GeoCovariogram: Computes the fitted variogram model.

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

Computes the fitted variogram model.

Description

The procedure computes and plots estimated covariance or semivariogram models of a Gaussian or a non Gaussian spatial (temporal or bivariate spatial) random field. It allows to add the empirical estimates in order to compare them with the fitted model.

Usage

GeoCovariogram(fitted, distance="Eucl",answer.cov=FALSE,
            answer.vario=FALSE, answer.range=FALSE, fix.lags=NULL, 
             fix.lagt=NULL, show.cov=FALSE, show.vario=FALSE, 
            show.range=FALSE, add.cov=FALSE, add.vario=FALSE,
            pract.range=95, vario, invisible=FALSE, ...)

Arguments

fitted	A fitted object obtained from the GeoFit or GeoWLS procedures.
distance	String; the name of the spatial distance. The default is Eucl, the euclidean distance. See GeoFit.
answer.cov	Logical; if TRUE a vector with the estimated covariance function is returned; if FALSE (the default) the covariance is not returned.
answer.vario	Logical; if TRUE a vector with the estimated variogram is returned; if FALSE (the default) the variogram is not returned.
answer.range	Logical; if TRUE the estimated pratical range is returned; if FALSE (the default) the pratical range is not returned.
fix.lags	Integer; a positive value denoting the spatial lag to consider for the plot of the temporal profile.
fix.lagt	Integer; a positive value denoting the temporal lag to consider for the plot of the spatial profile.
show.cov	Logical; if TRUE the estimated covariance function is plotted; if FALSE (the default) the covariance function is not plotted.
show.vario	Logical; if TRUE the estimated variogram is plotted; if FALSE (the default) the variogram is not plotted.
show.range	Logical; if TRUE the estimated pratical range is added on the plot; if FALSE (the default) the pratical range is not added.
add.cov	Logical; if TRUE the vector of the estimated covariance function is added on the current plot; if FALSE (the default) the covariance is not added.
add.vario	Logical; if TRUE the vector with the estimated variogram is added on the current plot; if FALSE (the default) the correlation is not added.
pract.range	Numeric; the percent of the sill to be reached.
vario	A Variogram object obtained from the GeoVariogram procedure.
invisible	Logical;If TRUE then a statistic the (sum of the squared diffeence between the empirical semivariogram and the estimated semivariogram) is computed.
...	other optional parameters which are passed to plot functions.

Details

The function computes the fitted variogram model

Value

Produces a plot. No values are returned.

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

References

Cressie, N. A. C. (1993) Statistics for Spatial Data. New York: Wiley.

Gaetan, C. and Guyon, X. (2010) Spatial Statistics and Modelling. Spring Verlang, New York.

See Also

GeoFit.

Examples

library(GeoModels)
library(scatterplot3d)

################################################################
###
### Example 1. Plot of fitted covariance and fitted 
### and empirical semivariogram from a  Gaussian RF 
### with Matern correlation. 
###
###############################################################
set.seed(21)
# Set the coordinates of the points:
x = runif(300, 0, 1)
y = runif(300, 0, 1)
coords=cbind(x,y)

# Set the model's parameters:
corrmodel = "Matern"
model = "Gaussian"
mean = 0
sill = 1
nugget = 0
scale = 0.2/3
smooth=0.5

param=list(mean=mean,sill=sill, nugget=nugget, scale=scale, smooth=smooth)
# Simulation of the Gaussian random field:
data = GeoSim(coordx=coords, corrmodel=corrmodel, model=model,param=param)$data
I=Inf
start=list(mean=0,scale=scale,sill=sill)
lower=list(mean=-I,scale=0,sill=0)
upper=list(mean= I,scale=I,sill=I)
fixed=list(nugget=nugget,smooth=smooth)
# Maximum composite-likelihood fitting of the Gaussian random field:
fit = GeoFit(data=data,coordx=coords, corrmodel=corrmodel,model=model,
            likelihood="Marginal",type='Pairwise',start=start,
            lower=lower,upper=upper,
            optimizer="nlminb", fixed=fixed,neighb=3)

# Empirical estimation of the variogram:
vario = GeoVariogram(data=data,coordx=coords,maxdist=0.5)

# Plot of covariance and variogram functions:
GeoCovariogram(fit,show.vario=TRUE, vario=vario,pch=20)

################################################################
###
### Example 2. Plot of fitted covariance and fitted 
### and empirical semivariogram from a  Bernoulli 
###  RF with Genwend  correlation. 
###
###############################################################
set.seed(2111)

model="Binomial";n=1
# Set the coordinates of the points:
x = runif(500, 0, 1)
y = runif(500, 0, 1)
coords=cbind(x,y)

# Set the model's parameters:
corrmodel = "GenWend"
mean = 0
nugget = 0
scale = 0.2
smooth=0
power=4
param=list(mean=mean, nugget=nugget, scale=scale,smooth=0,power2=4)
# Simulation of the Gaussian RF:
data = GeoSim(coordx=coords, corrmodel=corrmodel, model=model,param=param,n=n)$data

start=list(mean=0,scale=scale)
fixed=list(nugget=nugget,power2=4,smooth=0)
# Maximum composite-likelihood fitting of the Binomial random field:
fit = GeoFit(data,coordx=coords, corrmodel=corrmodel,model=model,
             likelihood="Marginal",type='Pairwise',start=start,n=n,
             optimizer="BFGS", fixed=fixed,neighb=4)

# Empirical estimation of the variogram:
vario = GeoVariogram(data,coordx=coords,maxdist=0.5)

# Plot of covariance and variogram functions:
GeoCovariogram(fit, show.vario=TRUE, vario=vario,pch=20,ylim=c(0,0.3))


################################################################
###
### Example 3. Plot of fitted covariance and fitted 
### and empirical semivariogram from a  Weibull  RF
###   with Wend0 correlation. 
###
###############################################################
set.seed(111)

model="Weibull";shape=4
# Set the coordinates of the points:
x = runif(700, 0, 1)
y = runif(700, 0, 1)
coords=cbind(x,y)

# Set the model's parameters:
corrmodel = "Wend0"
mean = 0
nugget = 0
scale = 0.4
power2=4


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

start=list(mean=0,scale=scale,shape=shape)
I=Inf
lower=list(mean=-I,scale=0,shape=0)
upper=list(mean= I,scale=I,shape=I)
fixed=list(nugget=nugget,power2=power2)

fit = GeoFit(data,coordx=coords, corrmodel=corrmodel,model=model,
             likelihood="Marginal",type='Pairwise',start=start,
             lower=lower,upper=upper,
             optimizer="nlminb", fixed=fixed,neighb=3)

# Empirical estimation of the variogram:
vario = GeoVariogram(data,coordx=coords,maxdist=0.5)

# Plot of covariance and variogram functions:
GeoCovariogram(fit, show.vario=TRUE, vario=vario,pch=20)

################################################################
###
### Example 4. Plot of  fitted  and empirical semivariogram
### from a space time Gaussian random fields  
### with double Matern correlation. 
###
###############################################################
set.seed(92)
# Define the spatial-coordinates of the points:
x = runif(50, 0, 1)
y = runif(50, 0, 1)
coords=cbind(x,y)
# Define the temporal sequence:
time = seq(0, 10, 1)


param=list(mean=mean,nugget=nugget,
  smooth_s=0.5,smooth_t=0.5,scale_s=0.5/3,scale_t=2/2,sill=sill)
# Simulation of the spatio-temporal Gaussian random field:
data = GeoSim(coordx=coords, coordt=time, corrmodel="Matern_Matern",param=param)$data

fixed=list(nugget=0, mean=0, smooth_s=0.5,smooth_t=0.5)
start=list(scale_s=0.2, scale_t=0.5, sill=1)
# Maximum composite-likelihood fitting of the space-time Gaussian random field:
fit = GeoFit(data, coordx=coords, coordt=time, corrmodel="Matern_Matern", maxtime=1,
             neighb=3, likelihood="Marginal", type="Pairwise",fixed=fixed, start=start)

# Empirical estimation of spatio-temporal covariance:
vario = GeoVariogram(data,coordx=coords, coordt=time, maxtime=5,maxdist=0.5)

# Plot of the fitted space-time variogram
GeoCovariogram(fit,vario=vario,show.vario=TRUE)

# Plot of covariance, variogram and spatio and temporal profiles:
GeoCovariogram(fit,vario=vario,fix.lagt=1,fix.lags=1,show.vario=TRUE,pch=20)


################################################################
###
### Example 5. Plot of  fitted  and empirical semivariogram
### from a bivariate Gaussian random fields  
### with  Matern correlation. 
###
###############################################################
set.seed(92)
# Define the spatial-coordinates of the points:
x <- runif(600, 0, 2)
y <- runif(600, 0, 2)
coords <- cbind(x,y)

# Simulation of a bivariate spatial Gaussian RF:
# with a  Bivariate Matern
set.seed(12)
param=list(mean_1=4,mean_2=2,smooth_1=0.5,smooth_2=0.5,smooth_12=0.5,
           scale_1=0.12,scale_2=0.1,scale_12=0.15,
           sill_1=1,sill_2=1,nugget_1=0,nugget_2=0,pcol=-0.5)
data <- GeoSim(coordx=coords,corrmodel="Bi_matern",
              param=param)$data



# selecting fixed and estimated parameters
fixed=list(mean_1=4,mean_2=2,nugget_1=0,nugget_2=0,
      smooth_1=0.5,smooth_2=0.5,smooth_12=0.5)
start=list(sill_1=var(data[1,]),sill_2=var(data[2,]),
           scale_1=0.1,scale_2=0.1,scale_12=0.1,
           pcol=cor(data[1,],data[2,]))


# Maximum marginal pairwise likelihood
fitcl<- GeoFit(data=data, coordx=coords, corrmodel="Bi_Matern",
                     likelihood="Marginal",type="Pairwise",
                     optimizer="BFGS" , start=start,fixed=fixed,
                     neighb=4)
print(fitcl)

# Empirical estimation of spatio-temporal covariance:
vario = GeoVariogram(data,coordx=coords,maxdist=0.4,bivariate=TRUE)
GeoCovariogram(fitcl,vario=vario,show.vario=TRUE,pch=20)

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