# Cross validation, n-fold and leave-one-out for thin plate splines ('TPS') This function is a cross validation function for 'Tps' method in 'fields' package. ```r tpscv( trainx, trainy, m = NULL, p = NULL, theta = 3, lambda = NULL, lon.lat = TRUE, validation = "CV", cv.fold = 10, predacc = "VEcv", ... ) ``` ## Arguments - `trainx`: a dataframe contains longitude (long), latitude (lat) and predictive variables of point samples. That is, they must be names as 'long' and 'lat'. - `trainy`: a vector of response, must have length equal to the number of rows in trainx. - `m`: A polynomial function of degree (m-1) will be included in the model as the drift (or spatial trend) component. Default is 'm = NULL' that is the value such that 2m-d is greater than zero where d is the dimension of x. - `p`: polynomial power for Wendland radial basis functions as in 'Tps'. 'p = NULL' that leads to a default value of 2 for spatial predictive modelling based on 'x' containing only the location information. - `theta`: the tapering range. 'theta = 3' degrees is a very generous taper range. For spatial predictive modeling the taper should be large enough to about 20 non zero nearest neighbors for every location. - `lambda`: smoothing parameter, the default is 'NULL'. See '?Tps' for further info. - `lon.lat`: if 'TRUE' locations are interpreted as longitude and latitude and great circle distance is used to find distances among locations. - `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. - `predacc`: can be either "VEcv" for vecv or "ALL" for all measures in function pred.acc. - `...`: other arguments passed on to '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 'krigecv' in this package and 'Tps' and 'fastTpsMLE' in 'fields' package. ## Examples ```r library(fields) library(spm) data(petrel) tpscv1 <- tpscv(petrel[, c(1,2)], petrel[, 5], cv.fold = 5, predacc = "VEcv") tpscv1 tpscv1 <- tpscv(petrel[, c(1,2)], petrel[, 5], lambda = 0.9, cv.fold = 5, predacc = "VEcv") tpscv1 tpscv1 <- tpscv(petrel[, c(1,2)], petrel[, 5], validation = "LOO", predacc = "VEcv") tpscv1 set.seed(1234) n <- 20 # number of iterations,60 to 100 is recommended. VEcv <- NULL for (i in 1:n) { tpscv1 <- tpscv(petrel[, c(1,2)], petrel[, 5], cv.fold = 10, lambda = 0.13, predacc = "VEcv") VEcv [i] <- tpscv1 } plot(VEcv ~ c(1:n), xlab = "Iteration for TPS", ylab = "VEcv (%)") points(cumsum(VEcv) / c(1:n) ~ c(1:n), col = 2) abline(h = mean(VEcv), col = 'blue', lwd = 2) n <- 20 # number of iterations,60 to 100 is recommended. # set.seed(1234) VEcv <- NULL for (i in 1:n) { set.seed(1234 + i) # set random seed for each iteration. You can remove # this line and use above set.seed(1234) and see what you can get. tpscv1 <- tpscv(petrel[, c(1,2)], petrel[, 5], predacc = "VEcv") VEcv [i] <- tpscv1 } plot(VEcv ~ c(1:n), xlab = "Iteration for TPS", ylab = "VEcv (%)") points(cumsum(VEcv) / c(1:n) ~ c(1:n), col = 2) abline(h = mean(VEcv), col = 'blue', lwd = 2) ``` ## References Douglas Nychka and Reinhard Furrer and John Paige and Stephan Sain and Florian Gerber and Matthew Iverson, 2020. fields: Tools for Spatial Data, R package version 10.3 https://CRAN.R-project.org/package=fields. ## Author(s) Jin Li

tpscv function