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 ANY,ANY,ANY,ANY
glgm(formula, data,  grid, covariates, buffer=0, shape=1, prior, ...) 
# S4 method for formula,SpatRaster,ANY,ANY
glgm(formula, data,  grid, covariates, buffer=0, shape=1, prior, ...) 
# S4 method for formula,SpatVector,ANY,ANY
glgm(formula, data,  grid, covariates, buffer=0, shape=1, prior, ...) 
# S4 method for formula,data.frame,SpatRaster,data.frame
glgm(formula, data,  grid, covariates, buffer=0, shape=1, prior, ...) 
lgcp(formula=NULL, data,  grid, covariates=NULL, border, ...)

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

Arguments

data: An object of class SpatVector 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.
prior: list with elements named range, sd, sdObs. 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.
border: boundary of the region on which an LGCP is defined, passed to mask
...: Additional options passed to c( '\\code{inla} in the \\code{INLA} package', '\\code{\\link[INLA]{inla}}' )[1+requireNamespace('INLA', quietly=TRUE)]

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 prior can be named range, sd, or sdObs. Elements can consist of:

a single value giving the prior median for penalized complexity priors (exponential on the sd or 1/range).
a vector c(u=a, alpha=b) giving an quantile and probability for pc priors. For standard deviations alpha is an upper quantile, for the range parameter b = pr(1/range > 1/a).
a vector c(lower=a, upper=b) giving a 0.025 and 0.975 quantiles for the sd or range.
a list of the form list(prior='loggamma', param=c(1,2)) passed directly to inla.
a two-column matrix of prior densities for the sd or range.

Examples

Run this code


# geostatistical model for the swiss rainfall data

if(requireNamespace("INLA", quietly=TRUE) ) {
  INLA::inla.setOption(num.threads=2)
  # not all versions of INLA support blas.num.threads
  try(INLA::inla.setOption(blas.num.threads=2), silent=TRUE)
} 

require("geostatsp")
data("swissRain")
swissRain = unwrap(swissRain)
swissAltitude = unwrap(swissAltitude)
swissBorder = unwrap(swissBorder)

swissRain$lograin = log(swissRain$rain)
swissFit =  glgm(formula="lograin", data=swissRain, 
	grid=30, 
	covariates=swissAltitude, family="gaussian", 
	buffer=2000,
	prior = list(sd=1, range=100*1000, sdObs = 2),
	control.inla = list(strategy='gaussian')
	)

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

	matplot(
		swissFit$parameters$range$postK[,'x'],
		swissFit$parameters$range$postK[,c('y','prior')],
		type="l", lty=1, xlim = c(0, 1000),
		xlab = 'km', ylab='dens')
	legend('topright', lty=1, col=1:2, legend=c('post','prior'))

	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))
}

		


# a log-Gaussian Cox process example

myPoints = vect(cbind(rbeta(100,2,2), rbeta(100,3,4)))


mycov = rast(matrix(rbinom(100, 1, 0.5), 10, 10), extent=ext(0, 1, 0, 1))
names(mycov)="x1"


if(requireNamespace("INLA", quietly=TRUE) ) {
  INLA::inla.setOption(num.threads=2)
  # not all versions of INLA support blas.num.threads
  try(INLA::inla.setOption(blas.num.threads=2), silent=TRUE)
}

res = lgcp(
	formula=~factor(x1),
	data=myPoints, 
	grid=squareRaster(ext(0,1,0,1), 20), covariates=mycov,
	prior=list(sd=c(0.9, 1.1), range=c(0.4, 0.41),
	control.inla = list(strategy='gaussian'), verbose=TRUE)
)
if(length(res$parameters)) {  
	plot(res$raster[["predict.exp"]])
	plot(myPoints,add=TRUE,col="#0000FF30",cex=0.5)
}