corSpher                package:nlme                R Documentation

_S_p_h_e_r_i_c_a_l _C_o_r_r_e_l_a_t_i_o_n _S_t_r_u_c_t_u_r_e

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

     This function is a constructor for the `corSpher' class,
     representing a spherical spatial correlation structure. Letting d
     denote the range and n denote the nugget effect, the correlation
     between two observations a distance r < d apart is
     1-1.5(r/d)+0.5(r/d)^3 when no nugget effect is present and
     (1-n)*(1-1.5(r/d)+0.5(r/d)^3)   when a nugget effect is assumed.
     If r >= d the correlation is zero. Objects created using this
     constructor must later be initialized using the appropriate
     `initialize' method.

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

     corSpher(value, form, nugget, metric, fixed)

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

   value: an optional vector with the parameter values in constrained
          form. If `nugget' is `FALSE', `value' can have only one
          element, corresponding to the "range" of the spherical
          correlation structure, which must be greater than zero. If
          `nugget' is `TRUE', meaning that a nugget effect is present,
          `value' can contain one or two elements, the first being the
          "range" and the second the "nugget effect" (one minus the
          correlation between two observations taken arbitrarily close
          together); the first must be greater than zero and the second
          must be between zero and one. Defaults to `numeric(0)', which
          results in a range of 90% of the minimum distance and a
          nugget effect of 0.1 being assigned to the parameters when
          `object' is initialized.

    form: a one sided formula of the form `~ S1+...+Sp', or `~
          S1+...+Sp | g', specifying spatial covariates `S1' through
          `Sp' and,  optionally, a grouping factor `g'.  When a
          grouping factor is present in `form', the correlation
          structure is assumed to apply only to observations within the
          same grouping level; observations with different grouping
          levels are assumed to be uncorrelated. Defaults to `~ 1',
          which corresponds to using the order of the observations in
          the data as a covariate, and no groups.

  nugget: an optional logical value indicating whether a nugget effect
          is present. Defaults to `FALSE'.

  metric: an optional character string specifying the distance metric
          to be used. The currently available options are `"euclidean"'
          for the root sum-of-squares of distances; `"maximum"' for the
          maximum difference; and `"manhattan"' for the sum of the
          absolute differences. Partial matching of arguments is used,
          so only the first three characters need to be provided.
          Defaults to `"euclidean"'.

   fixed: an optional logical value indicating whether the coefficients
          should be allowed to vary in the optimization, or kept fixed
          at their initial value. Defaults to `FALSE', in which case
          the coefficients are allowed to vary.

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

     an object of class `corSpher', also inheriting from class
     `corSpatial', representing a spherical spatial correlation
     structure.

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

     Jose Pinheiro and Douglas Bates

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

     Cressie, N.A.C. (1993), "Statistics for Spatial Data", J. Wiley &
     Sons. Venables, W.N. and Ripley, B.D. (1997) "Modern Applied
     Statistics with S-plus", 2nd Edition, Springer-Verlag. Littel,
     Milliken, Stroup, and Wolfinger (1996) "SAS Systems for Mixed
     Models", SAS Institute.

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

     `initialize.corStruct', `dist'

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

     sp1 <- corSpher(form = ~ x + y)

