profilelogLik: Profile Likelihood

In georob: Robust Geostatistical Analysis of Spatial Data

Profile Likelihood

Description

The function profilelogLik computes for an array of fixed variogram parameters the profile log-likelihood by maximizing the (restricted) log-likelihood with respect to the remaining variogram parameters, the fixed and random effects.

Usage

  profilelogLik(object, values, use.fitted = TRUE, verbose = 0,
    ncores = min(parallel::detectCores(), NROW(values)))

Arguments

object	an object of class "georob" (mandatory argument), see georobObject.
values	a data.frame or a matrix with the values of the variogram and anisotropy parameters that should be kept fixed (mandatory argument, see georob and georobPackage for information about the parametrization of variogram models). The names of the columns of values must match the names of variogram and anisotropy parameters.
use.fitted	a logical scalar controlling whether the fitted variogram parameters of object should be used as initial values (default TRUE) when maximizing the profile log-likelihood or the initial values used to generate object.
verbose	a positive integer controlling logging of diagnostic messages to the console during model fitting, see georob.
ncores	a positive integer controlling how many cores are used for parallelized computations, see Details.

Details

For robust REML fits profilelogLik returns (possibly with a warning) the log-likelihood of the Gaussian (RE)ML fit of the equivalent Gaussian spatial linear model with heteroscedastic nugget.

Note that the data frame passed as data argument to georob must exist in the user workspace when calling profilelogLik.

profilelogLik uses the packages parallel and snowfall for parallelized computation of the profile likelihood. By default, the function uses NROW(values) CPUs but not more than are physically available (as returned by detectCores).

profilelogLik uses the function update to re-estimated the model with partly fixed variogram parameters. Therefore, any argument accepted by georob except data can be changed when re-fitting the model. Some of them (e.g. verbose) are explicit arguments of profilelogLik, but also the remaining ones can be passed by ... to the function.

Value

A data.frame with the columns of values, a column loglik (contains the maximized [restricted] log-likelihood), columns with the estimated variogram and fixed effect parameters, columns with the gradient of the (restricted) log-likelihood (or the roots of the estimating equations) and a column converged, indicating whether convergence has occurred when fitting the respective model.

Author(s)

Andreas Papritz [e-mail].

See Also

georobPackage for a description of the model and a brief summary of the algorithms;

georob for (robust) fitting of spatial linear models;

georobObject for a description of the class georob;

plot.georob for display of RE(ML) variogram estimates;

control.georob for controlling the behaviour of georob;

georobModelBuilding for stepwise building models of class georob;

cv.georob for assessing the goodness of a fit by georob;

georobMethods for further methods for the class georob;

predict.georob for computing robust Kriging predictions;

lgnpp for unbiased back-transformation of Kriging prediction of log-transformed data;

georobSimulation for simulating realizations of a Gaussian process from model fitted by georob; and finally

sample.variogram and fit.variogram.model for robust estimation and modelling of sample variograms.

Examples

## define number of cores for parallel computations
if(interactive()) ncpu <- 2L else ncpu <- 1L

data(meuse)

r.logzn.ml <- georob(log(zinc)~sqrt(dist), data=meuse, locations=~x+y,
    variogram.model="RMexp", param=c(variance=0.15, nugget=0.05, scale=200),
    tuning.psi=1000, control=control.georob(ml.method="ML"))

if(interactive()){
  ## example is run only in interactive session because cpu times exceeds 5 s
  r.prflik <- profilelogLik(r.logzn.ml, values=expand.grid(scale=seq(75, 600, by=25)),
      ncores = ncpu)

  plot(loglik~scale, r.prflik, type="l")
  abline(v=r.logzn.ml$variogram.object[[1]]$param["scale"], lty="dotted")
  abline(h=r.logzn.ml$loglik-0.5*qchisq(0.95, 1), lty="dotted")
}

georob documentation built on April 4, 2025, 2:11 a.m.