Description Usage Arguments Details Value Author(s) See Also Examples
The function estimates the prediction variances by a cross-validation approach (see vignette) applied to each sample means of the involved statistics.
1 2 |
qsd |
object of class |
cvm |
list of prefitted covariance models from function |
theta |
optional, default |
type |
name of prediction variance measure |
cl |
cluster object, |
Other than the kriging prediction variance, which solely depends on interdistances of sample points
and estimated covariance parameters of some assumed to be known spatial covariance structure, the cross-validation
based approach (see [4] and the vignette) even takes into account the predicted values at 'theta
' and thus can be seen as a more robust
measure of variability between different spatial locations. By default, 'theta
' equals the current sampling set
stored in the object 'qsd
'.
If we set the error 'type
' equal to "cve
", the impact on the level of accuracy (predicting at unsampled
points) is measured by the delete-k jackknifed variance of prediction errors. This approach does not require further
simulations as a measure of uncertainty for predicting the sample means of statistics at new candidate points accross the parameter space.
Note that if the attribute attr(cvm,"type")
equals "max
", then the maximum of kriging and CV-based prediction
variances is returned.
In addition, other measures of prediction uncertainty are available, such as the root mean square deviation
(rmsd
) and mean square deviation (msd
) or the standardized cross-validation error
(scve
). The details are explained in the vignette. In order to assess the predictive quality of possibly
different covariance structures (also depending on the initial sample size), including the comparison of different
sizes of initial sampling designs, the following measures [8] are
also available for covariance model validation and adapted to the cross-validation approach here by using an
average cross-validation error (acve
), the mean square error (mse
) or the
average standardized cross-validation error (ascve
). These last measures can only be computed in case the total number
of sample points equals the number of leave-one-out covariance models. This requires to fit each cross-validation
covariance model by prefitCV
using the option 'reduce
'=FALSE
which is then based on exactly
one left out point. Also, we can calculate the kriging variance at the left-out sample points if we set the option 'type
'
equal to "sigK
".
A matrix of estimated prediction variances for each point given by the argument theta
(rows)
and for each statistic (columns).
M. Baaske
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | data(normal)
# design matrix and statistics
X <- as.matrix(qsd$qldata[,1:2])
Tstat <- qsd$qldata[grep("^mean.",names(qsd$qldata))]
# construct but do not re-estimate
# covariance parameters by REML for CV models
qsd$cv.fit <- FALSE
cvm <- prefitCV(qsd)
theta0 <- c("mu"=2,"sd"=1)
# get mean squared deviation using cross-validation at theta0
crossValTx(qsd, cvm, theta0, type = "msd")
# and kriging variance
varKM(qsd$covT,theta0,X,Tstat)
|
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.