R: Fitting model parameters to spatial data (regionalised...

RFfit {RandomFields}

R Documentation

Fitting model parameters to spatial data (regionalised variables) and to linear (mixed) models

Description

The function estimates arbitrary parameters of a random field specification with various methods. Currently, the models to be fitted can be

The fitting of max-stable random fields and others has not been implemented yet.

Usage

RFfit(model, x, y = NULL, z = NULL, T = NULL, grid=NULL, data,
      lower = NULL, upper = NULL, methods,
      sub.methods, optim.control = NULL, users.guess = NULL,
      distances = NULL, dim, transform = NULL, params=NULL, ...)

Arguments

`model,params`	object of class `RMmodel`, `RFformula` or `formula`; best is to consider the examples below, first. The argument `params` is a list that specifies free parameters in a formula description, see RMformula. All parameters that are set to `NA` will be estimated; see the examples below. Type `RFgetModelNames(type="variogram")` to get all options for `model`.
`x`	vector of x coordinates, or object of class `GridTopology` or `raster`; for more options see RFsimulateAdvanced.
`y,z`	optional vectors of y (z) coordinates, which should not be given if `x` is a matrix.
`T`	optional vector of time coordinates, `T` must always be an equidistant vector. Instead of `T=seq(from=From, by=By, len=Len)`, one may also write `T=c(From, By, Len)`.
`grid`	logical; the function finds itself the correct value in nearly all cases, so that usually `grid` need not be given. See also RFsimulateAdvanced.
`data`	matrix, data.frame or object of class `RFsp`; If a matrix is given the ordering of the colums is the following: space, time, multivariate, repetitions, i.e. the index for the space runs the fastest and that for repetitions the slowest.
`lower`	list or vector. Lower bounds for the parameters. If `lower` is a vector, `lower` has to be a vector as well and its length must equal the number of parameters to be estimated. The order of `lower` has to be maintained. A component being `NA` means that no manual lower bound for the corresponding parameter is set. If `lower` is a list, `lower` has to be of (exactly) the same structure of the model.
`upper`	list or vector. Upper bounds for the parameters. See `lower`.
`methods`	Main methods to be used for estimating. If several methods are given, estimation will be performed with each method and the results reported.
`sub.methods`	variants of the least squares fit of the variogram. variants of the maximum likelihood fit of the covariance function.. See Details.
`users.guess`	User's guess of the parameters. All the parameters must be given using the same rules as for `lower` (except that no NA's should be contained).
`distances,dim`	another alternative for the argument `x` to pass the (relative) coordinates, see RFsimulateAdvanced.
`optim.control`	control list for `optim`, which uses ‘L-BFGS-B’. However `parscale` may not be given.
`transform`	obsolete for users; use `param` instead. `transform=list()` will return structural information to set up the correct function.
`...`	for advanced use: further options and control arguments for the simulation that are passed to and processed by `RFoptions`. If `params` is given, then `...` may include also the variables used in `params`.

Details

For details on the simulation methods see

fitgauss for Gaussian random fields
fitgauss for linear models

If x-coordinates are not given, the function will check data for NAs and will perform imputing.

The function has many more options to tune the optimizer, see RFoptions for details.

If the model defines a Gaussian random field, the options for methods and submethods are currently "ml" and c("self", "plain", "sqrt.nr", "sd.inv", "internal"), respectively.

Value

The result depends on the logical value of spConform. If TRUE, an S4 object is created. In case the model indicates a Gaussian random field, an RFfit object is created.

If spConform=FALSE, a list is returned. In case the model indicates a Gaussian random field, the details are given in fitgauss.

Note

An important optional argument is boxcox which indicates a Box-Cox transformation; see boxcox in RFoptions and RFboxcox for details.
Instead of optim, other optimisers can be used, see RFfitOptimiser.
Several advanced options can be found in sections ‘General options’ and ‘fit’ of RFoptions.
In particular, boxcox, boxcox_lb, boxcox_ub allow Box-Cox transformation.
This function does not depend on the value of RFoptions()$PracticalRange. The function RFfit always uses the standard specification of the covariance model as given in RMmodel.

Author(s)

Martin Schlather, schlather@math.uni-mannheim.de, http://ms.math.uni-mannheim.de

References

Burnham, K. P. and Anderson, D. R. (2002) Model selection and Multi-Model Inference: A Practical Information-Theoretic Approach. 2nd edition. New York: Springer.

Examples

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again




RFoptions(modus_operandi="sloppy")


#########################################################
## simulate some data first                            ## 
points <- 100
x <- runif(points, 0, 3)
y <- runif(points, 0, 3) ## random points in square [0, 3]^2
model <- RMgencauchy(alpha=1, beta=2)
d <- RFsimulate(model, x=x, y=y, grid=FALSE, n=100) #1000


#########################################################
## estimation; 'NA' means: "to be estimated"           ##
estmodel <- RMgencauchy(var=NA, scale=NA, alpha=NA, beta=2) +
            RMtrend(mean=NA)
RFfit(estmodel, data=d)


#########################################################
## coupling alpha and beta                             ##
estmodel <- RMgencauchy(var=NA, scale=NA, alpha=NA, beta=NA) + 
            RMtrend(NA)
RFfit(estmodel, data=d, transform = NA) ## just for information
trafo <- function(a) c(a[1], rep(a[2], 2))
fit <- RFfit(estmodel, data=d,
             transform = list(c(TRUE, TRUE, FALSE), trafo))
print(fit)
print(fit, full=TRUE)

[Package RandomFields version 3.3.7 Index]