glgm-methods: Generalized Linear Geostatistical Models

Description

Fits a generalized linear geostatistical model or a log-Gaussian Cox process using inla

Usage

# S4 method for NULL,ANY,ANY,ANY
glgm(formula=NULL, data,  grid, 
	covariates=NULL, ...)
# S4 method for numeric,ANY,ANY,ANY
glgm(formula, data,  grid, 
	covariates=NULL, ...)
# S4 method for character,ANY,ANY,ANY
glgm(formula, data,  grid, 
	covariates=NULL, ...)
# S4 method for formula,ANY,numeric,ANY
glgm(formula, data,  grid, 
	covariates=NULL, ...)
# S4 method for formula,Raster,Raster,ANY
glgm(formula, data,  grid, 
	covariates=NULL, buffer=0, ...)
# S4 method for formula,Spatial,Raster,ANY
glgm(formula, data,  grid, covariates=NULL, buffer=0, ...)
# S4 method for formula,data.frame,Raster,data.frame
glgm(formula, data,  grid, covariates=NULL, 
  shape=1, priorCI=NULL, mesh=FALSE,...) 
lgcp(formula=NULL, data,  grid, covariates=NULL, border, ...)

Arguments

data

An object of class SpatialPointsDataFrame containing the data.

grid

Either an integer giving the number of cells in the x direction, or a raster object which will be used for the spatial random effect. If the cells in the raster are not square, the resolution in the y direction will be adjusted to make it so.

covariates

Either a single raster, a list of rasters or a raster stack containing covariate values used when making spatial predictions. Names of the raster layers or list elements correspond to names in the formula. If a covariate is missing from the data object it will be extracted from the rasters. Defaults to NULL for an intercept-only model.

formula

Model formula, defaults to a linear combination of each of the layers in the covariates object. The spatial random effect should not be supplied but the default can be overridden with a f(space,..) term. For glgm the response variable defaults to the first variable in the data object, and formula can be an integer or character string specifying the response variable. For lgcp, the formula should be one-sided.

priorCI

list with elements named range, sd, sdNugget, intercept, or betas. See Details.

shape

Shape parameter for the Matern correlation function, must be 1 or 2.

buffer

Extra space padded around the data bounding box to reduce edge effects.

mesh

Currently unimplemented options for using a mesh rather than a grid for the Markov random field approximation.

border

boundary of the region on which an LGCP is defined, passed to mask

...

Additional options passed to inla

Value

A list with two components named inla, raster, and parameters. inla contains the results of the call to the inla function. raster is a raster stack with the following layers:

random.

mean, sd, X0.0??quant: Posterior mean, standard deviation, and quantiles of the random effect

predict.

mean, sd, X0.0??quant: same for linear predictors, on the link scale

predict.exp

posterior mean of the exponential of the linear predictor

predict.invlogit

Only supplied if a binomial response variable was used.

parameters contains a list with elements:

summary

a table with parameter estimates and posterior quantiles

range, sd

prior and posterior distributions of range and standard deviations

Details

This function performs Bayesian inference for generalized linear geostatistical models with INLA. The Markov random field approximation on a regular lattice is used for the spatial random effect. The range parameter is the distance at which the correlation is 0.13, or $$cov[U(s+h), U(s)] = (2^{1-\nu}/Gamma(\nu)) d^\nu besselK(d, \nu) $$ $$d= |h| \sqrt{8 \nu}/range$$ where $\nu$ is the shape parameter. The range parameter produced by glgm multiplies the range parameter from INLA by the cell size.

Elements of priorCI can be named:

range for the range parameter (not the scale)
sd for the standard deviation (not the variance or precision)
sdNugget for the standard deviation of the observation error for Gaussian data
gammaShape for the shape parameter of a Gamma distributed observations
intercept for the intercept
betas for the regression coefficients

Each element is either a vector of length 2 or a two-column matrix.

c(lower=a, upper=b) specifies 0.025 and 0.975 quantiles of prior distributions
c(u=a, alpha=b) gives a penalized complexity prior for standard deviation parameters. $pr(\sigma > a) = b$
A matrix has a first column of parameter values and a second column of densities

Examples

Run this code

# NOT RUN {
# use the 'safe' version of INLA on linux systems
if(Sys.info()['sysname'] =='Linux' &
  requireNamespace("INLA")) {   
  INLA::inla.setOption(inla.call = system.file(paste("bin/linux/",          
          ifelse(.Machine$sizeof.pointer == 4, "32", "64"),
          'bit/inla.static', sep=''), package="INLA")) }

# geostatistical model for the swiss rainfall data
require("geostatsp")
data("swissRain")
swissRain$lograin = log(swissRain$rain)
swissFit =  glgm(formula="lograin", data=swissRain, grid=30, 
	covariates=swissAltitude, family="gaussian", buffer=20000,
	priorCI=list(sd=c(0.01, 5), range=c(50000,500000),
		sdNugget = c(0.01, 5)), 
	control.mode=list(theta=c(1.6,-0.25,2.9),restart=TRUE)
	)


if(!is.null(swissFit$parameters) ) {
	
	swissExc = excProb(swissFit, threshold=log(25))

	swissExcRE = excProb(swissFit$inla$marginals.random$space, 
		log(1.5),template=swissFit$raster)

	swissFit$parameters$summary

	plot(swissFit$parameters$range$prior,type="l",
		ylim=c(0,max(swissFit$parameters$range$posterior[,"y"])),
		xlim=c(0, 500000))
	abline(v=swissFit$parameters$range$userPriorCI,col="yellow")
	abline(v=swissFit$parameters$range$priorCI,col="orange")
	lines(swissFit$parameters$range$posterior, col='blue')


}


if(interactive()  | Sys.info()['user'] =='patrick') {
	plot(swissFit$raster[["predict.exp"]]) 

	mycol = c("green","yellow","orange","red")
	mybreaks = c(0, 0.2, 0.8, 0.95, 1)
	plot(swissBorder)
	plot(swissExc, breaks=mybreaks, col=mycol,add=TRUE,legend=FALSE)
	plot(swissBorder, add=TRUE)
	legend("topleft",legend=mybreaks, fill=c(NA,mycol))


	plot(swissBorder)
	plot(swissExcRE, breaks=mybreaks, col=mycol,add=TRUE,legend=FALSE)
	plot(swissBorder, add=TRUE)
	legend("topleft",legend=mybreaks, fill=c(NA,mycol))
}

		

# }
# NOT RUN {
load(url("http://www.filefactory.com/file/frd1mhownd9/n/CHE_adm0_RData"))
thenames = GNcities(bbox(gadm),max=12)
swissTiles = openmap(bbox(gadm),zoom=8,type="nps")

par(mar=c(0,0,0,0))
plot(gadm)
plot(swissTiles, add=TRUE)
library('RColorBrewer')
mycol=rev(brewer.pal(4,"RdYlGn"))
plot(mask(
		projectRaster(swissExc, crs=proj4string(gadm)),
		gadm), 
	breaks = c(0, 0.2, 0.8, 0.95, 1.00001), 
	col=mycol, alpha=0.5,add=TRUE)	
plot(gadm, add=TRUE, lwd=2, border='blue')

points(thenames,cex=0.5)
text(thenames, labels=thenames$name,pos=3,
  vfont=c("gothic german","plain"),cex=1.5)



# }
# NOT RUN {
# a log-Gaussian Cox process example

if(interactive()  | Sys.info()['user'] =='patrick') {
myPoints = SpatialPoints(cbind(rbeta(100,2,2), rbeta(100,3,4)))
myPoints@bbox = cbind(c(0,0), c(1,1))

mycov = raster(matrix(rbinom(100, 1, 0.5), 10, 10), 0, 1, 0, 1)
names(mycov)="x1"


res = lgcp(data=myPoints, grid=20, covariates=mycov,
	formula=~factor(x1),
	priorCI=list(sd=c(0.9, 1.1), range=c(0.4, 0.41))
)
plot(res$raster[["predict.exp"]])
plot(myPoints,add=TRUE,col="#0000FF30",cex=0.5)

}

# }