Variogram.default {nlme} | R Documentation

## Calculate Semi-variogram

### Description

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.

### Usage

    ## 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`.

### Author(s)

Jose Pinheiro Jose.Pinheiro@pharma.novartis.com and Douglas Bates bates@stat.wisc.edu

### References

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

### See Also

`Variogram.gls`, `Variogram.lme`, `plot.Variogram`

### Examples

    data(Ovary)
    ## Not run:
    fm1 <- lm(follicles ~ sin(2 * pi * Time) + cos(2 * pi * Time), Ovary,
              subset = Mare == 1)
    Variogram(resid(fm1), dist(1:29))[1:10,]
    ## End(Not run)

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