GeoResiduals: Computes fitted covariance and/or variogram

In GeoModels: Procedures for Gaussian and Non Gaussian Geostatistical (Large) Data Analysis

Computes fitted covariance and/or variogram

Description

The procedure return a GeoFit object associated to the estimated residuals. For a random field Y defined on the real line (Gaussian, Skew Gaussian, Tukeyh etcc) they are computed as (Y-m)/sqrt(v) where m and v are the estimated mean and variance respectively. For a random field Y defined on the positive real line (Gamma, Weibull, Log-Gaussian) they are computed as Y/m where m is the estimated mean. In the first case residuals have zero mean and unut variance with a specific distribution defined on the real line. In the second case residuals have unit mean with a specific distribution defined on the positive real line. When the function is coupled with the functions GeoQQ and GeoCovariogram, it is useful as diagnostic tool (See examples).

Usage

GeoResiduals(fit)

Arguments

fit	A fitted object obtained from the GeoFit.

Value

Returns an (updated) object of class GeoFit

Author(s)

Moreno Bevilacqua, [e-mail],https://sites.google.com/view/moreno-bevilacqua/home, Víctor Morales Oñate, [e-mail], https://sites.google.com/site/moralesonatevictor/, Christian", Caamaño-Carrillo, [e-mail],https://www.researchgate.net/profile/Christian-Caamano

See Also

GeoFit.

Examples

library(GeoModels)



###########################
###Example 1: Residuals using a Gaussian RF
###########################
set.seed(211)
model="Gaussian";
N=700 # number of location sites
# Set the coordinates of the points:
x = runif(N, 0, 1)
y = runif(N, 0, 1)
coords=cbind(x,y)

# regression parameters
mean = 5
mean1=0.8

X=cbind(rep(1,N),runif(N))
# correlation parameters:
corrmodel = "Wend0"
sill = 1
nugget = 0
scale = 0.3
power2=4

param=list(mean=mean,mean1=mean1, sill=sill, nugget=nugget, 
             scale=scale,power2=power2)
# Simulation of the Gaussian RF:
data = GeoSim(coordx=coords, corrmodel=corrmodel, X=X,model=model,param=param)$data

start=list(mean=mean,mean1=mean1, scale=scale,sill=sill)
fixed=list(nugget=nugget,power2=power2)
# Maximum composite-likelihood fitting 
fit = GeoFit(data,coordx=coords, corrmodel=corrmodel,model=model,X=X,
                    likelihood="Conditional",type='Pairwise',start=start,
                    fixed=fixed,neighb=3)

res=GeoResiduals(fit)
mean(res$data) # should be approx 0
var(res$data) # should be approx 1
# checking goodness of fit marginal model
GeoQQ(res);GeoQQ(res,type="D",col="red",ylim=c(0,0.5),breaks=20);
# Empirical estimation of the variogram for the residuals:
vario = GeoVariogram(res$data,coordx=coords,maxdist=0.5)
# Comparison between empirical amd estimated semivariogram for the residuals
GeoCovariogram(res, show.vario=TRUE, vario=vario,pch=20)





###########################
###Example 2: Residuals using a Weibull RF
###########################
model="Weibull";shape=4
N=700 # number of location sites
# Set the coordinates of the points:
x = runif(N, 0, 1)
y = runif(N, 0, 1)
coords=cbind(x,y)


# regression parameters
mean = 5
mean1=0.8

X=cbind(rep(1,N),runif(N))
# correlation parameters:
corrmodel = "Wend0"
sill = 1
nugget = 0
scale = 0.3
power2=4

param=list(mean=mean,mean1=mean1, sill=sill, nugget=nugget, 
	           scale=scale,shape=shape,power2=power2)
# Simulation of the Gaussian RF:
data = GeoSim(coordx=coords, corrmodel=corrmodel, X=X,model=model,param=param)$data

I=Inf
start=list(mean=mean,mean1=mean1, scale=scale,shape=shape)
lower=list(mean=-I,mean1=-I, scale=0,shape=0)
upper=list(mean= I,mean1= I, scale=I,shape=I)
fixed=list(nugget=nugget,sill=sill,power2=power2)
# Maximum composite-likelihood fitting 
fit = GeoFit(data,coordx=coords, corrmodel=corrmodel,model=model,X=X,
                    likelihood="Conditional",type='Pairwise',start=start,
                   optimizer="nlminb", lower=lower,upper=upper,
                    fixed=fixed,neighb=3)


res=GeoResiduals(fit)
mean(res$data) # should be approx 1
# checking goodness of fit marginal model
GeoQQ(res);GeoQQ(res,type="D",col="red",ylim=c(0,1.7),breaks=20);
# Empirical estimation of the variogram for the residuals:
vario = GeoVariogram(res$data,coordx=coords,maxdist=0.5)
# Comparison between empirical amd estimated semivariogram for the residuals
GeoCovariogram(res, show.vario=TRUE, vario=vario,pch=20)

GeoModels documentation built on April 13, 2025, 5:09 p.m.