geotoolsR (version 1.2.1)

gboot_variogram: Variogram bootstrap

Description

Perform a boostrap based on error from the fitted model of the variogram.

Usage

gboot_variogram(data,var,model,B)

Value

variogram_boot gives the variogram of each bootstrap.

variogram_or gives the original variogram.

pars_boot gives the estimatives of the nugget, sill, contribution, range and practical range for each bootstrap.

pars_or gives the original estimatives of the nugget, sill, contribution, range and practical range.

Invalid arguments will return an error message.

Arguments

data

object of the class geodata.

var

object of the class variogram.

model

object of the class variomodel.

B

number of the bootstrap that will be performed (default B=1000).

Author

Diogo Francisco Rossoni

Vinicius Basseto Felix

Details

The algorithm for the bootstrap variogram is the same presented for Davison and Hinkley (1997) for the non linear regression. We can write the variogram as \(\hat \gamma(h) = \gamma_{mod}(h)+\epsilon\), where \(\gamma_{mod}(h)\) is the fitted model. The steps of the algorithm are:

1. Set \(h^*=h\);

2. Sample with replacement \(\epsilon^*\) from \(\epsilon - \bar \epsilon\);

3. The new variogram will be \(\gamma^*(h^*) = \gamma_{mod}(h)+\epsilon^*\);

4. Calculate and save the statistics of interest;

5. Return to step 2 and repeat the process at least 1000 times.

References

DAVISON, A.C.; HINKLEY, D. V. Bootstrap Methods and their Application. [s.l.] Cambridge University Press, 1997. p. 582

Examples

# Example 1

## transforming the data.frame in an object of class geodata
data<- as.geodata(soilmoisture)

points(data) ## data visualization

var<- variog(data, max.dist = 140) ## Obtaining the variogram
plot(var)

## Fitting the model
mod<- variofit(var,ini.cov.pars = c(2,80),nugget = 2,cov.model = "sph")
lines(mod, col=2, lwd=2) ##fitted model

## Bootstrap procedure

boot<- gboot_variogram(data,var,mod,B=10)
## For better Confidence interval, try B=1000

gboot_CI(boot,digits = 4) ## Bootstrap Confidence Interval

gboot_plot(boot) ## Bootstrap Variogram plot

# \donttest{
# Example 2

## transforming the data.frame in an object of class geodata
data<- as.geodata(NVDI)

points(data) ## data visualization

var<- variog(data, max.dist = 18) ## Obtaining the variogram
plot(var)

## Fitting the model
mod<- variofit(var,ini.cov.pars = c(0.003,6),nugget = 0.003,cov.model = "gaus")
lines(mod, col=2, lwd=2) ##fitted model

## Bootstrap procedure

boot<- gboot_variogram(data,var,mod,B=10)
## For better Confidence interval, try B=1000

gboot_CI(boot,digits = 4) ## Bootstrap Confidence Interval

gboot_plot(boot) ## Bootstrap Variogram plot
# }