Methods to fit a regression-kriging model

Description

Tries to automatically fit a 2D or 3D regression-kriging model for a given set of points (object of type "SpatialPointsDataFrame" or "geosamples") and covariates (object of type "SpatialPixelsDataFrame"). It first fits a regression model (e.g. Generalized Linear Model, regression tree, random forest model or similar) following the formulaString, then fits variogram for residuals usign the fit.variogram method from the gstat package. Creates an output object of class gstatModel-class.

Usage

 
## S4 method for signature 
## 'SpatialPointsDataFrame,formula,SpatialPixelsDataFrame'
fit.gstatModel(observations, formulaString, covariates, 
     method = list("GLM", "rpart", "randomForest", "quantregForest",
      "xgboost", "ranger"), 
     dimensions = list("2D", "3D", "2D+T", "3D+T"),
     fit.family = gaussian(), stepwise = TRUE, vgmFun = "Exp", 
     subsample = 5000, subsample.reg = 10000, ...)
## S4 method for signature 'geosamples,formula,SpatialPixelsDataFrame'
fit.gstatModel(observations, formulaString, covariates, 
     method = list("GLM", "rpart", "randomForest", "quantregForest", 
     "xgboost", "ranger"), 
     dimensions = list("2D", "3D", "2D+T", "3D+T"),
     fit.family = gaussian(), stepwise = TRUE, 
     vgmFun = "Exp", subsample = 5000, subsample.reg = 10000, ...)
## S4 method for signature 'geosamples,formula,list'
fit.gstatModel(observations, formulaString, covariates, 
     method = list("GLM", "rpart", "randomForest", "quantregForest", 
     "xgboost", "ranger"), 
     dimensions = list("2D", "3D", "2D+T", "3D+T"),
     fit.family = gaussian(), stepwise = TRUE, 
     vgmFun = "Exp", subsample = 5000, subsample.reg = 10000, ...)
## S4 method for signature 'geosamples,list,list'
fit.gstatModel(observations, formulaString, covariates, 
     method = list("GLM", "rpart", "randomForest", "quantregForest",
      "xgboost", "ranger"), 
     dimensions = list("2D", "3D", "2D+T", "3D+T"),
     fit.family = gaussian(), stepwise = TRUE, 
     vgmFun = "Exp", subsample = 5000, subsample.reg = 10000, ...)

Arguments

Details

The GLM method by default assumes that the target variable follows a normal distribution fit.family = gaussian(). Other possible families are:

normal distribution

fit.family = gaussian() (default setting)

log-normal distribution

fit.family = gaussian(log)

binomial variable

fit.family = binomial(logit)

variable following a poisson distribution

fit.family = poisson(log)

Note

Residuals (response residuals from the model) will be checked for normality and problems reported by default. The warning messages should be taken with care, as when the sample size is small, even big departures from normality will not be reported; when the sample size is large, even the smallest deviation from normality might lead to a warning. Likewise, if the variogram fitting fails, consider fitting a variogram manually or using the fit.vgmModel method.

Author(s)

Tomislav Hengl, Gerard B.M. Heuvelink and Bas Kempen

References

• Meinshausen, N. (2006). Quantile regression forests. The Journal of Machine Learning Research, 7, 983-999.

• chapter 8 “Interpolation and Geostatistics” in Bivand, R., Pebesma, E., Rubio, V., (2008) Applied Spatial Data Analysis with R. Use R Series, Springer, Heidelberg, pp. 378.

• Hengl, T. (2009) A Practical Guide to Geostatistical Mapping, 2nd Edt. University of Amsterdam, www.lulu.com, 291 p.

See Also

gstatModel-class, fit.regModel, test.gstatModel, geosamples-class, stats::glm, gstat::fit.variogram

Examples

# 2D model:
library(sp)
library(boot)
library(aqp)
library(plyr)
library(rpart)
library(splines)
library(gstat)
library(randomForest)
library(quantregForest)
library(plotKML)

## load the Meuse data set:
demo(meuse, echo=FALSE)

## simple model:
omm <- fit.gstatModel(meuse, om~dist+ffreq, meuse.grid,
   family = gaussian(log))
om.rk <- predict(omm, meuse.grid)
plot(om.rk)
## it was succesful!

## fit a GLM with a gaussian log-link:
omm <- fit.gstatModel(meuse, om~dist+ffreq, meuse.grid, 
   fit.family = gaussian(log))
summary(omm@regModel)
om.rk <- predict(omm, meuse.grid)
plot(om.rk)

## fit a regression-tree:
omm <- fit.gstatModel(meuse, log1p(om)~dist+ffreq, meuse.grid, 
   method="rpart")
summary(omm@regModel)
## plot a regression-tree:
plot(omm@regModel, uniform=TRUE)
text(omm@regModel, use.n=TRUE, all=TRUE, cex=.8)
omm@vgmModel    

## fit a randomForest model:
omm <- fit.gstatModel(meuse, om~dist+ffreq, meuse.grid, 
   method="randomForest")
## plot to see how good is the fit:
plot(omm)
## plot the estimated error for number of bootstrapped trees:
plot(omm@regModel)
omm@vgmModel
om.rk <- predict(omm, meuse.grid)
plot(om.rk)
## Compare with "quantregForest" package:
omm <- fit.gstatModel(meuse, om~dist+ffreq, meuse.grid, 
   method="quantregForest")
## Not run: 
om.rk <- predict(omm, meuse.grid, nfold=0)
plot(om.rk)
## plot the results in Google Earth:
plotKML(om.rk)

## End(Not run)

## binary variable (0/1):
meuse$soil.1 <- as.numeric(I(meuse$soil==1))
som <- fit.gstatModel(meuse, soil.1~dist+ffreq, meuse.grid, 
   fit.family = binomial(logit))
summary(som@regModel)
som.rk <- predict(som, meuse.grid)
plot(som.rk)
## Not run: # plot the results in Google Earth:
plotKML(som.rk)

## End(Not run)

## 3D model:
library(plotKML)
data(eberg)
## list columns of interest:
s.lst <- c("ID", "soiltype", "TAXGRSC", "X", "Y")
h.lst <- c("UHDICM","LHDICM","SNDMHT","SLTMHT","CLYMHT")
sel <- runif(nrow(eberg))<.05
## get sites table:
sites <- eberg[sel,s.lst]
## get horizons table:
horizons <- getHorizons(eberg[sel,], idcol="ID", sel=h.lst)
## create object of type "SoilProfileCollection"
eberg.spc <- join(horizons, sites, type='inner')
depths(eberg.spc) <- ID ~ UHDICM + LHDICM
site(eberg.spc) <- as.formula(paste("~", paste(s.lst[-1], collapse="+"), sep=""))
coordinates(eberg.spc) <- ~X+Y
proj4string(eberg.spc) <- CRS("+init=epsg:31467")
## convert to geosamples:
eberg.geo <- as.geosamples(eberg.spc)
## covariates:
data(eberg_grid)
gridded(eberg_grid) <- ~x+y
proj4string(eberg_grid) <- CRS("+init=epsg:31467")
glm.formulaString = as.formula(paste("SNDMHT ~ ", 
  paste(names(eberg_grid), collapse="+"), "+ ns(altitude, df=4)"))
SNDMHT.m <- fit.gstatModel(observations=eberg.geo, glm.formulaString, 
  covariates=eberg_grid)
plot(SNDMHT.m)
## problems with the variogram?
## Not run: ## remove classes from the PRMGEO6 that are not represented in the model:
sel = !(levels(eberg_grid$PRMGEO6) %in% levels(SNDMHT.m@regModel$model$PRMGEO6))
fix.c = levels(eberg_grid$PRMGEO6)[sel]
summary(eberg_grid$PRMGEO6)
for(j in fix.c){
  eberg_grid$PRMGEO6[eberg_grid$PRMGEO6 == j] <- levels(eberg_grid$PRMGEO6)[7]
}
## prepare new locations:
new3D <- sp3D(eberg_grid)
## regression only:
SNDMHT.rk.sd1 <- predict(SNDMHT.m, new3D[[1]], vgmmodel=NULL)
## regression-kriging:
SNDMHT.rk.sd1 <- predict(SNDMHT.m, new3D[[1]])
## plot the results in Google Earth:
plotKML(SNDMHT.rk.sd1, z.lim=c(5,85))

## End(Not run)