krige.conv {geoR}R Documentation

Spatial Prediction - Conventional Kriging

Description

This function performs spatial prediction for fixed covariance parameters using global neighbourhood.

Available options implement the following kriging types: SK (simple kriging), OK (ordinary kriging), KTE (external trend kriging) and UK (universal kriging).

Usage

krige.conv(geodata, coords = geodata$coords, data = geodata$data, 
           locations,
           krige = krige.control(type.krige, beta = NULL,
                     trend.d, trend.l, cov.model, cov.pars,
                     kappa = 0.5, nugget = 0, micro.scale = 0,
                     dist.epsilon = 1e-10, aniso.pars = NULL, 
                     lambda = 1, signal = FALSE,
                     n.samples.backtransform = 500, n.sim = 0),
           messages.screen = TRUE)

Arguments

geodata a list containing elements coords and data as described next. Typically an object of the class "geodata" - a geoR data-set. If not provided the arguments coords and data must be provided instead.
coords an n x 2 matrix or data-frame with the 2-D coordinates of the n data locations. By default it takes the component coords of the argument geodata, if provided.
data a vector with n data values. By default it takes the component data of the argument geodata, if provided.
locations an N x 2 matrix or data-frame with the 2-D coordinates of the N prediction locations.
krige defines the model components and the type of kriging. See section DETAILS below.
ATTENTION: the argument cov.pars is obligatory whilst all the others have default options.
messages.screen logical. Indicates whether or not status messages are printed on the screen (or other output device) while the function is running.

Details

According to the arguments provided, one of the following different types of kriging: SK, OK, UK or KTE is performed. Defaults correspond to ordinary kriging.

Arguments for krige = krige.control(...) :

type.krige
type of kriging to be performed. Options are "SK", "OK" corresponding to simple or ordinary kriging. Kriging with external trend and universal kriging can be defined setting type.krige = "OK" and specifying the trend model using the arguments trend.d and trend.l.
beta
numerical value of the mean (vector) parameter. Only used if type.krige="SK".
trend.d
specifies the trend (covariate) values at the data locations. Possible values are: "cte" (constant mean), "1st" (first order polynomial on the coordinates), "2nd" - (second order polynomial on the coordinates). Alternatively a formula of the type ~X can be provided, where X is a matrix with covariates (external trend) at data locations. Defaults to "cte".
trend.l
specifies the trend (covariate) values at prediction locations. It must be of the same type as for trend.d. Only used if prediction locations are provided in the argument locations.
cov.model
string indicating the name of the model for the correlation function. Further details can be found in the documentation of the function cov.spatial.
cov.pars
a vector with 2 elements or an n x 2 matrix with the covariance parameters sigma^2 (partial sill) and phi (range parameter). If a vector, the elements are the values of sigma^2 and phi, respectively. If a matrix, corresponding to a model with several structures, the values of sigma^2 are in the first column and the values of phi are in the second.
kappa
additional smoothness parameter required by the following correlation functions: "matern", "powered.exponential", "cauchy" and "gneiting.matern".
nugget
the value of the nugget variance parameter tau^2. Defaults to zero.
micro.scale
micro-scale variance. If different from zero, the nugget variance is divided into 2 terms: micro-scale variance and measurement error. This affect the estimated precision of the predictions. Often in practice, these two variance components are indistinguishable but the distinction can be made here if justifiable.
dist.epsilon
a numeric value. Locations which are separated by a distance less than this value are considered co-located.
aniso.pars
parameters for geometric anisotropy correction. If aniso.pars = FALSE no correction is made, otherwise a two elements vector with values for the anisotropy parameters must be provided. Anisotropy correction consists of a transformation of the data and prediction coordinates performed by the function coords.aniso.
lambda
numeric value of the Box-Cox transformation parameter. The value lambda = 1 corresponds to no transformation and lambda = 0 corresponds to the log-transformation. Prediction results are back-transformed and returned is the same scale as for the original data.
signal
logical. If TRUE the signal is predicted, otherwise the observation is predicted. If no transformation is performed the expectations are the same in both cases and the difference is only for values of the kriging variance, when the value of the nugget is different from zero.
n.samples.backtransform
number of samples used in the back-transformation. When transformations are used (specified by an argument lambda), back-transformations are usually performed by sampling from the predictive distribution and then back-transforming the sampled values. The exceptions are for lambda = 0 (log-transformation) and lambda = 1 (no transformation).
n.sim
optional. Number of simulations from the posterior distribution. If n.sim is provided, samples are taken from the predictive distribution.

Value

An object of the class kriging which is a list with the following components:

predict a vector with predicted values.
krige.var a vector with predicted variances.
beta.est estimates of the beta, parameter implicit in kriging procedure. Not included if type.krige = "SK".
simulations an ni x n.sim matrix where ni is the number of prediction locations. Each column corresponds to a conditional simulation of the predictive distribution. Only returned if n.sim > 0.
message messages about the type of prediction performed.
call the function call.

Author(s)

Paulo J. Ribeiro Jr. Paulo.Ribeiro@est.ufpr.br,
Peter J. Diggle p.diggle@lancaster.ac.uk.

References

Further information about geoR can be found at:
http://www.maths.lancs.ac.uk/~ribeiro/geoR.html.

See Also

image.kriging for graphical output of the results, krige.bayes for Bayesian prediction and ksline for a different implementation of kriging allowing for moving neighborhood.

Examples

if(is.R()) data(s100) 
loci <- expand.grid(seq(0,1,l=31), seq(0,1,l=31))
kc <- krige.conv(s100, loc=loci,
                 krige=krige.control(cov.pars=c(1, .25)))
par(mfrow=c(1,2))
image.kriging(kc, loc=loci, main="kriging estimates")
image.kriging(kc, loc=loci, val=sqrt(kc$krige.var),
              main="kriging std. errors")