| variog {geoR} | R Documentation |
Computes sample (empirical) variograms with options for the classical or robust
estimator. Output can be returned as a binned variogram, a
variogram cloud or a smoothed variogram. Data
transformation (Box-Cox) is allowed. Trends fitted by ordinary least
squares can be removed. In this case variograms are computed using the
residuals.
variog(geodata, coords=geodata$coords, data=geodata$data,
uvec = "default", trend = "cte", lambda = 1,
option = c("bin", "cloud", "smooth"),
estimator.type = c("classical", "modulus"),
nugget.tolerance = 0, max.dist = NULL, pairs.min = 2,
bin.cloud = FALSE, direction = "omnidirectional",
tolerance = pi/8, unit.angle = c("radians", "degrees"),
messages.screen = TRUE, ...)
geodata |
a list containing element coords
as described next. Typically an object of the class
"geodata" - a geoR data-set.
If not provided the arguments
coords must be provided instead. |
coords |
an n x 2 matrix containing
coordinates of the n data locations in each row.
Defaults to geodata$coords, if provided. |
data |
a vector or matrix with data values.
If a matrix is provided, each column is regarded as one variable or realization.
Defaults to geodata$data, if provided. |
uvec |
a vector with values defining the variogram binning. Only
used when
option = "bin". The values of uvec defines the mid-points of the bins.If uvec[1] > 0 the first bin is: 0 < u <= uvec[2] - 0.5*(uvec[2] - uvec[1]). If uvec[1] = 0 first bin is: 0 < u <= 0.5*uvec[1] and uvec[1] is replaced by the midpoint of this interval. |
trend |
specifies the mean part of the model.
The options are:
"cte" (constant mean),
"1st" (a first degree polynomial
on the coordinates), "2nd" (a second degree polynomial
on the coordinates), or a formula of the type ~X where X
is a matrix with the covariates (external trend). Defaults to "cte". |
lambda |
values of the Box-Cox transformation parameter. Defaults to 1 (no transformation). If another value is provided the variogram is computed after transforming the data. A case of particular interest is lambda = 0 which corresponds to log-transformation. |
option |
defines the output type: the options "bin" returns values of
binned variogram, "cloud" returns the variogram cloud and
"smooth" returns the kernel smoothed variogram.
Defaults to "bin". |
estimator.type |
"classical" computes the classical method of
moments estimator. "modulus" returns the variogram
estimator suggested by Hawkins and Cressie (see Cressie, 1993, pg 75).
Defaults to "classical". |
nugget.tolerance |
a numeric value. Points which are separated by a distance less than this value are considered co-located. Defaults to zero. |
max.dist |
a numerical value defining the maximum distance for the variogram. Pairs of locations separated for distance larger than this value are ignored for the variogram calculation. Defaults to the maximum distance among the pairs of data locations. |
pairs.min |
a integer number defining the minimum numbers of
pairs for the bins.
For option = "bin",
bins with number of pairs smaller than this
value are ignored. Defaults to NULL. |
bin.cloud |
logical. If TRUE and
option = "bin" the cloud values for each class are
included in the output. Defaults to FALSE. |
direction |
a numerical value for the directional (azimuth) angle. This used to specify directional variograms. Default defines the omnidirectional variogram. The value must be in the interval [0, 180] degrees. |
tolerance |
numerical value for the tolerance angle, when computing directional variograms. The value must be in the interval [0, 90] degrees. Defaults to pi/8. |
unit.angle |
defines the unit for the specification of angles in
the two previous arguments. Options are "degrees" and "radians". |
messages.screen |
logical. Indicates whether status messages should be printed on the screen (or output device) while the function is running. |
... |
arguments to be passed to the function ksmooth, if
option = "smooth". |
Variograms are widely used in geostatistical analysis for exploratory purposes, to estimate covariance parameters and/or to compare theoretical and fitted models against sample variograms.
The two estimators currently implemented are:
gamma(h) = (1/N_h) sum (Y(x_i+h) - Y(x_i))^2
gamma(h) = ((1/N_h) sum |Y(x_(i+h)) - Y(x_i)|^(1/2))^4
An object of the class variogram which is a
list with the following components:
u |
a vector with distances. |
v |
a vector with estimated variogram values at distances given
in u. |
n |
number of pairs in each bin, if
option = "bin". |
var.mark |
variance of the data. |
output.type |
echoes the option argument. |
estimator.type |
echoes the type of estimator used. |
direction |
direction for which the variogram was computed. |
tolerance |
tolerance angle for directional variogram. |
uvec |
lags provided in the function call. |
call |
the function call. |
Paulo J. Ribeiro Jr. Paulo.Ribeiro@est.ufpr.br,
Peter J. Diggle p.diggle@lancaster.ac.uk.
Cressie, N.A.C (1993) Statistics for Spatial Data. New York: Wiley.
Further information about geoR can be found at:
http://www.maths.lancs.ac.uk/~ribeiro/geoR.html.
variog4 for more on computation of
directional variograms,
variog.model.env and variog.mc.env for
variogram envelopes,
variofit for variogram based
parameter estimation and
plot.variogram for graphical output.
# Loading data:
if(is.R()) data(s100)
#
# computing variograms:
#
# binned variogram
vario.b <- variog(s100, max.dist=1)
# variogram cloud
vario.c <- variog(s100, max.dist=1, op="cloud")
#binned variogram and stores the cloud
vario.bc <- variog(s100, max.dist=1, bin.cloud=TRUE)
# smoothed variogram
vario.s <- variog(s100, max.dist=1, op="sm", band=0.2)
#
#
# plotting the variograms:
par(mfrow=c(2,2))
plot(vario.b, main="binned variogram")
plot(vario.c, main="variogram cloud")
plot(vario.bc, bin.cloud=TRUE, main="clouds for binned variogram")
plot(vario.s, main="smoothed variogram")
# computing a directional variogram
vario.0 <- variog(s100, max.dist=1, dir=0, tol=pi/8)
plot(vario.b, type="l", lty=2)
lines(vario.0)
legend(0, 1.2, legend=c("omnidirectional", expression(0 * degree)), lty=c(2,1))
#