This page documents parameters used to control georob. It
describes the arguments of the functions control.georob,
param.transf, fwd.transf, dfwd.transf,
bwd.transf, control.rq, control.nleqslv,
control.nlminb and control.optim, which all serve to
control the behaviour of georob.
character keyword defining whether non-robust maximum
likelihood (ML) or restricted maximum likelihood (REML
default) estimates will be computed (ignored if
tuning.psi <= tuning.psi.nr).
reparam
logical. If TRUE (default) the reparametrized
variance parameters σ_Z^2, η and ξ are
estimated by Gaussian (RE)ML, otherwise the original parameters
τ^2, σ_n^2 and σ^2
(cf. subsection Estimating variance parameters by Gaussian
(RE)ML, section Details of georob).
maximizer
character keyword defining the Gaussian (restricted)
loglikelihood is maximized by nlminb (default) or
optim.
initial.param
logical, controlling whether initial values of
variogram parameters are computed for solving the estimating equations of
the variogram and anisotropy parameters. If initial.param = TRUE
(default) robust initial values of parameters are computed by discarding
outlying observations based on the “robustness weights” of the
initial fit of the regression model by lmrob
and fitting the spatial linear model by Gaussian REML to the pruned data
set. For initial.param = FALSE no initial parameter values are
computed and the estimating equations are solved with the initial values
passed by param and aniso to georob (see
Details of georob.
initial.fixef
character keyword defining whether the function
lmrob or rq is used to
compute robust initial estimates of the regression parameters
β (default "lmrob").
If the fixed effects model matrix has not full columns rank, then
lm is used to compute initial values of the
regression coefficients.
bhat
initial values for the spatial random effects
hatB, with
hatB=0
if bhat is equal to NULL (default).
min.rweight
positive numeric. “Robustness weight” of
the initial lmrob fit that observations must
exceed to be used for computing robust initial estimates of variogram
parameters by setting initial.param = TRUE (see
georob; default 0.25).
param.tf
a function such as param.transf, which returns a
named vector of character strings that define the transformations to be
applied to the variogram parameters for model fitting, see
Details.
fwd.tf
a function such as fwd.transf, which returns a named
list of invertible functions to be used to transform variogram
parameters, see Details.
deriv.fwd.tf
a function such as dfwd.transf, which
returns a named list of functions corresponding to the first derivatives
of fwd.tf, see Details.
bwd.tf
a function such as bwd.transf, which returns the
named list of inverse functions corresponding to fwd.tf, see
Details.
safe.param
maximum acceptable value for any variogram parameter.
If trial parameter values generated by nlminboptim or nleqslv exceed
safe.param then an error is signalled to force optim or
nleqslv to update the trial values (default 1.e12).
psi.func
character keyword defining what ψ_c-function should be
used for robust model fitting. Possible values are "logistic" (a
scaled and shifted logistic cdf, default), "t.dist" (re-descending
ψ_c-function associated with Student t-distribution with
c degrees of freedom) and "huber" (Huber's
ψ_c-function).
tuning.psi.nr
positive numeric. If tuning.psi is less than
tuning.psi.nr then the model is fitted robustly by solving the
robustified estimating equations, and for tuning.psi equal to or
larger than tuning.psi.nr the Gaussian (restricted) loglikelihood is
maximized (default 1000).
irwls.initial
logical. If TRUE (default) the estimating
equations of B and
β are always solved by
IRWLS from the initial estimates of
hatB and
hatβ. If
FALSE then IRWLS starts from respective estimates computed for the
variogram parameter estimates of the previous iteration of nleqslv
or optim.
irwls.maxiter
positive integer equal to the maximum number of
IRWLS iterations to solve the estimating equations of
B and
β (default 50).
irwls.ftol
numeric convergence criterion for IRWLS. Convergence is
assumed if the objective function changes in one IRWLS iteration does not
exceed ftol.
force.gradient
logical controlling whether the estimating
equations or the gradient of the Gaussian restricted loglikelihood are
evaluated even if all variogram parameters are fixed (default
FALSE).
min.condnum
positive numeric. Minimum acceptable ratio of smallest to
largest singular value of the model matrix
X (default 1.e-12).
zero.dist
positive numeric equal to the maximum distance, separating two
sampling locations that are still considered as being coincident.
error.family.estimation
character keyword, defining the
probability distribution for varepsilon (default:
"gaussian") that is used to approximate the covariance of
hatB, see
Details.
error.family.cov.effects
character keyword, defining the
probability distribution for varepsilon (default:
"gaussian") that is used to approximate the covariances of
hatβ,
hatB and
B-hatB,
see Details.
error.family.cov.residuals
character keyword, defining the
probability distribution for varepsilon (default:
"long.tailed") that is used to approximate the covariances of
hatε=Y-X hatβ -
hatB and hatε+ hatB=Y-X
hatβ, see Details.
cov.bhat
logical controlling whether the covariances of
hatB are returned by
georob (default FALSE).
full.cov.bhat
logical controlling whether the full covariance
matrix (TRUE) or only the variance vector of
hatB is returned (default
FALSE).
cov.betahat
logical controlling whether the covariance matrix of
hatβ is returned
(default TRUE).
cov.bhat.betahat
logical controlling whether the covariance matrix
of hatB and
hatβ is returned
(default FALSE).
cov.delta.bhat
logical controlling whether the covariances of
B-hatB are returned (default TRUE).
full.cov.delta.bhat
logical controlling whether the full covariance
matrix (TRUE) or only the variance vector of
B-hatB is returned (default TRUE).
cov.delta.bhat.betahat
logical controlling whether the covariance
matrix of B-hatB and
hatβ is returned
(default TRUE).
cov.ehat
logical controlling whether the covariances of
hatε=Y-X hatβ -
hatB are returned (default TRUE).
full.cov.ehat
logical controlling whether the full covariance
matrix (TRUE) or only the variance vector of
hatε=Y-X hatβ -
hatB is returned (default FALSE).
cov.ehat.p.bhat
logical controlling whether the covariances of
hatε+ hatB=Y-X
hatβ are returned (default FALSE).
full.cov.ehat.p.bhat
logical controlling whether the full
covariance matrix (TRUE) or only the variance vector
of hatε+ hatB=Y-X
hatβ is returned (default FALSE).
aux.cov.pred.target
logical controlling whether a covariance term
required for the back-transformation of kriging predictions of
log-transformed data is returned (default FALSE).
hessian
logical scalar controlling whether for Gaussian (RE)ML the
Hessian should be computed at the MLEs.
rq
a list of arguments passed to rq or a function such as
control.rq that generates such a list (see
rq for allowed arguments).
lmrob
a list of arguments passed to the control argument of
lmrob or a function such as
lmrob.control that generates such a list (see
lmrob.control for allowed arguments).
nleqslv
a list of arguments passed to
nleqslv or a function such as
control.nleqslv that generates such a list (see
nleqslv for allowed arguments).
nlminb
a list of arguments passed to nlminb
or a function such as control.nlminb that generates such a list
(see nlminb for allowed arguments).
optim
a list of arguments passed to optim or a function
such as control.optim that generates such a list (see
optim for allowed arguments).
pmm
a list of arguments, passed e.g. to pmm or a
function such as control.pmm that generates such a list
(see control.pmm for allowed arguments).
...
for fwd.transf, dfwd.transf and
bwd.transf a named vectors of functions, extending the definition
of transformations for variogram parameters (see Details).
arguments passed to related arguments of
nleqslv, nlminb and
optim, respectively.
Details
Parameter transformations
The arguments param.tf, fwd.tf, deriv.fwd.tf,
bwd.tf define the transformations of the variogram parameters for
RE(ML) estimation. Implemented are currently "log",
"logit1", "logit2", "logit3" (various variants of
logit-transformation, see code of function fwd.transf) and "identity" (= no)
transformations. These are the possible values that the many arguments
of the function param.transf accept (as quoted character strings)
and these are the names of the list components returned by
fwd.transf, dfwd.transf and bwd.transf. Additional
transformations can be implemented by:
Extending the function definitions by arguments like
fwd.tf = fwd.transf(c(my.fun = function(x) your transformation)), deriv.fwd.tf = dfwd.transf(c(my.fun = function(x) your derivative)), bwd.tf = bwd.transf(c(my.fun = function(x) your back-transformation)),
Assigning to a given argument of param.transf the name of
the new function, e.g. variance = "my.fun".
Note the values given for the arguments of param.transf must match
the names of the functions returned by fwd.transf,
dfwd.transf and bwd.transf.
Approximation of covariances of fixed and random efffects and
residuals
The robustified estimating equations of robust REML depend on the
covariances of hatB.
These covariances (and the covariances of
B-hatB,
hatβ,
hatε,
hatε+ hatB) are
approximated by expressions that in turn depend on the variances of
varepsilon, ψ(varepsilon/τ) and the expectation of
ψ'(varepsilon/τ) (= partial / partial varepsilon
ψ(varepsilon/τ)). The arguments
error.family.estimation, error.family.cov.effects and
error.family.cov.residuals control what parametric distribution
for varepsilon is used to compute the latter quantities.
Possible options are: "gaussian" or "long.tailed". In the
latter case the pdf of varepsilon is assumed to be proportional
to 1/τ exp(-ρ(varepsilon/τ)) where ψ(x)=ρ'(x).
georobIntro 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;
predict.georob for computing robust kriging predictions; and finally
georobMethods for further methods for the class georob.
providing 
.