krigeTg: TransGaussian kriging using Box-Cox transforms

In gstat: Spatial and Spatio-Temporal Geostatistical Modelling, Prediction and Simulation

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

Details

Function krigeTg uses transGaussian kriging as explained in https://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.

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}

Author(s)

Edzer Pebesma

References

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

http://www.gstat.org/

See Also

gstat, predict

Examples

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)

gstat documentation built on Sept. 11, 2024, 7:46 p.m.