Dear All, We know that the estimation of covariance parameters is an important problem for spatial processes because the variogram shows the spatial variation. In many cases to select the best variogram model some parametric models considered and some criterions such as mean prediction error, mean square error, correlation between the observed and predicted values and correlation between the predicted and the residual values in cross validation method uses to select the best variogram model.
Below codes get an example whit two variogram models which are have very different parameters (sill, range and nugget) but values of mentioned criterions are approximately equal for them. Why? What is the role of variogram? What is the role of empirical variogram when a variogram function which is so far away than it can has approximately equaled cross validation results. library(gstat) data(meuse) coordinates(meuse)<-~x+y v<-variogram(log(zinc)~1,meuse) v.f<-fit.variogram(v,vgm(.205,"Mat",700,0.008,kappa=1)) plot(v,v.f) v.ff<-fit.variogram(v,vgm(.205,"Mat",700,0.008,kappa=1) ,fit.sills =F, fit.ranges =F) plot(v,v.ff) k1<-krige.cv(log(zinc)~1,meuse,v.f) k2<-krige.cv(log(zinc)~1,meuse,v.ff) mean(k1$residual) mean(k2$residual) mean(k1$residual^2) mean(k2$residual^2) cor(k1$var1.pred,k1$observed) cor(k2$var1.pred,k2$observed) cor(k1$var1.pred,k1$residual) cor(k2$var1.pred,k2$residual) Best, Saman. -- Saman Monfared Msc, Department of Statistics, Shiraz University, Shiraz 71454, Iran Email: samanmonfar...@gmail.com Tel: +98 917 5305167 _______________________________________________ R-sig-Geo mailing list R-sig-Geo@r-project.org https://stat.ethz.ch/mailman/listinfo/r-sig-geo