# Cross validation, n-fold and leave-one-out for kriging methods ('krige') This function is a cross validation function for kriging methods ('krige') in 'gstat'. ```r krigecv( longlat, trainy, trainpredx = NULL, validation = "CV", cv.fold = 10, nmax = 12, transformation = "none", delta = 1, formula = var1 ~ 1, vgm.args = ("Sph"), anis = c(0, 1), alpha = 0, block = 0, beta, predacc = "VEcv", ... ) ``` ## Arguments - `longlat`: a dataframe contains longitude and latitude of point samples. - `trainy`: a vector of response, must have length equal to the number of rows in trainx. - `trainpredx`: a dataframe contains predictive variables of point samples. If longitude and latitude are going to be used as predictive variables, they should also be included but they should be named in names other than 'long' and 'lat'. - `validation`: validation methods, include 'LOO': leave-one-out, and 'CV': cross-validation. - `cv.fold`: integer; number of folds in the cross-validation. if > 1, then apply n-fold cross validation; the default is 10, i.e., 10-fold cross validation that is recommended. - `nmax`: for local kriging: the number of nearest observations that should be used for a kriging prediction or simulation, where nearest is defined in terms of the space of the spatial locations. By default, 12 observations are used. - `transformation`: transform response variable to normalise the data; can be "sqrt" for square root, "arcsine" for arcsine, "log" or "none" for non transformation. By default, "none" is used. - `delta`: numeric; to avoid 'log(0)' in "log" transformation. The default is 1. - `formula`: formula defining response vector and (possible) regressor. an object (i.e., 'variogram.formula') for 'variogram' or a formula for 'krige'. see 'variogram' and 'krige' in the 'gstat' package for details. - `vgm.args`: arguments for 'vgm', e.g. variogram model of response variable and anisotropy parameters. see 'vgm' in the 'gstat' package for details. By default, "Sph" is used. - `anis`: anisotropy parameters: see notes 'vgm' in the 'gstat' package for details. - `alpha`: direction in plane (x,y). see variogram in the 'gstat' package for details. - `block`: block size. see 'krige' in the 'gstat' package for details. - `beta`: for simple kriging. see 'krige' in the 'gstat' package for details. - `predacc`: can be either "VEcv" for vecv or "ALL" for all measures in function pred.acc. - `...`: other arguments passed on to the function 'gstat'. ## Returns A list with the following components: me, rme, mae, rmae, mse, rmse, rrmse, vecv and e1; or vecv only ## Note This function is largely based on rfcv in 'randomForest' and some functions in 'library(gstat)'. When 'A zero or negative range was fitted to variogram' occurs, to allow 'gstat' running, the range was set to be positive by using 'min(vgm1$dist)'. In this case, caution should be taken in applying this method. If it still occurs for 'okpred' function, different method may need to be used. ## Examples ```r library(sp) library(spm) data(swmud) data(petrel) set.seed(1234) okcv1 <- krigecv(longlat = swmud[, c(1,2)], trainy = swmud[, 3], nmax = 7, transformation = "arcsine", vgm.args = ("Sph"), predacc = "VEcv") okcv1 set.seed(1234) skcv1 <- krigecv(longlat = swmud[, c(1,2)], trainy = swmud[, 3], nmax = 7, transformation = "arcsine", vgm.args = ("Sph"), predacc = "VEcv", beta = mean(swmud[, 3])) skcv1 set.seed(1234) ukcv1 <- krigecv(longlat = swmud[, c(1,2)], trainy = swmud[, 3], nmax = 7, transformation = "arcsine", formula = var1 ~ long + lat, vgm.args = ("Sph"), predacc = "VEcv") ukcv1 set.seed(1234) okcv2 <- krigecv(longlat = swmud[, c(1,2)], trainy = swmud[, 3], validation = "LOO", nmax = 7, transformation = "arcsine", vgm.args = ("Sph"), predacc = "ALL") okcv2 set.seed(1234) n <- 20 # number of iterations,60 to 100 is recommended. VEcv <- NULL for (i in 1:n) { okcv1 <- krigecv(longlat = petrel[, c(1,2)], trainy = petrel[, 5], nmax = 12, transformation = "arcsine", predacc = "VEcv") VEcv [i] <- okcv1 } plot(VEcv ~ c(1:n), xlab = "Iteration for OK", ylab = "VEcv (%)") points(cumsum(VEcv) / c(1:n) ~ c(1:n), col = 2) abline(h = mean(VEcv), col = 'blue', lwd = 2) set.seed(1234) n <- 20 # number of iterations, 60 to 100 is recommended. measures <- NULL for (i in 1:n) { okcv1 <- krigecv(longlat = petrel[, c(1,2)], trainy = petrel[, 3], nmax = 12, transformation = "arcsine", predacc = "ALL") measures <- rbind(measures, okcv1$vecv) } plot(measures ~ c(1:n), xlab = "Iteration for OK", ylab = "VEcv (%)") points(cumsum(measures) / c(1:n) ~ c(1:n), col = 2) abline(h = mean(measures), col = 'blue', lwd = 2) ``` ## References Li, J., 2013. Predictive Modelling Using Random Forest and Its Hybrid Methods with Geostatistical Techniques in Marine Environmental Geosciences, In: Christen, P., Kennedy, P., Liu, L., Ong, K.-L., Stranieri, A., Zhao, Y. (Eds.), The proceedings of the Eleventh Australasian Data Mining Conference (AusDM 2013), Canberra, Australia, 13-15 November 2013. Conferences in Research and Practice in Information Technology, Vol. 146. A. Liaw and M. Wiener (2002). Classification and Regression by randomForest. R News 2(3), 18-22. Pebesma, E.J., 2004. Multivariable geostatistics in S: the gstat package. Computers & Geosciences, 30: 683-691. ## Author(s) Jin Li

krigecv function