Loglikelihood adjustment for mev fits

S3 alogLik method to perform loglikelihood adjustment for fitted extreme value model objects returned from the functions fit.gev, fit.gpd, and fit.pp and fit.rlarg in the mev package.

Usage

# S3 method for class 'mev_gev'
alogLik(x, cluster = NULL, use_vcov = TRUE, ...)

# S3 method for class 'mev_pp'
alogLik(x, cluster = NULL, use_vcov = TRUE, ...)

# S3 method for class 'mev_gpd'
alogLik(x, cluster = NULL, use_vcov = TRUE, ...)

# S3 method for class 'mev_egp'
alogLik(x, cluster = NULL, use_vcov = TRUE, ...)

# S3 method for class 'mev_rlarg'
alogLik(x, cluster = NULL, use_vcov = TRUE, ...)

Arguments

x

A fitted model object with certain associated S3 methods. See Details.

cluster

A vector or factor indicating from which cluster the respective log-likelihood contributions from loglik originate. The length of cluster must be consistent with the estfun method to be used in the estimation of the 'meat' V of the sandwich estimator of the covariance matrix of the parameters to be passed to adjust_loglik. In most cases, cluster must have length equal to the number of observations in data. The exception is the GP (only) model (binom = FALSE), where the cluster may either contain a value for each observation in the raw data, or for each threshold exceedance in the data.

If cluster is not supplied (is NULL) then it is assumed that each observation forms its own cluster. See Details for further details.

use_vcov

A logical scalar. Should we use the vcov S3 method for x (if this exists) to estimate the Hessian of the independence loglikelihood to be passed as the argument H to adjust_loglik? Otherwise, H is estimated inside adjust_loglik using optimHess.

...

Further arguments to be passed to the functions in the sandwich package meat (if cluster = NULL), or meatCL (if cluster is not NULL).

Value

An object inheriting from class "chandwich". See adjust_loglik. class(x) is a vector of length 5. The first 3 components are c("lax", "chandwich", "mev"). The 4th component depends on which model was fitted. "gev" if fit.gev was used; "gpd" if fit.gpd was used; "pp" fit.pp was used; "egp" fit.egp was used; "rlarg" fit.rlarg was used; The 5th component is "stat" (for stationary).

Details

See alogLik for details.

If x was returned from fit.pp then the data xdat supplied to fit.pp must contain all the data, both threshold exceedances and non-exceedances.

References

Chandler, R. E. and Bate, S. (2007). Inference for clustered data using the independence loglikelihood. Biometrika, 94(1), 167-183. doi:10.1093/biomet/asm015

Suveges, M. and Davison, A. C. (2010) Model misspecification in peaks over threshold analysis, The Annals of Applied Statistics, 4(1), 203-221. doi:10.1214/09-AOAS292

Zeileis (2006) Object-Oriented Computation and Sandwich Estimators. Journal of Statistical Software, 16, 1-16. doi:10.18637/jss.v016.i09

Examples

# We need the mev package
got_mev <- requireNamespace("mev", quietly = TRUE)

if (got_mev) {
  library(mev)
  # An example from the mev::gev.fit documentation
  gev_mev <- fit.gev(revdbayes::portpirie)
  adj_gev_mev <- alogLik(gev_mev)
  summary(adj_gev_mev)

  # Use simulated data
  set.seed(1112019)
  x <- revdbayes::rgp(365 * 10, loc = 0, scale = 1, shape = 0.1)
  pfit <- fit.pp(x, threshold = 1, npp = 365)
  adj_pfit <- alogLik(pfit)
  summary(adj_pfit)

  # An example from the mev::fit.gpd documentation
  gpd_mev <- fit.gpd(eskrain, threshold = 35, method = 'Grimshaw')
  adj_gpd_mev <- alogLik(gpd_mev)
  summary(adj_gpd_mev)

  # An example from the mev::fit.egp documentation
  # (model = "egp1" and model = "egp3" also work)
  xdat <- evd::rgpd(n = 100, loc = 0, scale = 1, shape = 0.5)
  fitted <- fit.egp(xdat = xdat, thresh = 1, model = "egp2", show = FALSE)
  adj_fitted <- alogLik(fitted)
  summary(adj_fitted)

  # An example from the mev::fit.rlarg documentation
  set.seed(31102019)
  xdat <- rrlarg(n = 10, loc = 0, scale = 1, shape = 0.1, r = 4)
  fitr <- fit.rlarg(xdat)
  adj_fitr <- alogLik(fitr)
  summary(adj_fitr)
}
#> 
#> Attaching package: 'mev'
#> The following object is masked _by_ '.GlobalEnv':
#> 
#>     venice
#> The following objects are masked from 'package:fExtremes':
#> 
#>     dgev, pgev, qgev, rgev
#> The following objects are masked from 'package:evir':
#> 
#>     dgev, pgev, qgev, rgev
#> The following objects are masked from 'package:eva':
#> 
#>     pgev, qgev
#> The following object is masked from 'package:extRemes':
#> 
#>     taildep
#> The following objects are masked from 'package:evd':
#> 
#>     dgev, pgev, qgev, rgev, venice
#>           MLE     SE adj. SE
#> loc   -0.1223 0.2859 0.29490
#> scale  1.0750 0.2450 0.20520
#> shape  0.2490 0.1552 0.07926