
anova(M0, M1, method = "CB")