# Variogram.default: Calculate Semi-variogram In nlme: Linear and Nonlinear Mixed Effects Models

## 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

 ```1 2``` ```## 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)

Jos<c3><a9> Pinheiro and Douglas Bates [email protected]

## References

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

## See Also

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

## Examples

 ```1 2 3 4 5 6``` ```## 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) ```

nlme documentation built on Feb. 17, 2018, 1:01 a.m.