spGaussCopPredict: spatial prediction using a Gaussian Copula

In BenGraeler/spcopula: Copula Driven Analysis - Multivariate, Spatial, Spatio-Temporal

Description

This function allows to do spatial prediction using a Gaussian Copula based on the spatial parametrization.

Usage

spGaussCopPredict(corFun, predNeigh, dataLocs, predLocs, margin, p = 0.5, ..., n = 1000)

Arguments

corFun	A valid correlogram (i.e. producing a valid correlation matrix; e.g. based on a variogram).
predNeigh	A neighbourhood object used for prediction.
dataLocs	a spatial object providing the data
predLocs	a spatial object providing the prediction locations
margin	a list containing the marginal distribution. Currently only the entry q is required defining the quantile function.
p	the fraction the quantile function shall be evaluated for. This can be used to calculate besides the median estimate confidence estimates as well.
...	currently unused
n	the approximate number of points used in the linear approximation of the conditional distribution function.

Details

Based on corFun provided with a distance matrix a Gaussian copula (normalCopula) is generated and conditioned under the data of the neighbouring locations. The 1-dimensional conditional distribution is approximated and evaluated for the given fraction p. This conditioned fraction is than passed on to the marginal quantile function and evaluated providing an estimate.

Value

According to the predLocs slot of the provided neighbourhood a spatial data structure extended with an variable holding the predicted values.

Author(s)

Benedikt Graeler

See Also

spCopPredict

Examples

# load data from the Meuse demo
data("spCopDemo")

# calculate the correlation function based on Kendall's tau
calcKTauPol <- fitCorFun(bins, degree=1)

# translate Kendall's tau correlation function into Gaussian Copula parameters 
# using a linear variogram
meuseGaussCorFun <- function(h) {
  res <- pmax(iTau(normalCopula(0), calcKTauPol(0))/658*(658-h),0)
  res[h ==0] <- 1
  return(res)
}

# get some prediction data
library("sp")
data("meuse.grid")
coordinates(meuse.grid) <- ~x+y
gridded(meuse.grid) <- TRUE

data("meuse")
coordinates(meuse) <- ~x+y

meuse$rtZinc <- rank(meuse$zinc)/(length(meuse)+1)

# obtain the prediction neighbourhoods
predMeuseNeigh <- getNeighbours(meuse[1:4,], meuse.grid[c(9:12,16:19,25:28),],
                                5, "rtZinc", prediction=TRUE, min.dist=-1)

qMar <- function(x) {
  qlnorm(x,mean(log(meuse$zinc)),sd(log(meuse$zinc)))
}

# predict using the Gaussian Copula
predMedian <- spGaussCopPredict(meuseGaussCorFun, predMeuseNeigh,
                                meuse[1:4,], meuse.grid[c(9:12,16:19,25:28),],
                                list(q=qMar))

## Not run: 
  spplot(predMedian,"quantile.0.5", 
         sp.layout=list("sp.points", meuse, pch = 19, col = "red"),
         col.regions=bpy.colors())

## End(Not run)

BenGraeler/spcopula documentation built on Nov. 20, 2020, 4:07 p.m.