corSpatial               package:nlme               R Documentation

Spatial Correlation Structure

Description:

     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 structures, associated with it: 'corExp',
     'corGaus', 'corLin', 'corRatio', and 'corSpher'. The returned
     object will inherit from one of these "real" classes, determined
     by the 'type' argument, and from the "virtual" 'corSpatial' class.
     Objects created using this constructor must later be initialized
     using the appropriate 'Initialize' method.

Usage:

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

Arguments:

   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 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'.

    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 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.

Value:

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

Author(s):

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

References:

     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.

See Also:

     'corExp', 'corGaus', 'corLin', 'corRatio', 'corSpher',
     'Initialize.corStruct', 'summary.corStruct', 'dist'

Examples:

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

