An object of class georob as returned by georob and
representing a (robustly) fitted spatial linear model. Objects of this
class have methods for model building (see
georobModelBuilding) and 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).
A georob object is a list with following components:
the maximized (restricted) Gaussian log-likelihood of a
non-robust (RE)ML fit or NA for a robust fit if
tuning.psi is less than tuning.psi.nr.
the estimated parameters of a possibly nested variograms model. This is a list that contains for each variogram model structure the following components:
variogram.model: the name of the fitted parametric variogram
model.
param: a named numeric vector with the (estimated) variogram
parameters.
fit.param: a named logical vector with the flags defining what
variogram parameters were estimated.
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 \(\omega\), \(\phi\) and \(\zeta\) that define the
orientation of the anisotropy ellipsoid.
rotmat: the matrix
\((\mbox{\boldmath$C$\unboldmath}_1,
\mbox{\boldmath$C$\unboldmath}_2,
\mbox{\boldmath$C$\unboldmath}_3)\) (see
georobIntro).
sclmat: a vector with the elements 1, \(1/f_1\),
\(1/f_2\) (see georobIntro).
a named numeric vector with the estimating equations (robust REML) or the gradient of the maximized (restricted) log-likelihood (Gaussian (RE)ML) evaluated at the solution .
the value of the tuning constant \(c\) of the \(\psi_c\)-function.
a named vector with the estimated regression coefficients.
a named vector with the fitted values of the external drift \(\mbox{\boldmath$X$\unboldmath}\widehat{\mbox{\boldmath$\beta$\unboldmath}}\).
a named vector with the predicted spatial random effects \(\widehat{\mbox{\boldmath$B$\unboldmath}}\) at the data locations.
a named vector with the residuals \(\widehat{\mbox{\boldmath$\varepsilon$\unboldmath}}=\mbox{\boldmath$Y$\unboldmath} - \mbox{\boldmath$X$\unboldmath} \widehat{\mbox{\boldmath$\beta$\unboldmath}} - \widehat{\mbox{\boldmath$B$\unboldmath}}\).
a named numeric vector with the “robustness weights” \(\psi(\widehat{\varepsilon}_i/\widehat{\tau}) / (\widehat{\varepsilon}_i/\widehat{\tau})\).
logical indicating whether numerical maximization of
the (restricted) log-likelihood by nlminb or optim or root
finding by nleqslv converged.
a diagnostic integer issued by
nlminb, optim (component
convergence) or nleqslv (component
termcd) about convergence.
a named integer vector of length two, indicating either
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).
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
control.georob). Possible components are:
cov.bhat: the covariances of
\(\widehat{\mbox{\boldmath$B$\unboldmath}}\).
cov.betahat: the covariances of
\(\widehat{\mbox{\boldmath$\beta$\unboldmath}}\).
cov.delta.bhat: the covariances of
\(\mbox{\boldmath$B$\unboldmath}- \widehat{\mbox{\boldmath$B$\unboldmath}}\).
cov.delta.bhat.betahat: the covariances of
\(\mbox{\boldmath$B$\unboldmath}- \widehat{\mbox{\boldmath$B$\unboldmath}}\)
and
\(\widehat{\mbox{\boldmath$\beta$\unboldmath}}\).
cov.ehat: the covariances of
\(\widehat{\mbox{\boldmath$\varepsilon$\unboldmath}}=\mbox{\boldmath$Y$\unboldmath} -
\mbox{\boldmath$X$\unboldmath} \widehat{\mbox{\boldmath$\beta$\unboldmath}} -
\widehat{\mbox{\boldmath$B$\unboldmath}}\).
cov.ehat.p.bhat: the covariances of
\(\widehat{\mbox{\boldmath$\varepsilon$\unboldmath}} +
\widehat{\mbox{\boldmath$B$\unboldmath}}
=\mbox{\boldmath$Y$\unboldmath} -
\mbox{\boldmath$X$\unboldmath} \widehat{\mbox{\boldmath$\beta$\unboldmath}}\).
cov.pred.target: a covariance term required for the
back-trans- formation of Kriging predictions of log-transformed data.
a named numeric vector with the expectations of
\(\partial \psi_c(x)/\partial x\) (dpsi) and
\(\psi_c^2(x)\) (psi2) with respect to a standard normal
distribution (exp.gauss) and the long-tailed distribution of
\(\varepsilon\) (exp.f0) implied by the choice of the
\(\psi_c\)-function.
a list of matrices in compressed form with (among others) the following components:
Valpha: a list with the (generalized) correlation
matrices (Valpha) of the nested variogram models structures
along with the constants (gcr.constant) added to the respective
semivariances matrices.
Valphaxi: the (generalized) correlation matrix
\(\mbox{\boldmath$V$\unboldmath}_{\alpha,\xi} =
\mbox{\boldmath$\Gamma$\unboldmath}_{\alpha,\xi} /
(\sigma_{\mathrm{n}}^2+\sigma^2 )\) that includes the spatial nugget effect.
Valphaxi.inverse: the inverse of
\(\mbox{\boldmath$V$\unboldmath}_{\alpha,\xi}\).
log.det.Valphaxi:
\(\log(\det(\mbox{\boldmath$V$\unboldmath}_{\alpha,\xi}))\).
a list of matrices in (partly) compressed form with the following components:
Aalphaxi: the matrix
\((\mbox{\boldmath$X$\unboldmath}^T
\mbox{\boldmath$V$\unboldmath}_{\alpha,\xi}^{-1}\mbox{\boldmath$X$\unboldmath})^{-1}
\mbox{\boldmath$X$\unboldmath}^T\mbox{\boldmath$V$\unboldmath}_{\alpha,\xi}^{-1}
\).
Palphaxi: the matrix
\(\mbox{\boldmath$I$\unboldmath}-
\mbox{\boldmath$X$\unboldmath} \mbox{\boldmath$A$\unboldmath}_{\alpha,\xi}
\).
Valphaxi.inverse.Palphaxi: the matrix
\(\mbox{\boldmath$V$\unboldmath}^{-1}_{\alpha,\xi}
\mbox{\boldmath$P$\unboldmath}_{\alpha,\xi} \).
a list with 3 components:
locations: a formula indicating the coordinates of the
measurement locations.
locations.coords: a numeric matrix with the coordinates
of the measurement locations.
lag.vectors: a numeric matrix with the lag vectors
between any distinct pairs of measurement locations.
a list with 3 components:
coefficients: initial estimates of
\(\mbox{\boldmath$\beta$\unboldmath}\) computed either by
lmrob or rq.
bhat: initial predictions of
\(\mbox{\boldmath$B$\unboldmath}\).
variogram.object: the initial values of the parameters of a
possibly nested variograms model. This is a list with the same
structure as described above for the component
variogram.object.
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 control.georob). Missing
otherwise.
a list with control parameters generated by
control.georob.
optionally a matrix of robust distances in the space spanned by
\(\mbox{\boldmath$X$\unboldmath}\) (see argument compute.rd
of lmrob.control and
control.georob).
if requested the model frame, the model matrix and the response, respectively.
na.action, offset, contrasts, xlevels,
rank, df.residual, call, termsfurther
components of the fit as described for an object of class
lm.
georobIntro for a description of the model and a brief summary of the algorithms;
georob for (robust) fitting of spatial linear models;
control.georob for controlling the behaviour of georob;
plot.georob for display of (RE)ML 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.