gstat (version 0.9-11)

variogram: Calculate Sample or Residual Variogram or Variogram Cloud

Description

Calculates the sample variogram from data, or in case of a linear model is given, for the residuals, with options for directional, robust, and pooled variogram, and for irregular distance intervals.

Usage

variogram(object, ...)
variogram(formula, locations, data, ...)
variogram(y, locations, X, cutoff, width = cutoff/15, alpha = 0, beta = 0, 
	tol.hor = 90/length(alpha), tol.ver = 90/length(beta), 
	cressie = FALSE, dX = numeric(0), boundaries = numeric(0), 
	cloud = FALSE, trend.beta = NULL, debug.level = 1, cross = TRUE, 
	...)
print.variogram(v, ...)
print.variogram.cloud(v, ...)

Arguments

object

object of class gstat; in this form, direct and cross (residual) variograms are calculated for all variables and variable pairs defined in object

formula

formula defining the response vector and (possible) regressors, in case of absence of regressors, use e.g. z~1

data

data frame where the names in formula are to be found

locations

spatial data locations. For variogram.formula: a formula with only the coordinate variables in the right hand (explanatory variable) side e.g. ~x+y; see examples.

For variogram.default: a matrix, with the number of rows matching that of y,

...

any other arguments that will be passed to variogram.default

y

vector with responses

X

(optional) matrix with regressors/covariates; the number of rows should match that of y, the number of columns equals the number of regressors (including intercept)

cutoff

spatial separation distance up to which point pairs are included in semivariance estimates

width

the width of subsequent distance intervals into which data point pairs are grouped for semivariance estimates

alpha

direction in plane (x,y), in positive degrees clockwise from positive y (North): alpha=0 for direction North (increasing y), alpha=90 for direction East (increasing x); optional a vector of directions in (x,y)

beta

direction in z, in positive degrees up from the (x,y) plane;

tol.hor

horizontal tolerance angle in degrees

tol.ver

vertical tolerance angle in degrees

cressie

logical; if TRUE, use Cressie's robust variogram estimate; if FALSE use the classical method of moments variogram estimate

dX

include a pair of data points $y(s_1),y(s_2)$ taken at locations $s_1$ and $s_2$ for sample variogram calculation only when $||x(s_1)-x(s_2)|| < dX$ with and $x(s_i)$ the vector with regressors at location $s_i$, and $||.||$ the 2-norm. This allows poole

boundaries

numerical vector with distance interval boundaries; values should be strictly increasing

cloud

logical; if TRUE, calculate the semivariogram cloud

trend.beta

vector with trend coefficients, in case they are known. By default, trend coefficients are estimated from the data.

debug.level

integer; set gstat internal debug level

cross

logical; if FALSE, no cross variograms are calculated when object is of class gstat and has more than one variable

v

object of class variogram or variogram.cloud to be printed

Value

• an object of class "variogram" with the following fields:
• np
  the number of point pairs for this estimate; in case of a variogram.cloud see below
• dist
  the average distance of all point pairs considered for this estimate
• gamma
  the actual sample variogram estimate
• dir.hor
  the horizontal direction
• dir.ver
  the vertical direction
• id
  the combined id pair
• If cloud is TRUE: an object of class "variogram.cloud", with the field np encoding the numbers of the point pair that contributed to a variogram cloud estimate, as follows. The first point is found by the integer division of np by $2^{16}$, the second point by the remainder of that division. print.variogram.cloud shows no np field, but does show in addition:
• left
  for variogram.cloud: data id (row number) of one of the data pair
• right
  for variogram.cloud: data id (row number) of the other data in the pair

synopsis

variogram(object, ...)

References

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

http://www.gstat.org/

See Also

print.variogram, plot.variogram, plot.variogram.cloud, for variogram models: vgm, to fit a variogram model to a sample variogram: fit.variogram

Examples

data(meuse)
# no trend:
variogram(log(zinc)~1, loc=~x+y, meuse)
# residual variogram w.r.t. a linear trend:
variogram(log(zinc)~x+y, loc=~x+y, meuse)
# directional variogram:
variogram(log(zinc)~x+y, loc=~x+y, meuse, alpha=c(0,45,90,135))