Computes fitted covariance and/or variogram
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).
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GeoResiduals(fit)
fit: A fitted object obtained from the GeoFit.Returns an (updated) object of class GeoFit
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) ########################### ###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)