variogram.cloud(formula, data=<<see below>>, subset=<<see below>>,
                na.action=<<see below>>, azimuth=0, tol.azimuth=90,
                maxdist=<<see below>>, bandwidth=1e+307,
                FUN=function(zi, zj) (zi - zj)^2/2))

formula:

formula defining the response and the predictors. In general, its form is: z ~ x + y The z variable is a numeric response. Variables x and y are the locations. All variables in the formula must be vectors of equal length with no missing values (NAs). The formula may also contain expressions for the variables, e.g. sqrt(count) or log(age+1). The right hand side may also be a call to the loc function e.g. loc(x,y). The loc function can be used to correct for geometric anisotropy, see the loc help file.

data:

an optional data frame in which to find the objects mentioned in formula.

subset:

expression saying which subset of the rows of the data should be used in the fit. This can be a logical vector (which is replicated to have length equal to the number of observations), or a numeric vector indicating which observation numbers are to be included, or a character vector of the row names to be included.

na.action:

a function to filter missing data. This is applied to the model.frame after any subset argument has been used. The default (with na.fail) is to create an error if any missing values are found. A possible alternative is na.omit, which deletes observations that contain one or more missing values.

azimuth:

the clockwise direction angle in degrees from North-South. Only pairs of points in this direction plus or minus tol.azimuth will be included in the output.

tol.azimuth:

the tolerance angle, in degrees. tol.azimuth greater than or equal to 90 implies the of use all directions.

maxdist:

the maximum distance to consider. The default is half the maximum observed distance.

bandwidth:

the maximum perpendicular distance to consider.

FUN:

a function of two variables that is to be computed. The default function is the contribution to the classical empirical variogram for the pair z[i], z[j].

distance:

the distance between the two points.

gamma:

the value of FUN for the z[iindex], z[jindex].

iindex:

the index into the original data for the first value of the pair.

jindex:

the index into the original data for the second value of the pair.

The return object has an attribute call with an image of the call that produced the object.

If all directions and distances are included the return object will have n*(n-1)/2 rows where n is the number of observations. This can get very large, even for relatively small n. May want to consider limiting the size by setting maxdist. Typically values beyond half the maximum distance in the data are not used in estimating the variogram function.

v1 <- variogram.cloud(coal ~ x + y, data=coal.ash)
plot(v1)
boxplot(v1)