

corRatio(nlme)                               R Documentation

_R_a_t_i_o_n_a_l _Q_u_a_d_r_a_t_i_c _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 `corRatio'
     class, representing a rational quadratic spatial corre-
     lation structure. Letting d denote the range and n
     denote the nugget effect, the correlation between two
     observations a distance r apart is (r/d)^2/(1+(r/d)^2)
     when no nugget effect is present and
     (1-n)*(r/d)^2/(1+(r/d)^2) when a nugget effect is
     assumed. Objects created using this constructor need to
     be later initialized using the appropriate `initialize'
     method.

_U_s_a_g_e_:

     corRatio(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 rational quadratic 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 ele-
          ments, 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 group-
          ing 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 dis-
          tance 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 argu-
          ments 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 `corRatio', also inheriting from
     class `corSpatial', representing a rational quadratic
     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_:

     library(nlme)
     sp1 <- corRatio(form = ~ x + y + z)

