georob (version 0.2-3)

cv.georob: Cross-Validating a Spatial Linear Model Fitted by georob

Description

This function assesses the goodness-of-fit of a spatial linear model by K-fold cross-validation. In more detail, the model is re-fitted K times by robust (or Gaussian) (RE)ML, excluding each time 1/Kth of the data. The re-fitted models are used to compute robust (or customary) external kriging predictions for the omitted observations. If the response variable is log-transformed then the kriging predictions can be optionally transformed back to the orginal scale of the measurements. S3methods for evaluating and plotting diagnostic summaries of the cross-validation errors are decribed for the function validate.predictions.

Usage

## S3 method for class 'georob':
cv(object, formula = NULL, subset = NULL, 
    method = c("block", "random"), nset = 10, 
    seed = NULL, sets = NULL, duplicates.in.same.set = TRUE, 
    re.estimate = TRUE, param = object[["param"]], 
    fit.param = object[["initial.objects"]][["fit.param"]],
    aniso = object[["aniso"]][["aniso"]], 
    fit.aniso = object[["initial.objects"]][["fit.aniso"]],
    return.fit = FALSE, reduced.output = TRUE, lgn = FALSE, 
    mfl.action = c("offset", "stop"),
    ncores = min(nset, detectCores()), verbose = 0, ...)

Arguments

object

an object of class of "georob", see georobObject.

formula

an optional formula for the regression model passed by update to georob, see Details.

subset

an optional vector specifying a subset of observations to be used in the fitting process, see Details.

method

keyword, controlling whether subsets are formed by partitioning data set into blocks by kmeans (default) or randomly. Ignored if sets is non-NULL

nset

positive integer defining the number K of subsets into which the data set is partitioned (default: nset = 10). Ignored if sets is non-NULL.

seed

optional integer seed to initialize random number generation, see set.seed. Ignored if sets is non-NULL.

sets

an optional vector of the same length as the response vector of the fitted model and with positive integers taking values in $(1,2,\ldots,K)$, defining in this way the $K$ subsets into which the data set is split. If sets = NULL (defau

duplicates.in.same.set

logical controlling whether replicated observations at a given location are assigned to the same subset when partitioning the data (default TRUE).

re.estimate

logical controlling whether the model is re-fitted to the reduced data sets before computing the kriging predictions (TRUE, default) or whether the model passed in object is used to compute the predictions for the omitted o

param

an optional named numeric vector or a matrix or data frame with variogram parameters passed by update to georob, see Details. If param

fit.param

an optional named logical vector or a matrix or data frame defining which variogram parameters should be adjusted when passed by update to georob, see

aniso

an optional named numeric vector or a matrix or data frame with anisotropy parameters passed by update to georob, see Details. If anis

fit.aniso

an optional named logical vector or a matrix or data frame defining which anisotropy parameters should be adjusted when passed by update to georob, se

return.fit

logical controlling whether information about the fit should be returned when re-estimating the model with the reduced data sets (default FALSE).

reduced.output

logical controlling whether the complete fitted model objects, fitted to the reduced data sets, are returned (FALSE) or only some components (TRUE, default, see Value). Ignored if return.fit = FALSE.

lgn

logical controlling whether kriging predictions of a log-transformed response should be transformed back to the original scale of the measurements (default FALSE).

mfl.action

character controlling what is done when some levels of factor(s) are not present in any of the subsets used to fit the model. The function either stops ("stop") or treats the respective factors as model offset ("offset", de

ncores

positive integer controlling how many cores are used for parallelized computations, see Details.

verbose

positive integer controlling logging of diagnostic messages to the console during model fitting. Passed by update to georob, see Details.

...

additional arguments passed by update to georob, see Details.

Value

• An object of class cv.georob, which is a list with the two components pred and fit. pred is a data frame with the coordinates and the cross-validation prediction results with the following variables:
• subset
  an integer vector defining to which of the $K$ subsets an observation was assigned.
• data
  the values of the (possibly log-transformed) response.
• pred
  the kriging predictions.
• se
  the kriging standard errors.
• If lgn = TRUE then pred has the additional variables:
• lgn.data
  the untransformed response.
• lgn.pred
  the unbiasedly back-transformed predictions of a log-transformed response.
• lgn.se
  the kriging standard errors of the back-transformed predictions of a log-transformed response.
• The second component fit contains either the full outputs of georob, fitted for the $K$ reduced data sets (reduced.output = FALSE), or $K$ lists with the components tuning.psi, converged, convergence.code, gradient, variogram.model, param, aniso[["aniso"]], coefficients along with the standard errors of $\widehat{\mbox{\boldmath$\beta$\unboldmath}}$, see georobObject.

encoding

macintosh

Details

Note that the dataframe passed as data argument to georob must exist in the user workspace when calling cv.georob. cv.georob then uses the package parallel for parallelized computations. By default, the function uses $K$ CPUs but not more than are physically available (as returned by detectCores). cv.georob uses the function update to re-estimated the model with the reduced data sets. Therefore, any argument accepted by georob can be changed when re-fitting the model. Some of them (e.g. formula, subset, etc.) are explicit arguments of cv.georob, but also the remaining ones can be passed by ... to the function. Practitioners in geostatistics commonly cross-validate a fitted model without re-estimating the model parameters with the reduced data sets. This is clearly an unsound practice (see Hastie et al., 2009, sec. 7.10). Therefore, the argument re.estimate should always be set to TRUE. The alternative is provided only for historic reasons.

References

Hastie, T., Tibshirani, R. and Friedman, J. (2009) The Elements of Statistical Learning; Data Mining, Inference and Prediction. New York: Springer-Verlag.

See Also

validate.predictions for computing statistics of the cross-validation errors; georob for (robust) fitting of spatial linear models; georobObject for a description of the class georob; predict.georob for computing robust kriging predictions.

Examples

data(meuse)

r.logzn <- 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)

r.logzn.cv.1 <- cv(r.logzn, seed = 1, lgn = TRUE)
r.logzn.cv.2 <- cv(r.logzn, formula = .~. + ffreq, seed = 1, lgn = TRUE)

plot(r.logzn.cv.1, type = "bs")
plot(r.logzn.cv.2, type = "bs", add = TRUE, col = "red")

legend("topright", lty = 1, col = c("black", "red"), bty = "n",
    legend = c("log(Zn) ~ sqrt(dist)", "log(Zn) ~ sqrt(dist) + ffreq"))