ksline                 package:geoR                 R Documentation

_S_p_a_t_i_a_l _P_r_e_d_i_c_t_i_o_n - _C_o_n_v_e_n_t_i_o_n_a_l _K_r_i_g_i_n_g

_D_e_s_c_r_i_p_t_i_o_n:

     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.

_U_s_a_g_e:

     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)

_A_r_g_u_m_e_n_t_s:

 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 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 x 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 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.  

  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.

_V_a_l_u_e:

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

 predict: the predicted values.  

krige.var: the kriging variances.  

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

 summary: 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. 

  ktrend: the matrix with trend if 'm0 = "kt"' (universal kriging).  

ktetrend: the matrix with trend if 'm0 = "kte"' (external trend
          kriging).

    beta: the value of the mean which is implicitly estimated for 'm0 =
          "ok", "kte"' or '"kt"'.

 wofmean: 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.  

locations: the coordinates of the prediction locations.  

 message: status messages returned by the algorithm.  

    call: the function call.  

_N_o_t_e:

     This is a preliminary and inefficient function implementing
     kriging methods. For predictions using global neighborhood the
     function 'krige.conv' should be used instead.

_A_u_t_h_o_r(_s):

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

_R_e_f_e_r_e_n_c_e_s:

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

_S_e_e _A_l_s_o:

     'krige.conv' for a more efficient implementation of conventional
     kriging methods, 
      'krige.bayes' for Bayesian prediction.

_E_x_a_m_p_l_e_s:

     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")

