gboot_variogram {geotoolsR}

Variogram bootstrap

Description

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

Usage

gboot_variogram(data,var,model,B)

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).

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.

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.

Author(s)

Diogo Francisco Rossoni [e-mail]

Vinicius Basseto Felix [e-mail]

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


# 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