corGaus                 package:nlme                 R Documentation

_G_a_u_s_s_i_a_n _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 'corGaus' class,
     representing a Gaussian spatial correlation structure. Letting d
     denote the range and n denote the nugget effect, the correlation
     between two observations a distance r apart is exp(-(r/d)^2) when
     no nugget effect is present and (1-n)*exp(-(r/d)^2) when a nugget
     effect is assumed. Objects created using this constructor must
     later be initialized using the appropriate `  'Initialize' method.

_U_s_a_g_e:

     corGaus(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 Gaussian
          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 'corGaus', also inheriting from class
     'corSpatial', representing a Gaussian spatial correlation
     structure.

_A_u_t_h_o_r(_s):

     Jose Pinheiro Jose.Pinheiro@pharma.novartis.com and Douglas Bates
     bates@stat.wisc.edu

_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.

     Pinheiro, J.C., and Bates, D.M. (2000) "Mixed-Effects Models in S
     and S-PLUS", Springer.

_S_e_e _A_l_s_o:

     'Initialize.corStruct', 'summary.corStruct', 'dist'

_E_x_a_m_p_l_e_s:

     sp1 <- corGaus(form = ~ x + y + z)

     # example lme(..., corGaus ...)
     # Pinheiro and Bates, pp. 222-249
     fm1BW.lme <- lme(weight ~ Time * Diet, BodyWeight,
                        random = ~ Time)
     # p. 223
     fm2BW.lme <- update(fm1BW.lme, weights = varPower())
     # p 246 
     fm3BW.lme <- update(fm2BW.lme,
                correlation = corExp(form = ~ Time))
     # p. 249
     fm8BW.lme <- update(fm3BW.lme, correlation = corGaus(form = ~ Time))

