evgram {gear}

Empirical (semi-)variogram

Description

evgram computes the empirical semivariogram of data based on the specified formula indicating the response and trend. See Details. The variogram is twice the semivariogram. If a trend is specified, then the semivariogram is constructed using the residuals of lm(formula, data).

Usage

evgram(
  formula,
  data,
  coordnames = NULL,
  nbins = 10,
  maxd = NULL,
  angle = 0,
  ndir = 1,
  type = "standard",
  npmin = 2,
  longlat = FALSE,
  verbose = TRUE,
  invert = TRUE
)

Arguments

formula

A formula describing the relationship between the response and any covariates of interest, e.g., response ~ 1. The variogram is computed for the residuals of the linear model lm(formula, data).

data

A data.frame, SpatialPointsDataFrame, SpatialPixelsDataFrame, or SpatialGridDataFrame object.

coordnames

The columns of data containing the spatial coordinates, provided as a formula (e.g., ~ x + y), column numbers (e.g., c(1, 2)), or column names (e.g., c("x", "y")). The default is NULL.

nbins

The number of bins (tolerance regions) to use when estimating the empirical semivariogram.

maxd

The maximum distance used when calculating the semivariogram. Default is NULL, in which case half the maximum distance between coordinates is used.

angle

A single value (in degrees) indicating the starting direction for a directional variogram. The default is 0.

ndir

The number of directions for which to calculate a empirical semivariogram. The default is 1, meaning calculate an omnidirectional semivariogram.

type

The name of the estimator to use in the estimation process. The default is "standard", the typical method-of-moments estimator. Other options include "cressie" for the robust Cressie-Hawkins estimator, and "cloud" for a semivariogram cloud based on the standard estimator. If "cloud" is specified, the nbins argument is ignored.

npmin

The minimum number of pairs of points to use in the semivariogram estimator. For any bins with fewer points, the estimate for that bin is dropped.

longlat

A logical indicating whether Euclidean (FALSE) or Great Circle distance (WGS84 ellipsoid) (longlat = TRUE) should be used. Default is FALSE.

verbose

Logical value indicating whether computation information should be printed. Default is TRUE.

invert

A logical value indicating whether the axes of the coordinates should be inverted (i.e., the x- and y-axis are switched). The default is TRUE to mimic results from other geostatistical R packages like gstat, geoR, and other software like GSLIB and GeoEAS. Set to FALSE to use the typical x- and y-axes.

Details

Note that the directions may be different from other packages (e.g., gstat or geoR packages) because those packages calculate angles clockwise from the y-axis, which is a convention frequently seen in geostatistics (e.g., the GSLIB software library). If invert = TRUE, the directions should be the same.

Computing the empirical semivariogram for the residuals of lm(response ~ 1) will produce identical results to simply computing the empirical semivariogram from the original response. However, if a trend is specified (the righthand side of ~ has non-trival covariates), then the empirical semivariogram of the residuals will differ from that of the original response. A trend should be specified when the mean is non-stationary over the spatial domain.

Value

Returns an evgram.

Author(s)

Joshua French

Examples

data(co)
v = evgram(Al ~ 1, co, ~ easting + northing)
plot(v)
v2 = evgram(Al ~ 1, co, c("easting", "northing"), angle = 22.5, ndir = 4)
plot(v2)