tpscv {spm2}

Cross validation, n-fold and leave-one-out for thin plate splines ('TPS')

Description

This function is a cross validation function for 'Tps' method in 'fields' package.

Usage

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'.

Value

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.

Author(s)

Jin Li

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.

Examples

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)