Loglikelihood adjustment for ismev fits

S3 alogLik method to perform loglikelihood adjustment for fitted extreme value model objects returned from the functions gev.fit, gpd.fit, pp.fit and rlarg.fit in the ismev package. If regression modelling is used then the model will need to be re-fitted, see ismev_refits.

Usage

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

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

# S3 method for class 'gpd.fit'
alogLik(
  x,
  cluster = NULL,
  use_vcov = TRUE,
  binom = FALSE,
  k,
  inc_cens = TRUE,
  ...
)

# S3 method for class 'rlarg.fit'
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).

binom

A logical scalar. This option is only relevant to GP models and is only available in the stationary (no covariates) case. If binom = FALSE then loglikelihood adjustment is only performed using the GP model. If binom = TRUE then loglikelihood adjustment is also performed for inferences about the probability of threshold exceedance, using a Bernoulli model for the instances of threshold exceedance.

k

A non-negative integer scalar. This option is only relevant to GP models and is only available in the stationary (no covariates) case. If k is supplied then it is passed as the run parameter \(K\) to kgaps for making inferences about the extremal index \(\theta\) using the \(K\)-gaps model of Suveges and Davison (2010).

inc_cens

A logical scalar. This argument is only relevant if k is supplied. Passed to kgaps to indicate whether or not to include censored inter-exceedance times, relating to the first and last observations.

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", "ismev"). The remaining 2 components depend on the model that was fitted. The 4th component is: "gev" if gev.fit (or gev_refit) was used; "gpd" if gpd.fit (or gpd_refit) was used; "pp" pp.fit (or pp_refit) was used; "rlarg" rlarg.fit (or rlarg_refit) was used. The 5th component is "stat" if x$trans = FALSE and "nonstat" if x$trans = TRUE.

Details

See alogLik for details.

If regression modelling is used then the ismev functions gev.fit, gpd.fit, pp.fit and rlarg.fit return residuals but alogLik needs the raw data. The model will need to be re-fitted, using one of the functions in ismev_refits, and the user will be prompted to do this by an error message produced by alogLik.

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

See also

alogLik: loglikelihood adjustment for model fits.

Examples

# We need the ismev package
got_ismev <- requireNamespace("ismev", quietly = TRUE)

if (got_ismev) {
  library(ismev)

  # GEV model -----

  # An example from the ismev::gev.fit documentation
  gev_fit <- gev.fit(revdbayes::portpirie, show = FALSE)
  adj_gev_fit <- alogLik(gev_fit)
  summary(adj_gev_fit)

  # An example from chapter 6 of Coles (2001)
  data(fremantle)
  xdat <- fremantle[, "SeaLevel"]
  # Set year 1897 to 1 for consistency with page 113 of Coles (2001)
  ydat <- cbind(fremantle[, "Year"] - 1896, fremantle[, "SOI"])
  gev_fit <- gev_refit(xdat, ydat, mul = 1:2, show = FALSE)
  adj_gev_fit <- alogLik(gev_fit)
  summary(adj_gev_fit)

  # An example from Chandler and Bate (2007)
  gev_fit <- gev_refit(ow$temp, ow, mul = 4, sigl = 4, shl = 4,
                       show = FALSE)
  adj_gev_fit <- alogLik(gev_fit, cluster = ow$year)
  summary(adj_gev_fit)
  # Get closer to the values reported in Table 2 of Chandler and Bate (2007)
  gev_fit <- gev_refit(ow$temp, ow, mul = 4, sigl = 4, shl = 4,
                       show = FALSE, method = "BFGS")
  # Call sandwich::meatCL() with cadjust = FALSE
  adj_gev_fit <- alogLik(gev_fit, cluster = ow$year, cadjust = FALSE)
  summary(adj_gev_fit)

  # GP model -----

  # An example from the ismev::gpd.fit documentation
  # \donttest{
  data(rain)
  rain_fit <- gpd.fit(rain, 10, show = FALSE)
  adj_rain_fit <- alogLik(rain_fit)
  summary(adj_rain_fit)
  # Continuing to the regression example on page 119 of Coles (2001)
  ydat <- as.matrix((1:length(rain)) / length(rain))
  reg_rain_fit <- gpd_refit(rain, 30, ydat = ydat, sigl = 1, siglink = exp,
                            show = FALSE)
  adj_reg_rain_fit <- alogLik(reg_rain_fit)
  summary(adj_reg_rain_fit)
  # }
  # Binomial-GP model -----

  # Use Newlyn seas surges data from the exdex package
  surges <- exdex::newlyn
  u <- quantile(surges, probs = 0.9)
  newlyn_fit <- gpd.fit(surges, u, show = FALSE)
  # Create 5 clusters each corresponding approximately to 1 year of data
  cluster <- rep(1:5, each = 579)[-1]
  adj_newlyn_fit <- alogLik(newlyn_fit, cluster = cluster, binom = TRUE,
                            cadjust = FALSE)
  summary(adj_newlyn_fit)
  summary(attr(adj_newlyn_fit, "pu_aloglik"))

  # Add inference about the extremal index theta, using K = 1
  adj_newlyn_theta <- alogLik(newlyn_fit, cluster = cluster, binom = TRUE,
                              k = 1, cadjust = FALSE)
  summary(attr(adj_newlyn_theta, "theta"))

  # PP model -----

  # An example from the ismev::pp.fit documentation
  data(rain)
  # Start from the mle to save time
  init <- c(40.55755732, 8.99195409, 0.05088103)
  muinit <- init[1]
  siginit <- init[2]
  shinit <- init[3]
  rain_fit <- pp_refit(rain, 10, muinit = muinit, siginit = siginit,
                       shinit = shinit, show = FALSE)
  adj_rain_fit <- alogLik(rain_fit)
  summary(adj_rain_fit)

  # An example from chapter 7 of Coles (2001).
  # Code from demo ismev::wooster.temps
  data(wooster)
  x <- seq(along = wooster)
  usin <- function(x, a, b, d) {
    return(a + b * sin(((x - d) * 2 * pi) / 365.25))
  }
  wu <- usin(x, -30, 25, -75)
  ydat <- cbind(sin(2 * pi * x / 365.25), cos(2 * pi *x / 365.25))
  # Start from the mle to save time
  init <- c(-15.3454188, 9.6001844, 28.5493828, 0.5067104, 0.1023488,
            0.5129783, -0.3504231)
  muinit <- init[1:3]
  siginit <- init[4:6]
  shinit <- init[7]
  wooster.pp <- pp_refit(-wooster, threshold = wu, ydat = ydat, mul = 1:2,
                         sigl = 1:2, siglink = exp, method = "BFGS",
                         muinit = muinit, siginit = siginit, shinit = shinit,
                         show = FALSE)
  adj_pp_fit <- alogLik(wooster.pp)
  summary(adj_pp_fit)

  # r-largest order statistics model -----

  # An example based on the ismev::rlarg.fit() documentation
  vdata <- revdbayes::venice
  rfit <- rlarg.fit(vdata, muinit = 120.54, siginit = 12.78,
                    shinit = -0.1129, show = FALSE)
  adj_rfit <- alogLik(rfit)
  summary(adj_rfit)

  # \donttest{
  # Adapt this example to add a covariate
  set.seed(30102019)
  ydat <- matrix(runif(nrow(vdata)), nrow(vdata), 1)
  rfit2 <- rlarg_refit(vdata, ydat = ydat, mul = 1,
                       muinit = c(120.54, 0), siginit = 12.78,
                       shinit = -0.1129, show = FALSE)
  adj_rfit2 <- alogLik(rfit2)
  summary(adj_rfit2)
  # }
}
#> Loading required package: mgcv
#> Loading required package: nlme
#> This is mgcv 1.9-3. For overview type 'help("mgcv-package")'.
#>            MLE      SE adj. SE
#> loc   122.8000 1.77100 3.17100
#> loc1   -5.5400 2.65700 4.46100
#> scale  12.6500 0.53290 0.81270
#> shape  -0.1172 0.01948 0.02741