This function performs spatial prediction for given covariance
parameters. Options implement
the following kriging types:
*SK* (simple kriging), *OK* (ordinary kriging),
*KTE* (external trend kriging) and *UK* (universal kriging).

The function `krige.conv`

should be preferred, unless
moving neighborhood is to be used.

```
ksline(geodata, coords = geodata$coords, data = geodata$data,
locations, borders = NULL,
cov.model = "matern",
cov.pars=stop("covariance parameters (sigmasq and phi) needed"),
kappa = 0.5, nugget = 0, micro.scale = 0,
lambda = 1, m0 = "ok", nwin = "full",
n.samples.backtransform = 500, trend = 1, d = 2,
ktedata = NULL, ktelocations = NULL, aniso.pars = NULL,
signal = FALSE, dist.epsilon = 1e-10, messages)
```

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 \(n \times 2\) matrix where each row has 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 \(N \times 2\) matrix or data-frame with the 2-D
coordinates of the \(N\) prediction locations, or a list for which
the first two components are used. Input is internally checked by the
function `check.locations`

.

borders

optional. If a two column matrix defining a polygon is provided the prediction is performed only at locations inside this polygon.

cov.pars

a vector with 2 elements or an \(n \times 2\) 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.

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 might affect the precision of
the predictions.
In practice, these two variance components are usually indistinguishable but the
distinction can be made here if justifiable.

cov.model

string indicating the name of the model for the
correlation function. Further details in the
documentation for
`cov.spatial`

.
Defaults are equivalent to the *exponential* model.

kappa

additional smoothness parameter required by the following correlation
functions: `"matern"`

,
`"powered.exponential"`

,
`"cauchy"`

and
` "gneiting.matern"`

.

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.

m0

The default value `"ok"`

indicates that ordinary
kriging will be performed. Other options are `"kt"`

for kriging
with a trend model (universal kriging) and `"kte"`

for kriging
with external trend (covariates). If a numeric value is provided it
is assumed to be the value of a know mean and simple kriging is then
performed.
If `"av"`

the arithmetic mean of the data is assumed to be the
know mean for simple kriging algorithm.

nwin

If `"full"`

*global neighborhood* is used
i.e., all data values are used in the
prediction of every prediction location.
An integer number defines the *moving neighborhood* algorithm.
The number provided is used as
the number closest neighbors to be used for the prediction at each
location.
Defaults to `"full"`

.

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).

trend

only required if `m0 = "kt"`

(universal kriging).
Possible values are \(1\) or \(2\), corresponding to a first or second degree
polynomial trend on the coordinates, respectively.

d

spatial dimension, \(1\) defines a prediction on a line, \(2\) on a plane (the default).

ktedata

only required if `m0 = "kte"`

. A vector or matrix
with the values of the
external trend (covariates) at the data locations.

ktelocations

only required if `m0 = "kte"`

. A vector or
matrix with the values of the
external trend (covariates) at the prediction locations.

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`

.

signal

logical. If `TRUE`

the signal is predicted, otherwise the
variable 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, if the value of the nugget is
different from zero.

dist.epsilon

a numeric value. Points which are separated by a distance less than this value are considered co-located.

messages

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

An object of the `class`

`kriging`

which is a list
with the following components:

the predicted values.

the kriging variances.

the difference between the predicted value and the global mean. Represents the contribution to the neighboring data to the prediction at each point.

values of the arithmetic and weighted mean of the data and standard deviations. The weighted mean corresponds to the estimated value of the global mean.

the matrix with trend if `m0 = "kt"`

(universal kriging).

the matrix with trend if `m0 = "kte"`

(external trend kriging).

the value of the mean which is implicitly estimated for
`m0 = "ok", "kte"`

or `"kt"`

.

weight of mean. The predicted value is an weighted average between the global mean and the values at the neighboring locations. The value returned is the weight of the mean.

the coordinates of the prediction locations.

status messages returned by the algorithm.

the function call.

Further information on the package geoR can be found at: http://www.leg.ufpr.br/geoR.

`krige.conv`

for a more efficient implementation of
conventional kriging methods, `krige.bayes`

for Bayesian prediction.

# NOT RUN { loci <- expand.grid(seq(0,1,l=31), seq(0,1,l=31)) kc <- ksline(s100, loc=loci, cov.pars=c(1, .25)) par(mfrow=c(1,2)) image(kc, main="kriging estimates") image(kc, val=sqrt(kc$krige.var), main="kriging std. errors") # }