cv.georob: Cross-Validating a Spatial Linear Model Fitted by 'georob'
In georob: Robust Geostatistical Analysis of Spatial Data

Description Usage Arguments Details Value Author(s) References See Also Examples

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) REML, 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.

## S3 method for class 'georob'
cv(object, formula = NULL, subset = NULL, 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, ...)

`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.
`nset`	positive integer defining the number `K` of subsets into which the data set is partitioned (default: `nset = 10`).
`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,…,K), defining in this way the K subsets into which the data set is split. If `sets = NULL` (default) the partition is randomly generated by `sample` (using possibly `seed`).
`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 observations, see Details.
`param`	an optional named numeric vector or a matrix or data frame with variogram parameters passed by `update` to `georob`, see Details. If `param` is a matrix (or a data frame) then it must have `nset` rows and `length(object[["param"]])` columns with initial values of variogram parameters for the `nset` cross-validation sets and `colnames(param)` must match `names(object[["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 Details. If `fit.param` is a matrix (or a data frame) then it must have `nset` rows and `length(object[["param"]])` columns with variogram parameter fitting flags for the `nset` cross-validation sets and `colnames(param)` must match `names(object[["param"]])`.
`aniso`	an optional named numeric vector or a matrix or data frame with anisotropy parameters passed by `update` to `georob`, see Details. If `aniso` is a matrix (or a data frame) then it must have `nset` rows and `length(object[["aniso"]][["aniso"]])` columns with initial values of anisotropy parameters for the `nset` cross-validation sets and `colnames(aniso)` must match `names(object[["aniso"]][["aniso"]])`.
`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`, see Details. If `fit.aniso` is a matrix (or a data frame) then it must have `nset` rows and `length(object[["aniso"]][["aniso"]])` columns with anisotropy parameter fitting flags for the `nset` cross-validation sets and `colnames(aniso)` must match `names(object[["aniso"]][["aniso"]])`.
`return.fit`	logical controlling whether information about the fit should be returned for 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 factors as model offset (`"offset"`, default).
`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.

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 cross-validation. 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 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.

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 set (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 hatβ, see georobObject.

Andreas Papritz andreas.papritz@env.ethz.ch

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

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.

## Not run: 
data( meuse )

r.logzn <- georob(log(zinc) ~ sqrt(dist), data = meuse, locations = ~ x + y,
    variogram.model = "exponential",
    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"))
## End(Not run)