

   SSppaattiiaall CCoorrrreellaattiioonn SSttrruuccttuurree

        corSpatial(value, form, nugget, type, metric, fixed)

   AArrgguummeenntts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 spatial 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 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'.

       type: an optional character string specifying the
             desired type of correlation structure. Available
             types include `"spherical"', `"exponential"',
             `"gaussian"', `"linear"', and `"rational"'. See
             the documentation on the functions `corSpher',
             `corExp', `corGaus', `corLin', and `corRatio' for
             a description of these correlation structures.
             Partial matching of arguments is used, so only the
             first character needs to be provided.Defaults to
             `"spherical"'.

     metric: an optional character string specifying the dis-
             tance metric to be used. The currently available
             options are `"euclidian"' 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 `"euclidian"'.

      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.

   DDeessccrriippttiioonn::

        This function is a constructor for the `corSpatial'
        class, representing a spatial correlation structure.
        This class is "virtual", having four "real" classes,
        corresponding to specific spatial correlation struc-
        tures, associated with it: `corExp', `corGaus', `cor-
        Lin', `corRatio', and `corSpher'. The returned object
        will inherit from one of these "real" classes, deter-
        mined by the `type' argument, and from the "virtual"
        `corSpatial' class. Objects created using this con-
        structor need to be later initialized using the appro-
        priate `initialize' method.

   VVaalluuee::

        an object of class determined by the `type' argument
        and also inheriting from class `corSpatial', represent-
        ing a spatial correlation structure.

   AAuutthhoorr((ss))::

        Jose Pinheiro and Douglas Bates

   RReeffeerreennccees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 (1997) "SAS Systems for Mixed Models",
        SAS Institute.

   SSeeee AAllssoo::

        `corExp', `corGaus', `corLin', `corRatio', `corSpher',
        `initialize.corStruct', `dist'

   EExxaammpplleess::

        library(lme)
        sp1 <- corSpatial(form = ~ x + y + z, type = "g", metric = "man")

