Variogram.gls {nlme} | R Documentation

## Calculate Semi-variogram for Residuals from a gls Object

### Description

This method function calculates the semi-variogram for the residuals from a `gls` fit. The semi-variogram values are calculated for pairs of residuals within the same group level, if a grouping factor is present. If `collapse` is different from `"none"`, the individual semi-variogram values are collapsed using either a robust estimator (`robust = TRUE`) defined in Cressie (1993), or the average of the values within the same distance interval. The semi-variogram is useful for modeling the error term correlation structure.

### Usage

    ## S3 method for class 'gls':
    Variogram(object, distance, form, resType, data,
          na.action, maxDist, length.out, collapse, nint, breaks,
          robust, metric, ...)

### Arguments

`object` | an object inheriting from class `gls`, representing a generalized least squares fitted model.
`distance` | an optional numeric vector with the distances between residual pairs. If a grouping variable is present, only the distances between residual pairs within the same group should be given. If missing, the distances are calculated based on the values of the arguments `form`, `data`, and `metric`, unless `object` includes a `corSpatial` element, in which case the associated covariate (obtained with the `getCovariate` method) is used.
`form` | an optional one-sided formula specifying the covariate(s) to be used for calculating the distances between residual pairs and, optionally, a grouping factor for partitioning the residuals (which must appear to the right of a `|` operator in `form`). Default is `~1`, implying that the observation order within the groups is used to obtain the distances.
`resType` | an optional character string specifying the type of residuals to be used. If `"response"`, the "raw" residuals (observed - fitted) are used; else, if `"pearson"`, the standardized residuals (raw residuals divided by the corresponding standard errors) are used; else, if `"normalized"`, the normalized residuals (standardized residuals pre-multiplied by the inverse square-root factor of the estimated error correlation matrix) are used. Partial matching of arguments is used, so only the first character needs to be provided. Defaults to `"pearson"`.
`data` | an optional data frame in which to interpret the variables in `form`. By default, the same data used to fit `object` is used.
`na.action` | a function that indicates what should happen when the data contain `NA`s. The default action (`na.fail`) causes an error message to be printed and the function to terminate, if there are any incomplete observations.
`maxDist` | an optional numeric value for the maximum distance used for calculating the semi-variogram between two residuals. By default all residual pairs are included.
`length.out` | an optional integer value. When `object` includes a `corSpatial` element, its semi-variogram values are calculated and this argument is used as the `length.out` argument to the corresponding `Variogram` method. Defaults to `50`.
`collapse` | an optional character string specifying the type of collapsing to be applied to the individual semi-variogram values. If equal to `"quantiles"`, the semi-variogram values are split according to quantiles of the distance distribution, with equal number of observations per group, with possibly varying distance interval lengths. Else, if `"fixed"`, the semi-variogram values are divided according to distance intervals of equal lengths, with possibly different number of observations per interval. Else, if `"none"`, no collapsing is used and the individual semi-variogram values are returned. Defaults to `"quantiles"`.
`nint` | an optional integer with the number of intervals to be used when collapsing the semi-variogram values. Defaults to `20`.
`robust` | an optional logical value specifying if a robust semi-variogram estimator should be used when collapsing the individual values. If `TRUE` the robust estimator is used. Defaults to `FALSE`.
`breaks` | an optional numeric vector with the breakpoints for the distance intervals to be used in collapsing the semi-variogram values. If not missing, the option specified in `collapse` is ignored.
`metric` | an optional character string specifying the distance metric to be used. The currently available options are `"euclidean"` for the root sum-of-squares of distances; `"maximum"` for the maximum difference; and `"manhattan"` for the sum of the absolute differences. Partial matching of arguments is used, so only the first three characters need to be provided. Defaults to `"euclidean"`.
`...` | 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. If the semi-variogram values are collapsed, an extra column, `n.pairs`, with the number of residual pairs used in each semi-variogram calculation, is included in the returned data frame. If `object` includes a `corSpatial` element, a data frame with its corresponding semi-variogram is included in the returned value, as an attribute `"modelVariog"`. 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

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

### Examples

    data(BodyWeight)
    ## Not run:
    fm1 <- gls(weight ~ Time * Diet, BodyWeight)
    Variogram(fm1, form = ~ Time | Rat)[1:10,]
    ## End(Not run)

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