Calculate Semi-variogram

This method function calculates the semi-variogram for an arbitrary vector object, according to the distances in distance. For each pair of elements \(x,y\) in object, the corresponding semi-variogram is \((x-y)^2/2\). The semi-variogram is useful for identifying and modeling spatial correlation structures in observations with constant expectation and constant variance.

# Default S3 method
Variogram(object, distance, ...)

Arguments

object

a numeric vector with the values to be used for calculating the semi-variogram, usually a residual vector from a fitted model.

distance

a numeric vector with the pairwise distances corresponding to the elements of object. The order of the elements in distance must correspond to the pairs (1,2), (1,3), ..., (n-1,n), with n representing the length of object, and must have length n(n-1)/2.

...

some methods for this generic require additional arguments. None are used in this method.

Value

a data frame with columns variog and dist representing, respectively, the semi-variogram values and the corresponding distances. The returned value inherits from class Variogram.

References

Cressie, N.A.C. (1993), "Statistics for Spatial Data", J. Wiley & Sons.

Author

José Pinheiro and Douglas Bates bates@stat.wisc.edu

Examples

fm1 <- lm(follicles ~ sin(2 * pi * Time) + cos(2 * pi * Time), Ovary,
          subset = Mare == 1)
Variogram(resid(fm1), dist(1:29))[1:10,]
#>          variog dist
#> 1  10.098577567    1
#> 2   0.003014275    2
#> 3   3.876160700    3
#> 4  15.892707794    4
#> 5  37.412782986    5
#> 6  23.258010769    6
#> 7  13.180732207    7
#> 8  21.562480671    8
#> 9   0.003450613    9
#> 10  0.923619345   10