gboot_variogram: Variogram bootstrap

Description Usage Arguments Details Value Author(s) References Examples

Description

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

Usage

1

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 γ(h) = γ_{mod}(h)+ε, where γ_{mod}(h) is the fitted model. The steps of the algorithm are:

  1. Set h^*=h;

  2. Sample with replacement ε^* from ε - \bar ε;

  3. The new variogram will be γ^*(h^*) = γ_{mod}(h)+ε^*;

  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 [email protected]

Vinicius Basseto Felix [email protected]

References

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

Examples

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# 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

## Not run: 
# 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

## End(Not run)

Example output

Loading required package: geoR
--------------------------------------------------------------
 Analysis of Geostatistical Data
 For an Introduction to geoR go to http://www.leg.ufpr.br/geoR
 geoR version 1.7-5.2.1 (built on 2016-05-02) is now loaded
--------------------------------------------------------------

Loading required package: tidyr
Loading required package: dplyr

Attaching package: 'dplyr'

The following objects are masked from 'package:stats':

    filter, lag

The following objects are masked from 'package:base':

    intersect, setdiff, setequal, union

Loading required package: ggplot2
Warning message:
no DISPLAY variable so Tk is not available 
variog: computing omnidirectional variogram
variofit: covariance model used is spherical 
variofit: weights used: npairs 
variofit: minimisation function used: optim 
Parameters confidence interval (95%): 
        Parameter   Lower Estimate    Upper
1          Nugget  2.1125   2.4997   3.0046
2            Sill  4.0451   4.1215   4.2388
3    Contribution  1.1950   1.6217   2.0159
4           Range 68.8660  78.8282 127.7923
5 Practical Range 68.8660  78.8282 127.7923
variog: computing omnidirectional variogram
variofit: covariance model used is gaussian 
variofit: weights used: npairs 
variofit: minimisation function used: optim 
Parameters confidence interval (95%): 
        Parameter  Lower Estimate  Upper
1          Nugget 0.0018   0.0029 0.0038
2            Sill 0.0064   0.0064 0.0070
3    Contribution 0.0029   0.0036 0.0047
4           Range 2.0676   4.3071 3.7444
5 Practical Range 3.5786   7.4548 6.4808

geotoolsR documentation built on May 2, 2019, 5:51 a.m.