R: Fit a spatio-temporal sample variogram to a sample variogram

fit.StVariogram {gstat} | R Documentation

## Fit a spatio-temporal sample variogram to a sample variogram

### Description

Fits a spatio-temporal variogram of a given type to spatio-temporal sample variogram.

### Usage

    fit.StVariogram(object, model, ...,  method = "L-BFGS-B",
    	lower, upper, fit.method = 6, stAni=NA, wles)

### Arguments

`object` | The spatio-temporal sample variogram. Typically output from `variogramST`
`model` | The desired spatio-temporal model defined through `vgmST`.
`...` | further arguments passed to `optim`. `extractParNames` provides the parameter structure of spatio-temporal variogram models that help to provide sensible `upper` and `lower` limits.
`lower` | Lower limits used by optim. If missing, the smallest well defined values are used (mostly near 0).
`upper` | Upper limits used by optim. If missing, the largest well defined values are used (mostly `Inf`).
`method` | fit method, pass to `optim`
`fit.method` | an integer between 0 and 13 determine the fitting routine (i.e. weighting of the squared residuals in the LSE). Values 0 to 6 correspond with the pure spatial version (see `fit.variogram`). See the details section for the meaning of the other values (partly experimental).
`stAni` | The spatio-temporal anisotropy that is used in the weighting. Might be missing if the desired spatio-temporal variogram model does contain a spatio-temporal anisotropy parameter (this might cause bad convergence behaviour). The default is `NA` and will be understood as identity (1 temporal unit = 1 spatial unit). As this only in very few cases a valid assumption, a warning is issued.
`wles` | Should be missing; only for backwards compatibility, `wles = TRUE` corresponds to `fit.method = 1` and `wles = FALSE` corresponds to `fit.method = 6`.

### Details

The following list summarizes the meaning of the `fit.method` argument which is essential a weighting of the squared residuals in the least-squares estimation. Please note, that weights based on the models gamma value might fail to converge properly due to the dependence of weights on the variogram estimate:

`fit.method = 0`

  no fitting, however the MSE between the provided variogram model and sample variogram surface is calculated.

`fit.method = 1`

  Number of pairs in the spatio-temporal bin: N[j]

`fit.method = 2`

  Number of pairs in the spatio-temporal bin divided by the square of the current variogram model's value: N[j]/gamma(h[j],u[j])^2

`fit.method = 3`

  Same as `fit.method = 1` for compatibility with `fit.variogram` but as well evaluated in R.

`fit.method = 4`

  Same as `fit.method = 2` for compatibility with `fit.variogram` but as well evaluated in R.

`fit.method = 5`

  Reserved for REML for compatibility with `fit.variogram`, not yet implemented.

`fit.method = 6`

  No weights.

`fit.method = 7`

  Number of pairs in the spatio-temporal bin divided by the square of the bin's metric distance. If `stAni` is not specified, the model's parameter is used to calculate the metric distance across space and time: N[j]/(h[j]^2+ stAni^2*u[j]^2)

`fit.method = 8`

  Number of pairs in the spatio-temporal bin divided by the square of the bin's spatial distance. N[j]/h[j]^2. Note that the 0 distances are replaced by the smallest non-zero distances to avoid division by zero.

`fit.method = 9`

  Number of pairs in the spatio-temporal bin divided by the square of the bin's temporal distance. N[j]/u[j]^2. Note that the 0 distances are replaced by the smallest non-zero distances to avoid division by zero.

`fit.method = 10`

  Reciprocal of the square of the current variogram model's value: 1/gamma(h[j],u[j])^2

`fit.method = 11`

  Reciprocal of the square of the bin's metric distance. If `stAni` is not specified, the model's parameter is used to calculate the metric distance across space and time: 1/(h[j]^2+ stAni^2*u[j]^2)

`fit.method = 12`

  Reciprocal of the square of the bin's spatial distance. 1/h[j]^2. Note that the 0 distances are replaced by the smallest non-zero distances to avoid division by zero.

`fit.method = 13`

  Reciprocal of the square of the bin's temporal distance. 1/u[j]^2. Note that the 0 distances are replaced by the smallest non-zero distances to avoid division by zero.

See also Table 4.2 in the gstat manual for the original spatial version.

### Value

Returns a spatio-temporal variogram model, as S3 class StVariogramModel. It carries the temporal and spatial unit as attributes `"temporal unit"` and `"spatial unit"` in order to allow `krigeST` to adjust for different units. The units are obtained from the provided empirical variogram. Further attributes are the optim output `"optim.output"` and the always not weighted mean squared error `"MSE"`.

### Author(s)

Benedikt Graeler

### See Also

`fit.variogram` for the pure spatial case. `extractParNames` helps to understand the parameter structure of spatio-temporal variogram models.

### Examples

    # separable model: spatial and temporal sill will be ignored
    # and kept constant at 1-nugget respectively. A joint sill is used.
    ## Not run:
    separableModel <- vgmST("separable",
                            method = "Nelder-Mead", # no lower & upper needed
                            space=vgm(0.9,"Exp", 123, 0.1),
                            time =vgm(0.9,"Exp", 2.9, 0.1),
                            sill=100)

    data(vv)
    separableModel <- fit.StVariogram(vv, separableModel,
                                      method="L-BFGS-B",
                                      lower=c(10,0,0.01,0,1),
                                      upper=c(500,1,20,1,200))
    plot(vv, separableModel)

    ## End(Not run) # dontrun

[Package gstat version 2.0-3 Index]