Computes the fitted variogram model.
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. UTF-8
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, ...)
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.The function computes the fitted variogram model
Produces a plot. No values are returned.
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.
GeoFit.
Moreno Bevilacqua, moreno.bevilacqua89@gmail.com ,https://sites.google.com/view/moreno-bevilacqua/home, Víctor Morales Oñate, victor.morales@uv.cl , https://sites.google.com/site/moralesonatevictor/, Christian", Caamaño-Carrillo, chcaaman@ubiobio.cl ,https://www.researchgate.net/profile/Christian-Caamano
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)