est.variogram {sgeostat}

Variogram Estimator

Description

Calculate empirical variogram estimates.

An object of class variogram contains empirical variogram estimates generated from a point object and a pair object. A variogram object is stored as a data frame containing six columns: lags, bins, classic, robust, med, 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, and med vectors contain the classical,

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

robust,

\gamma_{m}(h)=\frac{(\frac{1}{n}\sum_{(i,j) \in N(h)} (\sqrt{|z(x_{i})-z(x_{j})|}))^{4}}{0.457 + \frac{0.494}{n}}

and median

\gamma_{m}(h)=\frac{(\mbox{median}_{(i,j) \in N(h)} (\sqrt{|z(x_{i})-z(x_{j})|}))^{4}}{0.457 + \frac{0.494}{|N(h)|}}

variogram estimates for each lag, respectively (see Cressie, 1993, p. 75). The n vector contains the number |N(h)| of pairs of points in each lag N(h).

Usage

est.variogram(point.obj, pair.obj, a1, a2) 

Arguments

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

Value

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

n

vector of the number of pairs in each lag

References

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

See Also

point, pair

Examples

maas.v<-est.variogram(maas.point,maas.pair,'zinc')