R: Predict Method for Robustly Fitted Spatial Linear Models
predict.georob
R Documentation
Predict Method for Robustly Fitted Spatial Linear Models
Description
Robust and customary external drift kriging prediction
based on a spatial linear models fitted by georob. The
predict method for the class georob computes fitted values, point
and block kriging predictions as
well as model terms for display by termplot.
an optional data frame,
SpatialPointsDataFrame,
SpatialPixelsDataFrame,
SpatialGridDataFrame or
SpatialPolygonsDataFrame in which to look for variables
with which to compute fitted values or kriging predictions. If
newdata is a SpatialPolygonsDataFrame then
block kriging predictions are computed, otherwise point kriging
predictions.
type
character keyword defining what target quantity should be
predicted (computed). Possible values are
"signal": the “signal”
Y(s) = x(s)^T β + B(s) of
the process (default),
"response": the observations
Y(s)=Z(s) + ε(s),
"trend": the external drift
x(s)^T β,
"terms": the model terms.
terms
If type = "terms", which terms (default is all terms).
se.fit
logical, only used if type is equal to
"terms", see predict.lm.
signif
positive numeric equal to the tolerance or confidence level
for computing respective intervals. If NULL no intervals are
computed.
locations
an optional one-sided formula specifying what variables
of newdata are the coordinates of the prediction points
(default: object[["locatons.objects"]]$locations).
control
a list with the arguments full.covmat,
extended.output, mmax, ncores, pwidth,
pheight, napp and pmm or a function such as
control.predict.georob that generates such a list.
full.covmat
logical controlling whether the full covariance matrix
of the prediction errors is returned (TRUE) or only the vector
with its diagonal elements (FALSE, default), see Value for
an explanation of the effect of full.covmat.
extended.output
logical controlling whether the covariance
matrices of the kriging predictions and of the data should be computed, see
Details (default FALSE).
mmax
integer equal to the maximum number (default 10000) of
prediction items, computed in a sub-task, see Details.
ncores
positive integer controlling how many cores are used for
parallelized computations, see Details.
pwidth, pheight, napp
numeric scalars, used to tune numeric
integration of semivariances for block kriging, see
preCKrige.
pmm
a list of arguments passed to pmm or a
function such as control.pmm that generates such a list
(see control.pmm for allowed arguments).
verbose
positive integer controlling logging of diagnostic
messages to the console. verbose = 0 (default) largely suppresses
such messages.
...
arguments passed to control.predict.georob.
Details
The predict method for class georob uses the package
parallel for parallelized computation of kriging predictions. If
there are m items to predict, the task is split into
ceiling(m/mmax) sub-tasks that are then distributed to
ncores CPUs. Evidently, ncores = 1 suppresses parallel
execution. By default, the function uses all available CPUs as returned
by detectCores. Note that if
full.covmat is TRUEmmax must exceed m (and parallel
execution is not possible).
The argument extended.output = TRUE is used to compute all
quantities required for (approximately) unbiased back-transformation of
kriging predictions of log-transformed data to the original scale of the
measurements by lgnpp. In more detail, the following items
are computed:
trend: the fitted values,
x(s)^T hatβ,
var.pred: the variances of the kriging predictions,
Var[hatY(s)] or
Var[hatS(s)],
cov.pred.target: the covariances between the predictions and the
prediction targets, Cov[hatY(s),Y(s)] or
Cov[hatS(s),Z(s)],
var.target: the variances of the prediction targets
Var[Y(s)] or
Var[Z(s)].
Note that the component var.pred is also present if
type is equal to "trend", irrespective of the choice for extended.output.
This component contains then the variances of the fitted values.
Value
If type is equal to "terms" then a vector, a matrix, or a
list with prediction results along with bounds and standard errors, see
predict.lm. Otherwise, the structure and contents
of the output generated by predict.georob are determined by the
class of newdata and the logical flags full.covmat and
extended.output:
If full.covmat is FALSE then the result is an object of the same
class as newdata (data frame,
SpatialPointsDataFrame,
SpatialPixelsDataFrameSpatialGridDataFrame, SpatialPolygonsDataFrame). The data frame or the
data slot of the Spatial...DataFrame objects
have the following components:
the coordinates of the prediction points (only present if
newdata is a data frame).
pred: the kriging predictions (or fitted values).
se: the root mean squared prediction errors (kriging
standard errors).
lower, upper: the limits of tolerance/confidence
intervals,
trend, var.pred, cov.pred.target,
var.target: only present if extended.output is TRUE,
see Details.
If full.covmat is TRUE then predict.georob returns a list
with the following components:
pred: a data frame or a Spatial...DataFrame object
as described above for full.covmat = FALSE.
mse.pred: the full covariance matrix of the prediction errors,
Y(s)-hatY(s) or
s(s)-hatS(s)
see Details.
var.pred: the full covariance matrix of the
kriging predictions, see Details.
cov.pred.target: the full covariance matrix of the
predictions and the prediction targets, see Details.
var.target: the full covariance matrix of the
prediction targets, see Details.
Nussbaum, M., Papritz, A., Baltensweiler, A. and Walthert, L. (2012)
Organic Carbon Stocks of Swiss Forest Soils,
Institute of Terrestrial Ecosystems, ETH Zurich and
Swiss Federal Institute for Forest, Snow and Landscape Research
(WSL), pp. 51.
http://e-collection.library.ethz.ch/eserv/eth:6027/eth-6027-01.pdf
KŸnsch, H. R., Papritz, A., Schwierz, C. and Stahel, W. A. (2011) Robust
estimation of the external drift and the variogram of spatial data.
Proceedings of the ISI 58th World Statistics Congress of the International
Statistical Institute.
http://e-collection.library.ethz.ch/eserv/eth:7080/eth-7080-01.pdf
See Also
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.
Examples
## Not run:
data(meuse)
data(meuse.grid)
coordinates(meuse.grid) <- ~x+y
meuse.grid.pixdf <- meuse.grid
gridded(meuse.grid.pixdf) <- TRUE
library(constrainedKriging)
data(meuse.blocks)
r.logzn.rob <- 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 = 1., control = control.georob(cov.bhat = TRUE, full.cov.bhat = TRUE,
cov.bhat.betahat = TRUE, aux.cov.pred.target = TRUE))
## point predictions of log(Zn)
r.pred.points <- predict(r.logzn.rob, newdata = meuse.grid.pixdf,
control = control.predict.georob(extended.output = TRUE, full.covmat = TRUE))
str(r.pred.points$pred@data)
## back-transformation of point predictions
r.backtf.pred.points <- lgnpp(r.pred.points)
str(r.pred.points$pred@data)
spplot(r.backtf.pred.points[["pred"]], zcol = "lgn.pred", main = "Zn content")
## predicting mean Zn content for whole area
r.block <- lgnpp(r.pred.points, is.block = TRUE, all.pred = r.backtf.pred.points[["pred"]])
r.block
## block predictions of log(Zn)
r.pred.block <- predict(r.logzn.rob, newdata = meuse.blocks,
control = control.predict.georob(extended.output = TRUE,
pwidth = 75, pheight = 75))
r.backtf.pred.block <- lgnpp(r.pred.block, newdata = meuse.grid)
spplot(r.backtf.pred.block, zcol = "lgn.pred", main = "block means Zn content")
## End(Not run)
providing 
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