| variofit {geoR} | R Documentation |
Estimate covariance parameters by fitting a parametric model to a empirical variogram. Variograms models can be fitted by using weighted or ordinary least squares.
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, ...)
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 is used: "matern", "powered.exponential", "cauchy"
and "gneiting.matern". Defaults to 0.5. |
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 "optim". |
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 further 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:
"npairs""cressie""equal"See also Barry, Crowder and Diggle (1997) for a discussion on the methods to estimate variogram parameters.
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. |
Paulo Justiniano Ribeiro Jr. Paulo.Ribeiro@est.ufpr.br,
Peter J. Diggle p.diggle@lancaster.ac.uk.
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.
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.
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)