est.variograms: Variogram Estimator
In geospt: Geostatistical Analysis and Design of Optimal Spatial Sampling Networks

Description Usage Arguments Value Note References See Also Examples

Calculate empirical variogram estimates. An object of class variogram contains empirical variogram estimates which are generated from a point object and a pair object. A variogram object is stored as a data frame containing seven columns: lags, bins, classic, robust,med, trim and n. The length of each vector is equal to the number of lags in the pair object used to create the variogram object, say l. The lags vector contains the lag numbers for each lag, beginning with one (1) and going to the number of lags (l). The bins vector contains the spatial midpoint of each lag. The classic, robust, med and trimmed.mean vectors contain: the classical, robust, median, and trimmed mean, respectively, which are given, respectively, by (see Cressie, 1993, p. 75)

classical

γ_{c}(h)=\frac{1}{n}∑_{(i,j)\in N(h)}(z(x_{i})-z(x_{j}))^{2}

robust,

γ_{m}(h)=\frac{(\frac{1}{n}∑_{(i,j)\in N(h)} (√{|z(x_{i})-z(x_{j})|}))^{4}}{0.457+\frac{0.494}{|N(h)|}}

median

γ_{me}(h)=\frac{\mbox(median_{(i,j)\in N(h)} (√{|z(x_{i})-z(x_{j})|}))^{4}}{0.457+\frac{0.494}{|N(h)|}}

and trimmed mean

γ_{tm}(h)=\frac{(trimmed.mean(√{|z(x_{i})-z(x_{j})|}))^{4}}{0.457+\frac{0.494}{|N(h)|}}

The n vector contains the number |N(h)| of pairs of points in each lag N(h).

1	est.variograms(point.obj, pair.obj, a1, a2, trim)

`point.obj`	a point object generated by `point()`
`pair.obj`	a pair object generated by `pair()`
`a1`	a variable to calculate semivariogram for
`a2`	an optional variable name, if entered cross variograms will be created between `a1` and `a2`
`trim`	percent of trimmed mean

A variogram object:

`lags`	vector of lag identifiers
`bins`	vector of midpoints of each lag
`classic`	vector of classic variogram estimates for each lag
`robust`	vector of robust variogram estimates for each lag
`med`	vector of median variogram estimates for each lag
`trimmed.mean`	vector of trimmed mean variogram estimates for each lag
`n`	vector of the number of pairs in each lag

Based on the est.variogram function of the sgeostat package

Bardossy, A., 2001. Introduction to Geostatistics. University of Stuttgart.

Cressie, N.A.C., 1993. Statistics for Spatial Data. Wiley.

Majure, J., Gebhardt, A., 2009. sgeostat: An Object-oriented Framework for Geostatistical Modeling in S+. R package version 1.0-23.

Roustant O., Dupuy, D., Helbert, C., 2007. Robust Estimation of the Variogram in Computer Experiments. Ecole des Mines, D<e9>partement 3MI, 158 Cours Fauriel, 42023 Saint-Etienne, France

http://www.gis.iastate.edu/SGeoStat/homepage.html

point, pair

library(sgeostat, pos=which(search()=="package:gstat")+1)
data(maas)
maas.point <- point(maas) 
maas.pair <- pair(maas.point, num.lags=24, maxdist=2000) 
maas.v <- est.variograms(maas.point,maas.pair,'zinc',trim=0.1) 
maas.v