GeoResiduals {GeoModels}

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 estimated mean.

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
##############
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
##############
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)