georobObject: Fitted georob Object

In georob: Robust Geostatistical Analysis of Spatial Data

Description

An object of class georob as returned by georob and representing a (robustly) fitted spatial linear model. Objects of this class have methods for cross-validation (see cv.georob), for computing (robust) kriging predictions (see predict.georob), for plotting (see plot.georob) and for common generic functions (see georobMethods).

Value

The following components are included in a georob object:

loglik	the maximized restricted Gaussian loglikelihood of a non-robust REML fit or NA for a robust fit if tuning.psi is less than 1000.
variogram.model	the name of the fitted parametric variogram model.
param	a named numeric vector with the (estimated) variogram parameters.
aniso	a list with the following components: isotropic: logical indicating whether an isotropic variogram was fitted. aniso: a named numeric vector with the (estimated) anisotropy parameters. sincos: a list with sin and cos of the angles ω, φ and ζ that define the orientation of the anisotropy ellipsoid. rotmat: the matrix (C_1, C_2, C_3) (see georobIntro). sclmat: a vector with the elements 1, 1/f_1, 1/f_2 (see georobIntro).
gradient	a named numeric vector with the estimating equations (robust REML) evaluated at the solution or the gradient of the maximized restricted loglikelihood (Gaussian REML).
psi.func	the name of the parametric psi.function used for the robust model fit (see georob.control).
tuning.psi	the value of the tuning constant c of the ψ_c-function.
coefficients	a named vector with the estimated regression coefficients.
fitted.values	a named vector with the fitted values of the external drift X hatβ.
bhat	a named vector with the predicted spatial random effects hatB at the data locations.
residuals	a named vector with the residuals hatε=Y-X hatβ - hatB.
rweights	a named numeric vector with the “robustness weights” ψ(hatε_i/hatτ) / (hatε_i/hatτ).
converged	logical indicating whether numerical maximization of the restricted loglikelihood by optim or root finding by nleqslv converged.
convergence.code	a diagnostic integer issued by optim (component convergence) or nleqslv (component termcd) about convergence.
iter	a named integer vector of length two, indicating either the number of function and gradient evaluations when maximizing the restricted Gaussian loglikelihood by optim, or the number of function and Jacobian evaluations when solving the robustified estimating equations by nleqslv.
Tmat	the compressed design matrix for replicated observations at coincident locations (integer vector that contains for each observation the row index of the respective unique location).
cov	a list with covariance matrices (or diagonal variance vectors). Covariance matrices are stored in compressed form (see compress) and can be expanded to square matrices by expand. What cov actually contains depends on the flags passed to georob for computing covariances (see georob.control). Possible components are: cov.bhat: the covariances of hatB. cov.betahat: the covariances of hatβ. cov.bhat.betahat: the covariances of hatB and hatβ. cov.delta.bhat: the covariances of B-hatB. cov.delta.bhat.betahat: the covariances of B-hatB and hatβ. cov.ehat: the covariances of hatε=Y-X hatβ - hatB. cov.ehat.p.bhat: the covariances of hatε+ hatB=Y-X hatβ. aux.cov.pred.target: a covariance term required for the back-trans- formation of kriging predictions of log-transformed data.
param.tf	a character vector indicating the transformations of the variogram parameters for model fitting.
fwd.tf	a list of functions for variogram parameter transformations.
bwd.tf	a list of inverse functions for inverse variogram parameter transformations.
hessian	a symmetric matrix giving an estimate of the Hessian at the solution if the model was fitted non-robustly with the argument hessian = TRUE (see georob.control). Missing otherwise.
expectations	a named numeric vector with the expectations of dψ_c'(x)/dx (dpsi) and ψ_c^2(x) (psi2) with respect to a standard normal distribution.
Valpha.objects	a list of matrices in compressed form with the components: Valpha.inverse: the inverse of V_α. Valpha.ilcf: the inverse of the lower triangular factor L of the Cholesky decomposition V_α=L L^T. Valpha.ucf: the upper triangular Cholesky factor L^T. gcr.constant: the constant γ_0 (see expression for Valpha in section Model of georobIntro.
locations.object	a list with 2 components: locations: a formula indicating the coordinates of the measurement locations. locations.coords: a numeric matrix with the coordinates of the measurement locations.
initial.objects	a list with 5 components: coefficients: initial estimates of β computed either by lmrob or rq. bhat: initial predictions of B. param: numeric vector with initial estimates of the variogram parameters, either computed (initial.param = TRUE) or as passed to georob (initial.param = FALSE). fit.param: logical vector indicating which variogram parameters were fitted. aniso: numeric vector with initial estimates of the anisotropy parameters, either either computed (initial.param = TRUE) or as passed to georob (initial.param = FALSE). fit.aniso: logical vector indicating which anisotropy parameters were fitted. initial.param: logical flag indicating whether robust initial variogram parameter estimates were computed (see georob, Details).
MD	optionally a matrix of robust distances in the space spanned by X (see argument compute.rd of lmrob.control and georob.control).
model, x, y	if requested the model frame, the model matrix and the response, respectively.
na.action, offset, contrasts, xlevels, rank, df.residual, call, terms	further components of the fit as described for an object of class lm.

Author(s)

Andreas Papritz [e-mail]

See Also

georobIntro for a description of the model and a brief summary of the algorithms; georob for (robust) fitting of spatial linear models; georob.control for controlling the behaviour of georob; plot.georob for display of REML variogram estimates; cv.georob for assessing the goodness of a fit by georob; predict.georob for computing robust kriging predictions; and finally georobModelBuilding for stepwise building models of class georob; georobMethods for further methods for the class georob.

georob documentation built on May 2, 2019, 6:53 p.m.