variog                 package:geoR                 R Documentation

_C_o_m_p_u_t_e _E_m_p_i_r_i_c_a_l _V_a_r_i_o_g_r_a_m_s

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

     Computes sample (empirical) variograms with options for  the
     classical or robust estimator. Output can be returned as a `binned
     variogram', a ` variogram cloud' or a `smoothed variogram'. Data
     transformation (Box-Cox) is allowed. Trends fitted by ordinary
     least squares can be removed. In this case variograms are computed
     using the residuals.

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

     variog(geodata, coords=geodata$coords, data=geodata$data, 
            uvec = "default", trend = "cte", lambda = 1, 
            option = c("bin", "cloud", "smooth"), 
            estimator.type = c("classical", "modulus"), 
            nugget.tolerance = 0, max.dist = NULL, pairs.min = 2, 
            bin.cloud = FALSE, direction = "omnidirectional",
            tolerance = pi/8, unit.angle = c("radians", "degrees"),
            messages.screen = TRUE, ...) 

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

 geodata: a list containing element `coords' as described next.
          Typically an object of the class `"geodata"' - a geoR
          data-set. If not provided the arguments `coords' must be
          provided instead.  

  coords: an n x 2 matrix containing coordinates of the n data
          locations in each row. Defaults to `geodata$coords', if
          provided.

    data: a vector or matrix with data values. If a matrix is provided,
          each column is regarded as one variable or realization.
          Defaults to `geodata$data', if provided.

    uvec: a vector with values defining the variogram binning. Only
          used when `option = "bin"'. The values of `uvec' defines the
          mid-points of the bins.
          If uvec[1] > 0 the first bin is: 0 < u <= uvec[2] -
          0.5*(uvec[2] - uvec[1]).
          If uvec[1] = 0 first bin is: 0 < u <= 0.5*uvec[1] and uvec[1]
          is replaced by the midpoint of this interval.

   trend: specifies the mean part of the model. The options are:
          `"cte"' (constant mean), `"1st"' (a first degree polynomial
          on the coordinates), `"2nd"' (a second degree polynomial on
          the coordinates), or a formula of the type `~X' where `X' is
          a matrix with the covariates (external trend). Defaults to
          `"cte"'.  

  lambda: values of the Box-Cox transformation parameter. Defaults to 1
          (no transformation). If another value is provided the
          variogram is computed after transforming the  data. A case of
          particular interest is lambda = 0 which corresponds to
          log-transformation.  

  option: defines the output type: the options `"bin"' returns values
          of binned variogram, `"cloud"' returns the variogram cloud
          and `"smooth"' returns the kernel smoothed variogram.
          Defaults to `"bin"'.

estimator.type: `"classical"' computes the classical method of moments
          estimator.  `"modulus"' returns the variogram estimator
          suggested by Hawkins and Cressie (see Cressie, 1993, pg 75).
          Defaults to `"classical"'.  

nugget.tolerance: a numeric value. Points which are separated by a
          distance less than this value are considered co-located.
          Defaults to zero.  

max.dist: a numerical value defining the maximum distance for the
          variogram. Pairs of locations separated for distance larger
          than this value are ignored for the variogram calculation.
          Defaults to the maximum distance among the pairs of data
          locations.  

pairs.min: a integer number defining the minimum numbers of pairs for
          the bins. For `option = "bin"', bins with number of pairs
          smaller than this value are ignored. Defaults to `NULL'.  

bin.cloud: logical. If `TRUE' and `option = "bin"' the cloud values for
          each class are included in the output. Defaults to `FALSE'.  

direction: a numerical value for the directional (azimuth) angle. This
          used to specify directional variograms. Default defines the
          omnidirectional variogram. The value must be in the interval
          [0, 180] degrees.  

tolerance: numerical value for the tolerance angle, when computing
          directional variograms. The value must be in the interval [0,
          90] degrees.  Defaults to pi/8.  

unit.angle: defines the unit for the specification of angles in the two
          previous arguments. Options are `"degrees"' and `"radians"'. 

messages.screen: logical. Indicates whether status messages should be
          printed on the screen (or output device) while the function
          is running.  

     ...: arguments to be passed to the function `ksmooth', if `option
          = "smooth"'.  

_D_e_t_a_i_l_s:

     Variograms are widely used in geostatistical analysis for
     exploratory purposes, to estimate covariance parameters and/or to
     compare theoretical and fitted models against sample variograms.

     The two estimators currently implemented are:

        *  classical estimator:

             gamma(h) = (1/N_h) sum (Y(x_i+h) - Y(x_i))^2


        *  Hawkins and Cressie's modulus estimator

        gamma(h) = ((1/N_h) sum |Y(x_(i+h)) - Y(x_i)|^(1/2))^4


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

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

      u : a vector with distances.  

      v : a vector with estimated variogram values at distances given
          in `u'.  

      n : number of pairs in each bin, if `option = "bin"'.  

var.mark : variance of the data.  

output.type : echoes the `option' argument.  

estimator.type : echoes the type of estimator used.  

direction : direction for which the variogram was computed.  

tolerance : tolerance angle for directional variogram.  

   uvec : lags provided in the function call.  

   call : the function call.  

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

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

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

     Cressie, N.A.C (1993) Statistics for Spatial Data. New York:
     Wiley.

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

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

     `variog4' for more on computation of directional variograms, 
     `variog.model.env' and `variog.mc.env' for variogram envelopes,
     `variofit'  for variogram based parameter estimation and
     `plot.variogram' for graphical output.

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

     # Loading data:
     if(is.R()) data(s100)
     #
     # computing variograms:
     #
     # binned variogram
     vario.b <- variog(s100, max.dist=1)
     # variogram cloud
     vario.c <- variog(s100, max.dist=1, op="cloud")
     #binned variogram and stores the cloud
     vario.bc <- variog(s100, max.dist=1, bin.cloud=TRUE)
     # smoothed variogram
     vario.s <- variog(s100, max.dist=1, op="sm", band=0.2)
     #
     #
     # plotting the variograms:
     par(mfrow=c(2,2))
     plot(vario.b, main="binned variogram") 
     plot(vario.c, main="variogram cloud")
     plot(vario.bc, bin.cloud=TRUE, main="clouds for binned variogram")  
     plot(vario.s, main="smoothed variogram") 

     # computing a directional variogram
     vario.0 <- variog(s100, max.dist=1, dir=0, tol=pi/8)
     plot(vario.b, type="l", lty=2)
     lines(vario.0)
     legend(0, 1.2, legend=c("omnidirectional", expression(0 * degree)), lty=c(2,1))
     #

