

   SSpphheerriiccaall CCoorrrreellaattiioonn SSttrruuccttuurree

        corLin(value, form, nugget, metric)

   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 exponential 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
             ratio" (the ratio between the variance of an
             observation and the covariance between two obser-
             vations 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 ratio of 0.9
             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 `"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"'.

   DDeessccrriippttiioon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 ratio, 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 n*(1-1.5(r/d)+0.5(r/d)^3)
        when a nugget effect is assumed. If r >= d the correla-
        tion is zero. Objects created using this constructor
        need to be later initialized using the appropriate
        `initialize' method.

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

        and object of class `corSpher', also inheriting from
        class `corSpatial', representing a spherical 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::

        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::

        `initialize.corStruct', `dist'

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

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

