spm2 (version 1.1.3)

gbmkrigeidwcv: Cross validation, n-fold and leave-one-out for the hybrid methods of generalized boosted regression modeling ('gbm'), 'kriging' and inverse distance weighted ('IDW').

Description

This function is a cross validation function for 38 hybrid methods of 'gbm', 'kriging' and 'IDW', including the average of 'gbmkrige' and 'gbmidw' ('gbmkrigegbmidw') and the average of 'gbm', 'gbmkrige' and 'gbmidw' ('gbmgbmkrigegbmidw'), where 'kriging' methods include ordinary kriging ('OK'), simple kriging ('SK'), block 'OK' ('BOK') and block 'SK'('BSK') and 'IDW' also covers 'NN' and 'KNN'. The data splitting is based on a stratified random sampling method (see the 'datasplit' function for details).

Usage

gbmkrigeidwcv(
  longlat,
  trainx,
  trainy,
  var.monotone = rep(0, ncol(trainx)),
  family = "gaussian",
  n.trees = 3000,
  learning.rate = 0.001,
  interaction.depth = 2,
  bag.fraction = 0.5,
  train.fraction = 1,
  n.minobsinnode = 10,
  transformation = "none",
  weights = rep(1, nrow(trainx)),
  keep.data = FALSE,
  verbose = TRUE,
  delta = 1,
  formula = res1 ~ 1,
  vgm.args = "Sph",
  anis = c(0, 1),
  alpha = 0,
  block = 0,
  beta,
  nmaxkrige = 12,
  idp = 2,
  nmaxidw = 12,
  hybrid.parameter = 2,
  lambda = 1,
  validation = "CV",
  cv.fold = 10,
  predacc = "VEcv",
  n.cores = 6,
  ...
)

Value

A list with the following components: me, rme, mae, rmae, mse, rmse, rrmse, vecv and e1; or vecv only

Arguments

longlat

a dataframe contains longitude and latitude of point samples.

trainx

a dataframe or matrix contains columns of predictive variables.

trainy

a vector of the response variable.

var.monotone

an optional vector, the same length as the number of predictors, indicating which variables have a monotone increasing (+1), decreasing (-1), or arbitrary (0) relationship with the outcome. By default, a vector of 0 is used.

family

either a character string specifying the name of the distribution to use or a list with a component name specifying the distribution and any additional parameters needed. See gbm for details. By default, "gaussian" is used.

n.trees

the total number of trees to fit. This is equivalent to the number of iterations and the number of basis functions in the additive expansion. By default, 3000 is used.

learning.rate

a shrinkage parameter applied to each tree in the expansion. Also known as step-size reduction.

interaction.depth

the maximum depth of variable interactions. 1 implies an additive model, 2 implies a model with up to 2-way interactions, etc. By default, 2 is used.

bag.fraction

the fraction of the training set observations randomly selected to propose the next tree in the expansion. By default, 0.5 is used.

train.fraction

The first train.fraction * nrows(data) observations are used to fit the gbm and the remainder are used for computing out-of-sample estimates of the loss function.

n.minobsinnode

minimum number of observations in the trees terminal nodes. Note that this is the actual number of observations not the total weight. By default, 10 is used.

transformation

transform the residuals of 'gbm' to normalize the data for 'krige'; can be "sqrt" for square root, "arcsine" for arcsine, "log" or "none" for non transformation. By default, "none" is used.

weights

an optional vector of weights to be used in the fitting process. Must be positive but do not need to be normalized. If keep.data = FALSE in the initial call to gbm then it is the user's responsibility to resupply the weights to gbm.more. By default, a vector of 1 is used.

keep.data

a logical variable indicating whether to keep the data and an index of the data stored with the object. Keeping the data and index makes subsequent calls to gbm.more faster at the cost of storing an extra copy of the dataset. By default, 'FALSE' is used.

verbose

If TRUE, gbm will print out progress and performance indicators. By default, 'TRUE' is used.

delta

numeric; to avoid log(0) in the log transformation. The default is 1.

formula

formula defining the response vector and (possible) regressor. an object (i.e., 'variogram.formula') for 'variogram' or a formula for 'krige'. see 'variogram' and 'krige' in 'gstat' for details. The default is 'formula = res1 ~ 1'.

vgm.args

arguments for 'vgm', e.g. variogram model of response variable and anisotropy parameters. see 'vgm' in 'gstat' for details. By default, "Sph" is used.

anis

anisotropy parameters: see notes 'vgm' in 'gstat' for details.

alpha

direction in plane (x,y). see variogram in 'gstat' for details.

block

block size. see 'krige' in 'gstat' for details.

beta

for simple kriging. see 'krige' in 'gstat' for details.

nmaxkrige

for a local predicting: the number of nearest observations that should be used for a prediction or simulation, where nearest is defined in terms of the space of the spatial locations. By default, 12 observations are used.

idp

a numeric number specifying the inverse distance weighting power.

nmaxidw

for a local predicting: the number of nearest observations that should be used for a prediction or simulation, where nearest is defined in terms of the space of the spatial locations. By default, 12 observations are used.

hybrid.parameter

the default is 2 that is for 'gbmkrigegbmidw'; for 'gbmgbmkrigegbmidw', it needs to be 3.

lambda,

ranging from 0 to 2; the default is 1 for 'gbmkrigegbmidw' and 'gbmgbmkrigegbmidw'; and if it is < 1, more weight is placed on 'krige', otherwise more weight is placed on 'idw'; and if it is 0, 'idw' is not considered and the resultant methods is 'gbmkrige' when the default 'hybrid.parameter' is used; and if it is 2, then the resultant method is 'gbmidw' when the default 'hybrid.parameter' is used.

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.

n.cores

The number of CPU cores to use. See gbm for details. By default, 6 is used.

...

other arguments passed on to 'randomForest', 'krige' and 'gstat'.

Author

Jin Li

References

Li, J. (2022). Spatial Predictive Modeling with R. Boca Raton, Chapman and Hall/CRC.

Li, J., Potter, A., Huang, Z., and Heap, A. (2012). Predicting Seabed Sand Content across the Australian Margin Using Machine Learning and Geostatistical Methods, Geoscience Australia, Record 2012/48, 115pp.

Li, J., Heap, A., Potter, A., and Danilel, J.J. (2011). Predicting Seabed Mud Content across the Australian Margin II: Performance of Machine Learning Methods and Their Combination with Ordinary Kriging and Inverse Distance Squared, Geoscience Australia, Record 2011/07, 69pp.

Greg Ridgeway with contributions from others (2015). gbm: Generalized Boosted Regression Models. R package version 2.1.1. https://CRAN.R-project.org/package=gbm

Pebesma, E.J., 2004. Multivariable geostatistics in S: the gstat package. Computers & Geosciences, 30: 683-691.

Examples

# \donttest{
library(spm)
# gbmgbmokgbmidw
data(sponge)
longlat <- sponge[, 1:2]
set.seed(1234)
gbmgbmkrigegbmidwcv1 <- gbmkrigeidwcv(longlat = longlat,
trainx = sponge[, -3], trainy = sponge[, 3], family = "poisson", interaction.depth = 3,
transformation = "none", formula = res1 ~ 1, vgm.args = "Sph",
nmaxkrige = 12, idp = 2, nmaxidw = 12, hybrid.parameter = 3, validation = "CV",
predacc = "ALL", n.cores = 2)
gbmgbmkrigegbmidwcv1

# gbmokgbmidw for count data
data(sponge)
longlat <- sponge2[, 1:2]
y = sponge[, 3]
trainx = sponge[, -3]
set.seed(1234)
n <- 20 # number of iterations,60 to 100 is recommended.
VEcv <- NULL
for (i in 1:n) {
  gbmkrigegbmidwcv1 <- gbmkrigeidwcv(longlat = longlat,
  trainx = trainx, trainy = y, family = "poisson", interaction.depth = 3,
  transformation = "none", formula = res1 ~ 1, vgm.args = ("Sph"),
  nmaxkrige = 12, idp = 2, nmaxidw = 12, hybrid.parameter = 2, validation = "CV",
  predacc = "VEcv", n.cores = 2)
  VEcv [i] <- gbmkrigegbmidwcv1
 }
 plot(VEcv ~ c(1:n), xlab = "Iteration for gbmokgbmidw", ylab = "VEcv (%)")
 points(cumsum(VEcv) / c(1:n) ~ c(1:n), col = 2)
 abline(h = mean(VEcv), col = 'blue', lwd = 2)
# }