variogram               package:gstat               R Documentation

_C_a_l_c_u_l_a_t_e _S_a_m_p_l_e _o_r _R_e_s_i_d_u_a_l _V_a_r_i_o_g_r_a_m _o_r _V_a_r_i_o_g_r_a_m _C_l_o_u_d

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

     Calculates the sample variogram from data, or in case of a linear
     model is given, for the residuals, with options for directional,
     robust, and pooled variogram, and for irregular distance
     intervals.

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

     variogram.formula(object, ...)
     variogram.gstat(formula, locations, data, ...)
     variogram.default(y, locations, X, cutoff, width = cutoff/15, alpha =
             0, beta = 0, tol.hor = 90/length(alpha), tol.ver =
             90/length(beta), cressie = FALSE, dX = numeric(0), boundaries =
             numeric(0), cloud = FALSE, trend.beta = NULL, debug.level = 1,
             cross = TRUE, grid, map = FALSE, ...)

     print.gstatVariogram(v, ...)
     print.variogramCloud(v, ...)

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

  object: object of class 'gstat'; in this form, direct and cross
          (residual) variograms are calculated for all variables and
          variable pairs defined in 'object'

 formula: formula defining the response vector and (possible) 
          regressors, in case of absence of regressors, use e.g. 'z~1'

    data: data frame where the names in formula are to be found

locations: spatial data locations.  For variogram.formula: a formula
          with only the coordinate variables in the right hand
          (explanatory variable) side e.g. '~x+y'; see examples.

          For variogram.default: list with coordinate matrices, each
          with the number of rows matching that of corresponding
          vectors in y; the number of columns should match the number
          of spatial dimensions spanned by the data (1 (x), 2 (x,y) or
          3 (x,y,z)).  

     ...: any other arguments that will be passed to  variogram.default

       y: list with for each variable the vector with responses 

       X: (optional) list with for each variable the matrix with
          regressors/covariates; the number of rows should match that
          of the correspoding element in y, the number of columns
          equals the number of regressors (including intercept) 

  cutoff: spatial separation distance up to which point pairs are
          included in semivariance estimates 

   width: the width of subsequent distance intervals into which data
          point pairs are grouped for semivariance estimates 

   alpha: direction in  plane (x,y), in positive degrees clockwise from
          positive y (North): alpha=0 for direction North (increasing
          y), alpha=90 for direction East (increasing x); optional a
          vector of directions in (x,y) 

    beta: direction in z, in positive degrees up from the (x,y) plane; 

 tol.hor: horizontal tolerance angle in degrees 

 tol.ver: vertical tolerance angle in degrees 

 cressie: logical; if TRUE, use Cressie's robust variogram estimate; if
          FALSE use the classical method of moments variogram estimate 

      dX: include a pair of data points $y(s_1),y(s_2)$ taken at
          locations $s_1$ and $s_2$ for sample variogram calculation
          only when $||x(s_1)-x(s_2)|| < dX$ with and $x(s_i)$ the
          vector with regressors at location $s_i$, and $||.||$ the
          2-norm.  This allows pooled estimation of within-strata
          variograms (use a factor variable as regressor, and dX=0.5),
          or variograms of (near-)replicates in a linear model
          (addressing point pairs having similar values for regressors
          variables) 

boundaries: numerical vector with distance interval boundaries;  values
          should be strictly increasing 

   cloud: logical; if TRUE, calculate the semivariogram cloud 

trend.beta: vector with trend coefficients, in case they are known. By
          default, trend coefficients are estimated from the data.

debug.level: integer; set gstat internal debug level 

   cross: logical; if FALSE, no cross variograms are calculated when
          object is of class 'gstat' and has more than one variable 

       v: object of class 'variogram' or 'variogramCloud' to be printed

    grid: grid parameters, if data are gridded 

     map: logical; if TRUE, and 'cutoff' and 'width' are given, a
          variogram map is returned. This requires package sp.
          Alternatively, a map can be passed, of class
          SpatialDataFrameGrid (see sp docs) 

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

     If map is TRUE (or a map is passed), a grid map is returned
     containing the (cross) variogram map(s). See package sp.

     In other cases, an object of class "gstatVariogram" with the 
     following fields: 

      np: the number of point pairs for this estimate;  in case of a
          'variogramCloud' see below

    dist: the average distance of all point pairs considered for this
          estimate

   gamma: the actual sample variogram estimate

 dir.hor: the horizontal direction

 dir.ver: the vertical direction

      id: the combined id pair

    left: for variogramCloud: data id (row number) of one of  the data
          pair

   right: for variogramCloud: data id (row number) of the other  data
          in the pair


     In the past, gstat returned an object of class "variogram";
     however, this resulted in confusions for users of the package
     geoR: the geoR variog function also returns objects of class
     "variogram", incompatible to those returned by this function.
     That's why I changed the class name.

_N_o_t_e:

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

     Edzer J. Pebesma

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

     Cressie, N.A.C., 1993, Statistics for Spatial Data, Wiley.

     <URL: http://www.gstat.org/>

     Pebesma, E.J., 2004. Multivariable geostatistics in S: the gstat
     package. Computers & Geosciences, 30: 683-691.

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

     print.gstatVariogram, plot.gstatVariogram, plot.variogramCloud;
     for variogram models: vgm, to fit a variogram model to a sample
     variogram:  fit.variogram

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

     data(meuse)
     # no trend:
     variogram(log(zinc)~1, loc=~x+y, meuse)
     # residual variogram w.r.t. a linear trend:
     variogram(log(zinc)~x+y, loc=~x+y, meuse)
     # directional variogram:
     variogram(log(zinc)~x+y, loc=~x+y, meuse, alpha=c(0,45,90,135))

