krigeTg: TransGaussian kriging using Box-Cox transforms

Description

TransGaussian (ordinary) kriging function using Box-Cox transforms

Usage

krigeTg(formula, locations, newdata, model = NULL, ...,
	nmax = Inf, nmin = 0, maxdist = Inf, block = numeric(0),
	nsim = 0, na.action = na.pass, debug.level = 1,
	lambda = 1.0)

Arguments

formula

formula that defines the dependent variable as a linear model of independent variables; suppose the dependent variable has name z, for ordinary and use a formula like z~1; the dependent variable should be NOT transformed.

locations

object of class Spatial, with observations

newdata

Spatial object with prediction/simulation locations; the coordinates should have names as defined in locations

model

variogram model of the TRANSFORMED dependent variable, see vgm, or fit.variogram

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, all observations are used

nmin

for local kriging: if the number of nearest observations within distance maxdist is less than nmin, a missing value will be generated; see maxdist

maxdist

for local kriging: only observations within a distance of maxdist from the prediction location are used for prediction or simulation; if combined with nmax, both criteria apply

block

does not function correctly, afaik

nsim

does not function correctly, afaik

na.action

function determining what should be done with missing values in 'newdata'. The default is to predict 'NA'. Missing values in coordinates and predictors are both dealt with.

lambda

value for the Box-Cox transform

debug.level

debug level, passed to predict; use -1 to see progress in percentage, and 0 to suppress all printed information

…

other arguments that will be passed to gstat

Value

an SpatialPointsDataFrame object containing the fields: m for the m (Lagrange) parameter for each location; var1SK.pred the \(c_0 C^{-1}\) correction obtained by muhat for the mean estimate at each location; var1SK.var the simple kriging variance; var1.pred the OK prediction on the transformed scale; var1.var the OK kriging variance on the transformed scale; var1TG.pred the transGaussian kriging predictor; var1TG.var the transGaussian kriging variance, obtained by \(\phi'(\hat{\mu},\lambda)^2 \sigma^2_{OK}\)

Details

Function krigeTg uses transGaussian kriging as explained in http://www.math.umd.edu/~bnk/bak/Splus/kriging.html.

As it uses the R/gstat krige function to derive everything, it needs in addition to ordinary kriging on the transformed scale a simple kriging step to find m from the difference between the OK and SK prediction variance, and a kriging/BLUE estimation step to obtain the estimate of \(\mu\).

For further details, see krige and predict.

References

N.A.C. Cressie, 1993, Statistics for Spatial Data, Wiley.

http://www.gstat.org/

Examples

Run this code

# NOT RUN {
library(sp)
data(meuse)
coordinates(meuse) = ~x+y
data(meuse.grid)
gridded(meuse.grid) = ~x+y
v = vgm(1, "Exp", 300)
x1 = krigeTg(zinc~1,meuse,meuse.grid,v, lambda=1) # no transform
x2 = krige(zinc~1,meuse,meuse.grid,v)
summary(x2$var1.var-x1$var1TG.var)
summary(x2$var1.pred-x1$var1TG.pred)
lambda = -0.25
m = fit.variogram(variogram((zinc^lambda-1)/lambda ~ 1,meuse), vgm(1, "Exp", 300))
x = krigeTg(zinc~1,meuse,meuse.grid,m,lambda=-.25)
spplot(x["var1TG.pred"], col.regions=bpy.colors())
summary(meuse$zinc)
summary(x$var1TG.pred)
# }

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