georob.control: Tuning Parameters for georob
In georob: Robust Geostatistical Analysis of Spatial Data

Description Usage Arguments Details Author(s) See Also Examples

This page documents the tuning parameters for georob. It describes the arguments of the functions control.georob, param.transf, fwd.transf, dfwd.transf, bwd.transf, rq.control, nleqslv.control and optim.control, which all serve to control the behaviour of georob.

georob.control(initial.method = c("lmrob", "rq", "lm"), bhat = NULL, 
    param.tf = param.transf(),fwd.tf = fwd.transf(), 
    deriv.fwd.tf = dfwd.transf(), bwd.tf = bwd.transf(), 
    safe.param = 1.e12, psi.func = c("logistic", "t.dist", "huber"),
    tuning.psi.nr = 1000, min.rweight = 0.25,
    irwls.initial = TRUE, irwls.maxiter = 50, 
    irwls.reltol = sqrt(.Machine[["double.eps"]]),
    force.gradient = FALSE, zero.dist = sqrt(.Machine[["double.eps"]]),
    cov.bhat = FALSE, full.cov.bhat = FALSE, cov.betahat = TRUE, 
    cov.bhat.betahat = FALSE, 
    cov.delta.bhat = TRUE, full.cov.delta.bhat = TRUE,
    cov.delta.bhat.betahat = TRUE,
    cov.ehat = TRUE, full.cov.ehat = FALSE,
    cov.ehat.p.bhat = FALSE, full.cov.ehat.p.bhat = FALSE,
    aux.cov.pred.target = FALSE, min.condnum = 1.e-12,
    rq = rq.control(), lmrob = lmrob.control(),
    nleqslv = nleqslv.control(), 

    optim = optim.control(), full.output = TRUE)
    
param.transf( variance = "log", snugget = "log", nugget = "log", scale = "log", 
    alpha = "identity", beta = "log", delta = "identity", 
    gamma = "identity", kappa = "identity", lambda = "identity", 
    mu = "log", nu = "log",
    f1 = "log", f2  ="log", omega = "rad", phi = "rad", zeta = "rad"
  )
  
fwd.transf(...)

dfwd.transf(...)

bwd.transf(...)

rq.control(tau = 0.5, rq.method = "br", rq.alpha = 0.1, ci = FALSE, iid = TRUE, 
    interp = TRUE, tcrit = TRUE, rq.beta = 0.99995, eps = 1e-06, 
    Mm.factor = 0.8, max.bad.fixup = 3)
               
nleqslv.control(nleqslv.method = c("Broyden", "Newton"), 
    global = c( "dbldog", "pwldog", "qline", "gline", "none" ),
    xscalm = c( "fixed", "auto" ), nleqslv.control = NULL)
    

    
optim.control(optim.method = c("BFGS", "Nelder-Mead", "CG", 
        "L-BFGS-B", "SANN", "Brent"), lower = -Inf, upper = Inf, 
    optim.control = NULL, hessian = TRUE)

`initial.method`	character keyword defining whether the function `lmrob` or `rq` is used to compute robust initial estimates of the regression parameters β (default `"lmrob"`). If the fixed effects model matrix has not full columns rank, then `lm` is used to compute initial values of the regression coefficients. Note that this requires robust estimation.
`bhat`	initial values for the spatial random effects hatB, with hatB=0 if `bhat` is equal to `NULL` (default).
`param.tf`	a function such as `param.transf`, which returns a named vector of character strings that define the transformations to be applied to the variogram parameters for model fitting, see Details.
`fwd.tf`	a function such as `fwd.transf`, which returns a named list of invertible functions to be used to transform variogram parameters, see Details.
`deriv.fwd.tf`	a function such as `dfwd.transf`, which returns a named list of functions corresponding to the first derivatives of `fwd.tf`, see Details.
`bwd.tf`	a function such as `bwd.transf`, which returns the named list of inverse functions corresponding to `fwd.tf`, see Details.
`safe.param`	maximum acceptable value for any variogram parameter. If trial parameter values generated by `optim` or `nleqslv` exceed `safe.param` then an error is signalled to force `optim` or `nleqslv` to update the trial values (default `1.e12`).
`psi.func`	character keyword defining what ψ_c-function should be used for robust model fitting. Possible values are `"logistic"` (a scaled and shifted logistic cdf, default), `"t.dist"` (re-descending ψ_c-function associated with Student t-distribution with c degrees of freedom) and `"huber"` (Huber's ψ_c-function).
`tuning.psi.nr`	positive numeric. If `tuning.psi` is less than `tuning.psi.nr` then the model is fitted robustly by solving the robustified estimating equations, and for `tuning.psi` equal to or larger than `tuning.psi.nr` the Gaussian restricted loglikelihood is maximized (default `1000`).
`min.rweight`	positive numeric. “Robustness weight” of the initial `lmrob` fit that observations must exceed to be used for computing robust initial estimates of variogram parameters by setting `initial.param = TRUE` (see `georob`; default `0.25`).
`irwls.initial`	logical. If `TRUE` (default) the estimating equations of B and β are always solved by IRWLS from the initial estimates of hatB and hatβ. If `FALSE` then IRWLS starts from respective estimates computed for the variogram parameter estimates of the previous iteration of `nleqslv` or `optim`.
`irwls.maxiter`	positive integer equal to the maximum number of IRWLS iterations to solve the estimating equations of B and β (default `50`).
`irwls.reltol`	numeric convergence criterion for IRWLS. Convergence is assumed if `max(abs(oldres-newres)) < sqrt(reltolnugget)`, where `oldres` and `newres` are the estimated residuals ε_i* of the previous and current iterations, respectively.
`force.gradient`	logical controlling whether the estimating equations or the gradient of the Gaussian restricted loglikelihood are evaluated even if all variogram parameters are fixed (default `FALSE`).
`zero.dist`	positive numeric equal to the maximum distance, separating two sampling locations that are still considered as being coincident.
`cov.bhat`	logical controlling whether the covariances of hatB are returned by `georob` (default `FALSE`).
`full.cov.bhat`	logical controlling whether the full covariance matrix (`TRUE`) or only the variance vector of hatB is returned (default `FALSE`).
`cov.betahat`	logical controlling whether the covariance matrix of hatβ is returned (default `TRUE`).
`cov.bhat.betahat`	logical controlling whether the covariance matrix of hatB and hatβ is returned (default `FALSE`).
`cov.delta.bhat`	logical controlling whether the covariances of B-hatB are returned (default `TRUE`).
`full.cov.delta.bhat`	logical controlling whether the full covariance matrix (`TRUE`) or only the variance vector of B-hatB is returned (default `TRUE`).
`cov.delta.bhat.betahat`	logical controlling whether the covariance matrix of B-hatB and hatβ is returned (default `TRUE`).
`cov.ehat`	logical controlling whether the covariances of hatε=Y-X hatβ - hatB are returned (default `TRUE`).
`full.cov.ehat`	logical controlling whether the full covariance matrix (`TRUE`) or only the variance vector of hatε=Y-X hatβ - hatB is returned (default `FALSE`).
`cov.ehat.p.bhat`	logical controlling whether the covariances of hatε+ hatB=Y-X hatβ are returned (default `FALSE`).
`full.cov.ehat.p.bhat`	logical controlling whether the full covariance matrix (`TRUE`) or only the variance vector of hatε+ hatB=Y-X hatβ is returned (default `FALSE`).
`aux.cov.pred.target`	logical controlling whether a covariance term required for the back-transformation of kriging predictions of log-transformed data is returned (default `FALSE`).
`min.condnum`	positive numeric. Minimum acceptable ratio of smallest to largest singular value of the model matrix X (default `1.e-12`).
`rq`	a list of arguments passed to `rq` or a function such as `rq.control` that generates such a list (see `rq` for allowed arguments).
`lmrob`	a list of arguments passed to the `control` argument of `lmrob` or a function such as `lmrob.control` that generates such a list (see `lmrob.control` for allowed arguments).
`nleqslv`	a list of arguments passed to `{nleqslv}` or a function such as `nleqslv.control` that generates such a list (see `nleqslv` for allowed arguments).
`optim`	a list of arguments passed to `optim` or a function such as `optim.control` that generates such a list (see `optim` for allowed arguments).
`full.output`	logical controlling how much output is returned in `georob` object. Proper functioning requires default (`TRUE`)

`...`	named vectors of functions, extending the definition of transformations for variogram parameters (see Details).
`variance, snugget, nugget, scale, alpha, beta, delta, gamma, kappa, lambda, mu, nu`	character strings with names of transformation functions of the variogram parameters.
`f1, f2, omega, phi, zeta`	character strings with names of transformation functions of the variogram parameters.
`tau, rq.method, rq.alpha, ci, iid, interp, tcrit`	arguments passed as `...` to `rq`. Note that `rq.` is stripped on passing from the argument names on passing.
`rq.beta, eps, Mm.factor, max.bad.fixup`	arguments passed as `...` to `rq`. Note that `rq.` is stripped on passing from the argument names on passing.
`nleqslv.method, global, xscalm, nleqslv.control`	arguments passed to related arguments of `nleqslv`. Note that `nleqslv.` is stripped from the argument names on passing.
`optim.method, lower, upper, hessian, optim.control`	arguments passed to related arguments of `optim`. Note that `optim.` is stripped from the argument names on passing.

The arguments param.tf, fwd.tf, deriv.fwd.tf, bwd.tf define the transformations of the variogram parameters for robust REML estimation. Implemented are currently "log", "rad" (conversion from degree to radian) and "identity" (= no) transformations. These are the possible values that the many arguments of the function param.transf accept (as quoted character strings) and these are the names of the list components returned by fwd.transf, dfwd.transf and bwd.transf. Additional transformations can be implemented by:

Extending the function definitions by arguments like

fwd.tf = fwd.transf(c(my.fun = function(x) your transformation)),
deriv.fwd.tf = dfwd.transf(c(my.fun = function(x) your derivative)),
bwd.tf = bwd.transf(c(my.fun = function(x) your back-transformation)),
Assigning to a given argument of param.transf the name of the new function, e.g.
variance = "my.fun".

Note the values given for the arguments of param.transf must match the names of the functions returned by fwd.transf, dfwd.transf and bwd.transf.

Andreas Papritz andreas.papritz@env.ethz.ch

georobIntro for a description of the model and a brief summary of the algorithms; georob for (robust) fitting of spatial linear models; georobObject for a description of the class georob; plot.georob for display of REML variogram estimates; predict.georob for computing robust kriging predictions; and finally georobMethods for further methods for the class georob.

## Not run: 
data( meuse )

r.logzn.rob <- georob(log(zinc) ~ sqrt(dist), data = meuse, locations = ~ x + y,
    variogram.model = "exponential",
    param = c( variance = 0.15, nugget = 0.05, scale = 200 ),
    tuning.psi = 1, initial.method = "rq", 
    control = georob.control(cov.bhat = TRUE, cov.ehat.p.bhat = TRUE), verbose = 2)
  
qqnorm(rstandard(r.logzn.rob, level = 0)); abline(0, 1)
qqnorm(ranef(r.logzn.rob, standard = TRUE)); abline(0, 1)

## End(Not run)