georobObject: Fitted georob Object
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 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). Value
A georob object is a list with following components:- loglik
- the maximized (restricted) Gaussian loglikelihood of a
non-robust (RE)ML fit or
NA for a robust fit if
tuning.psi is less than tuning.psi.nr. - 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 $\omega$, $\phi$ and $\zeta$ 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) or the gradient of the maximized (restricted) loglikelihood
(Gaussian (RE)ML) evaluated at the solution .
- tuning.psi
- the value of the tuning constant $c$ of the
$\psi_c$-function.
- coefficients
- a named vector with the estimated regression coefficients.
- fitted.values
- a named vector with the fitted values of the
external drift
$X
hat\beta$.
- bhat
- a named vector with the predicted spatial random effects
$hatB$ at the data locations.
- residuals
- a named vector with the residuals
$hat\epsilon=Y-X hat\beta - hatB$.
- rweights
- a named numeric vector with the “robustness weights”
$
\psi(hat\epsilon_i/hat\tau) / (hat\epsilon_i/hat\tau)$.
- converged
- logical indicating whether numerical maximization of
the (restricted) loglikelihood by
nlminb or optim or root
finding by nleqslv converged. - convergence.code
- a diagnostic integer issued by
nlminb, 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
nlminb
or 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
control.georob). Possible components are:
-
cov.bhat: the covariances of
$hatB$.
-
cov.betahat: the covariances of
$hat\beta$.
-
cov.bhat.betahat: the covariances of
$hatB$ and
$hat\beta$.
-
cov.delta.bhat: the covariances of
$B-hatB$.
-
cov.delta.bhat.betahat: the covariances of
$B-hatB$
and
$hat\beta$.
-
cov.ehat: the covariances of
$hat\epsilon=Y-X hat\beta - hatB$.
-
cov.ehat.p.bhat: the covariances of
$hat\epsilon+ hatB=Y-X hat\beta$.
-
cov.pred.target: a covariance term required for the
back-trans- formation of kriging predictions of log-transformed data.
- expectations
- a named numeric vector with the expectations of
$d\psi_c'(x)/dx$ (
dpsi) and
$\psi_c^2(x)$ (psi2) with respect to a standard normal
distribution. - Valphaxi.objects
- a list of matrices in compressed form with
(among others) the following components:
-
gcr.constant: the constant $\gamma_0$ (see
expression for $V_{\alpha,\xi}$ in
section Model of georobIntro).
-
Valphaxi: the correlation matrix
$V_{\alpha, \xi} = \Gamma_\theta /
(\sigma_n^2+\sigma^2)$ that includes the spatial nugget effect.
-
Valphaxi.inverse: the inverse of
$V_{\alpha, \xi}$.
-
log.det.Valphaxi:
$log(det(V_{\alpha, \xi}))$.
- zhat.objects
- a list of matrices in (partly) compressed form with
the following components:
-
Aalphaxi: the matrix
$(X^T V_{\alpha, \xi}^-1 X)^-1 X^T V_{\alpha, \xi}^-1 $.
-
Palphaxi: the matrix
$I - X A_{\alpha, \xi}$.
-
Valphaxi.inverse.Palphaxi: the matrix
$V^-1_{\alpha, \xi}
P_{\alpha, \xi}$.
- locations.object
- 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.
- initial.objects
- a list with 5 components:
-
coefficients: initial estimates of
$\beta$ 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.
- 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 control.georob). Missing
otherwise. - control
- a list with control parameters generated by
control.georob. - MD
- optionally a matrix of robust distances in the space spanned by
$X$ (see argument
compute.rd
of lmrob.control and
control.georob). - 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.
See Also
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.