geoR (version 1.1-5)

variofit: Variogram Based Parameter Estimation

Description

Estimate covariance parameters by fitting a parametric model to a empirical variogram. Variograms models can be fitted by using weighted or ordinary least squares.

Usage

variofit(vario, ini.cov.pars, cov.model = "matern",
         fix.nugget = FALSE, nugget = 0,
         fix.kappa = TRUE, kappa = 0.5,
         simul.number = NULL, max.dist = "all",
         weights = c("npairs", "equal", "cressie"),
         minimisation.function, messages.screen = TRUE, ...)

Arguments

vario

an object of the class "variogram", typically an output of the function variog. The object is a list with information about the empirical variogram.

ini.cov.pars

initial values for the covariance parameters: $\sigma^2$ (partial sill) and $\phi$ (range parameter). See DETAILS below.

cov.model

a string with the name of the correlation function. For further details see documentation for cov.spatial. Defaults are equivalent to the exponential model.

fix.nugget

logical, indicating whether the parameter $\tau^2$ (nugget variance) should be regarded as fixed (fix.nugget = TRUE) or should be estimated (fix.nugget = FALSE). Defaults to FALSE.

nugget

value for the nugget parameter. Regarded as a fixed values if fix.nugget = TRUE or as a initial value for the minimization algorithm if fix.nugget = FALSE. Defaults to zero.

fix.kappa

logical, indicating whether the parameter $\kappa$ should be regarded as fixed or be estimated. Defaults to TRUE.

kappa

value of the smoothness parameter. Regarded as a fixed values if fix.kappa = TRUE or as a initial value for the minimization algorithm if fix.kappa = FALSE. Only required if one of the following correlation functions

simul.number

number of simulation. To be used when the object passed to the argument vario has empirical variograms for more than one data-set (or simulation). Indicates to which one the model will be fitted.

max.dist

maximum distance considered when fitting the variogram. Defaults to vario$max.dist.

weights

type weights used in the loss function. See DETAILS below.

minimisation.function

minimization function used to estimate the parameters. Options are "optim", "nlm". If weights = "equal" the option "nls" is also valid and det as default. Otherwise defaults to "op

messages.screen

logical. Indicates whether or not status messages are printed on the screen (or other output device) while the function is running.

...

further parameters to be passed to the minimization function. Typically arguments of the type control() which controls the behavior of the minimization algorithm. See documentation for the selected minimization function for furth

Value

• An object of the class "variomodel" which is list with the following components:
• nugget
  value of the nugget parameter. An estimated value if fix.nugget = FALSE or a fixed value if fix.nugget = TRUE.
• cov.pars
  a two elements vector with estimated values of the covariance parameters $\sigma^2$ and $\phi$, respectively.
• cov.model
  a string with the name of the correlation function.
• kappa
  fixed value of the smoothness parameter.
• value
  minimized value of the loss function.
• max.dist
  maximum distance considered in the variogram fitting.
• minimisation.function
  minimization function used.
• message
  status messages returned by the function.
• wieghts
  a string indicating the weights used for the variogram fitting.
• fix.kappa
  logical indicating whether the parameter $\kappa$ was fixed.
• fix.nugget
  logical indicating whether the nugget parameter was fixed.
• lambda
  transformation parameters inherith from the object provided in the argument vario.
• call
  the function call.

Details

Initial values The algorithms for minimization functions require initial values of the parameters. A unique initial value is used if a vector is provided in the argument ini.cov.pars. The elements are initial values for $\sigma^2$ and $\phi$, respectively. This vector is concatenated with the value of the argument nugget if fix.nugget = FALSE and kappa if fix.kappa = TRUE. Specification of multiple initial values is also possible. If this is the case, the function searches for the one which minimizes the loss function and uses this as the initial value for the minimization algorithm. Multiple initial values are specified by providing a matrix in the argument ini.cov.pars and/or, vectors in the arguments nugget and kappa (if included in the estimation). If ini.cov.pars is a matrix, the first column has values of $\sigma^2$ and the second has values of $\phi$. If minimisation.function = "nls" only the values of $\phi$ and $\kappa$ (if this is included in the estimation) are used. The remaning are not need by this algorithm. Weights Three different types of weights can be used within the loss function: [object Object],[object Object],[object Object],See also Barry, Crowder and Diggle (1997) for a discussion on the methods to estimate variogram parameters.

References

Barry, J.T., Crowder, M.J. and Diggle, P.J. (1997) Parametric estimation of the variogram. Tech. Report, Dept Maths & Stats, Lancaster University. Cressie, N.A.C (1993) Statistics for Spatial Data. New York: Wiley. Further information about geoR can be found at: http://www.maths.lancs.ac.uk/~ribeiro/geoR.html.

See Also

cov.spatial for a detailed description of the available correlation (variogram) functions, likfit for maximum and restricted maximum likelihood estimation, lines.variomodel for graphical output of the fitted model. For details on the minimization functions see optim, nlm and nls.

Examples

if(is.R()) data(s100)
vario100 <- variog(s100, max.dist=1)
ini.vals <- expand.grid(seq(0,1,l=5), seq(0,1,l=5))
ols <- variofit(vario100, ini=ini.vals, fix.nug=TRUE, wei="equal")
summary(ols)
wls <- variofit(vario100, ini=ini.vals, fix.nug=TRUE)
summary(wls)
plot(vario100)
lines(wls)
lines(ols, lty=2)

<testonly>vr <- variog(s100, max.dist=1)
## OLS#
o1 <- variofit(vr, ini = c(.5, .5), fix.nug=T, wei = "equal")
o2 <- variofit(vr, ini = c(.5, .5), wei = "equal")
o3 <- variofit(vr, ini = c(.5, .5), fix.nug=T,
      fix.kappa = F, wei = "equal")
o4 <- variofit(vr, ini = c(.5, .5), fix.kappa = F, wei = "equal")
## WLS
w1 <- variofit(vr, ini = c(.5, .5), fix.nug=T)
w2 <- variofit(vr, ini = c(.5, .5))
w3 <- variofit(vr, ini = c(.5, .5), fix.nug=T, fix.kappa = F)
w4 <- variofit(vr, ini = c(.5, .5), fix.kappa = F)</testonly>