lgm-methods: Linear Geostatistical Models

Description

Calculate MLE's of model parameters and perform spatial prediction.

Usage

## S3 method for class 'NULL,ANY,ANY,ANY':
lgm(
formula=NULL, data,
		grid,
		covariates=NULL, 
		...) 
## S3 method for class 'numeric,ANY,ANY,ANY':
lgm(formula, data,
		grid,
		covariates=NULL, 
		...) 
## S3 method for class 'character,ANY,ANY,ANY':
lgm(formula, data,
		grid,
		covariates=NULL, 
		...) 
## S3 method for class 'formula,Spatial,ANY,missing':
lgm(formula, data,
		grid=NULL,
		covariates=NULL, 
		...) 
## S3 method for class 'formula,Raster,ANY,ANY':
lgm(formula, data,
		grid,
		covariates=NULL, 
		...) 
## S3 method for class 'formula,Raster,ANY,ANY':
lgm(
		formula, data,
		grid=NULL,
		covariates=NULL, 
		...) 
## S3 method for class 'formula,Spatial,numeric,ANY':
lgm(formula, data,
		grid,
		covariates=NULL, 
		...) 
## S3 method for class 'formula,Spatial,Raster,ANY':
lgm(formula, data,
		grid,
		covariates=NULL, buffer=0,
		...) 
## S3 method for class 'formula,Spatial,Raster,data.frame':
lgm(formula, data,
		grid,
		covariates=NULL, 
			shape=1, boxcox=1, nugget = 0, 
		expPred=FALSE, nuggetInPrediction=TRUE,
		reml=TRUE,mc.cores=1,
		aniso=FALSE,
		fixShape=TRUE,
		fixBoxcox=TRUE,
		fixNugget = FALSE,
		...) 
## S3 method for class 'formula,data.frame,Raster,data.frame':
lgm(formula, data,
		grid,
		covariates=NULL, 
		            shape=1,boxcox=1,nugget=0,
				  expPred=FALSE, nuggetInPrediction=TRUE,
				  reml = TRUE,
				  mc.cores=1,		
				  oneminusar=seq(0.01, 0.4,len=4), 
                  range=NULL, 
		...)

Arguments

formula

A model formula for the fixed effects, or a character string specifying the response variable.

data

A SpatialPointsDataFrame or Raster layer, brick or stack containing the locations and observations, and possibly covariates.

grid

Either a raster, or a single integer giving the number of cells in the X direction which predictions will be made on. If the later the predictions will be a raster of square cells covering the boundin

covariates

The spatial covariates used in prediction, either a raster stack or list of rasters. Covariates in formula but not in data will be extracted from covariates.

shape

Order of the Matern correlation

boxcox

Box-Cox transformation parameter (or vector of parameters), set to 1 for no transformation.

nugget

Value for the nugget effect (observation error) variance, or vector of such values.

expPred

Should the predictions be exponentiated, defaults to FALSE.

nuggetInPrediction

If TRUE, predict new observations by adding the nugget effect. The prediction variances will be adjusted accordingly, and the predictions on the natural scale for logged or Box Cox transformed data will be affected. Otherwise predict fitt

reml

If TRUE (the default), use restricted maximum likelihood.

mc.cores

If mc.cores>1, this argument is passed to mcmapply and computations are done in parallel where possible.

aniso

Set to TRUE to use geometric anisotropy.

fixShape

Set to FALSE to estimate the Matern order

fixBoxcox

Set to FALSE to estimate the Box-Cox parameter.

fixNugget

Set to FALSE to estimate the nugget effect parameter.

oneminusar

Vector of GMRF autoregressive parameters over which the likelihood is computed.

range

Vector of range parameters over which the likelihood is computed, ignored if oneminusar is non-NULL

buffer

Extra distance to add around grid.

...

Additional arguments passed to likfitLgm. Starting values can be specified with a vector param of named elements

Value

A list is returned which includes a RasterStack named predict having layers:
fixedEstimated means from the fixed effects portion of the model
randomPredicted random effect
krigeSdConditional standard deviation of predicted random effect (on the transformed scale if applicable)
predictPrediction of the response, sum of predicted fixed and random effects. For Box-Cox or log-transformed data on the natural (untransformed) scale.
predict.logIf exp.pred=TRUE, the prediction of the logged process.
predict.boxcoxIf a box cox transformation was used, the prediction of the process on the transformed scale.
In addition, the element summery contains a table of parameter estimates and confidence intervals. optim contains the output from the call to the optim function.

Details

When data is a SpatialPointsDataFrame, parameters are estimated using optim to maximize the log-likelihood function computed by likfitLgm and spatial prediction accomplished with krigeLgm.

With data being a Raster object, a Markov Random Field approximation to the Matern is used (experimental). Parameters to be estimated should be provided as vectors of possible values, with optimization only considering the parameter values supplied.

Examples

Run this code

data("swissRain")
 
swissRes =  lgm( formula="rain", 
	data=swissRain[1:60,], grid=20,
	covariates=swissAltitude, boxcox=0.5, fixBoxcox=TRUE, 
	shape=1, fixShape=TRUE,
	aniso=FALSE, nugget=0, fixNugget=FALSE,
	nuggetInPrediction=FALSE
)

swissRes$summary

plot(swissRes$predict[["predict"]], main="predicted rain") 
plot(swissBorder, add=TRUE)

data("swissRainR")
swissRainR2 = brick(swissRainR[['alt']], 
	 sqrt(swissRainR[['prec1']]))

if(interactive() | Sys.info()['user'] =='patrick') {	 
swissResR =  lgm( formula=layer ~ alt, 
	data=swissRainR2, shape=1,
	oneminusar=seq(0.06, 0.09, len=2),
	nugget =  seq(0,0.0001,len=2)
	)

swissResR$summary[c('oneminusar','range','propNugget','(Intercept).betaHat', 'alt.betaHat'),]
}


load(url("http://www.filefactory.com/file/frd1mhownd9/n/CHE_adm0_RData"))

library('RColorBrewer')
par(mar=c(0,0,0,3))
plot(gadm) 
plot(mask(projectRaster(
	swissRes$predict[["predict"]],  crs=gadm@proj4string),gadm), 
add=T,alpha=0.6, col=brewer.pal(9, "Blues"))
plot(gadm, add=TRUE)