Description Usage Arguments Details Value Author(s) Examples
This function combines some input arguments with defaults for other to create a list describing the LatticeKrig spatial model.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17  LKrigSetup(
x = NULL, nlevel = NULL, alpha = NA, alphaObject =
NULL, nu = NULL, a.wght = NA, a.wghtObject = NULL,
normalize = TRUE, lambda = NA, sigma = NA, rho = NA,
rho.object = NULL, latticeInfo = NULL, basisInfo =
NULL, LKGeometry = "LKRectangle", distance.type =
"Euclidean", BasisFunction = "WendlandFunction",
overlap = 2.5, V = NULL, BasisType = "Radial",
fixedFunction = "LKrigDefaultFixedFunction",
fixedFunctionArgs = list(m = 2), collapseFixedEffect =
FALSE, max.points = NULL, mean.neighbor = 50,
choleskyMemory = NULL, verbose = FALSE, noCheck =
FALSE, returnCall = FALSE, dense = FALSE, ...)
LatticeKrigEasyDefaults(argList, nlevel, x)
LKinfoUpdate(LKinfo, ... )

argList 
Argument supplied to the top level LatticeKrig function. 
alpha 
A vector of length 
alphaObject 
For nonstationary models an object to be used with the predict function to give the alpha values at the process locations. Typically this is a list of "predict" objects. See nonstationaryModels for examples how to use this option. 
a.wght 
This parameter controls the correlation range in the SAR
model. In most cases, a scalar value and for the 2d model by default
greater than 4.
If a vector this can specify an anisotropic set of weights. To
specify a.wght parameters that are different for each level they
should be in the form of a list
of length The details of how this is connected to the covariance function
varies
based on the geometry. However, qualitatively this is related to a
range parameter. For the LKRectangle geometry and a stationary
model, at level k the center point has
weight 1 with the 4 nearest neighbors given weight
1/a.wght[k]. In this case a.wght must be greater than 4 for the
fields to be
stationary and following Lindgren and Rue the range parameter is
approximately 
a.wghtObject 
For nonstationary models an object to be used with the predict function to give the a.wght values at the lattice locations. See nonstationaryModels for examples how to used option. 
basisInfo 
A list with extra components the object used to describe the multiresolution basis. Usually this will not be needed for standard models. 
BasisType 
A character string indicating the type of basis function. Currently
this is either 
choleskyMemory 
A list that will be used in the spam call to
do the Cholesky decomposition. See the 
collapseFixedEffect 
If FALSE the fixed part of the model is found seperately for each replicated data set. If TRUE the estimate is polled across replicates.This is largely a modeling decision whether variation among the replicate fields is due to the spatial component or also include variation in the fixed effects across replicates – guess they are not really fixed then! 
dense 
If FALSE sparse linear algebra is used for the computations . If TRUE the matrices are made "dense" (zeroes are filled in) and the ordinary Lapack functions are used for the linear algebra. This option is primarily for testing and timing sparse verses standard algorithms. 
distance.type 
A text string indicate type distance to use between spatial locations when evaluating the basis functions. Default is "Euclidean". Other choices when locations are in degrees longitude and latitude are "Chordal" and "GreatCircle". The default radius is in miles (3963.34) but can be reset using the "Radius" attribute to the text string. e.g. will set radius to kilometers. 
fixedFunction 
A text string that is the name of the function used to find the fixed part of the spatial model based on the locations. The default is a linear (m=2) polynomial in the spatial coordinates. 
fixedFunctionArgs 
A list containing arguments to supply when evaluating the fixed function. 
lambda 
The "noise to signal ratio" or also known as the
smoothing parameter it is the parameter 
latticeInfo 
Part
or all of the object used to describe the Markov random field
lattice. In the standard cases this list is created in the
setup function and need not be specified. See

LKGeometry 
A text string that gives the names of the model geometry. The default is "LKrectangle" assuming the spatial domain is a rectangle. Other common choices are "LKInterval" (1 d problem ) and "LKBox" (3 d problem) 
LKinfo 
A list that has class "LKinfo". 
mean.neighbor 
The average number of nonzero points when each basis function is evaluated at a set of points points in the spatial domain. 
max.points 
This is a parameter for the nearest neighbor distance function that sets the maximum array size for the nonzero distances among points. e.g. with 100 points each with 20 nonzero neighbors max.points needs to be 2000 = 100*20. Specifically if the total number of nonzero values when each basis function is evaluated at all the spatial locations. The easier way to specify space is by using the mean.neighbor argument. 
nlevel 
Number of levels in multiresolution. Note that each subsequent level increases the number of basis functions within the spatial domain size by a factor of roughly 4. 
noCheck 
If FALSE do not make any checks on the consistency of the different parts of the final LKinfo object. e.q. values of a.wght within the range of a stationary Markov random field. 
normalize 
If TRUE the basis functions will be normalized to
give a marginal variance of one for each level of
multiresolution. (Normalizing by levels makes it easier to
interpret the 
nu 
A
smoothness parameter that controls relative sizes of

overlap 
Controls the overlap among the radial basis functions and
should be in units of the lattice spacing. For the rectangular
case the default of 2.5 means that the support of the Wenland
basis function will overlap 2.5 lattice units in each
direction. See 
rho 
A scalar, the sill or marginal variance of the process. 
BasisFunction 
Text string giving the 1d form for basis function. 
rho.object 
A prediction object to specify part of the
marginal variance for the process. Specifically the form is
VAR(g(x1))= rho*h(x1) Calling 
returnCall 
If TRUE the call to LKrigSetup is also included as part of the LKinfo object. 
sigma 
The measurement error standard deviation. Also called the nugget variance in geostatistics. 
V 
See entry in 
verbose 
If TRUE print out intermediate information. 
x 
Spatial locations that define the spatial domain for prediction. This is only used to determine ranges of the grid for the basis functions so, for example, for a rectangular domain only two points are required that bound the rest of the data locations. E.g. x= rbind( c( 0,0), c(1,1)) will set the domain to be the unit square. 
... 
Specific arguments that will be included in the

Many of the functions within LKrigSetup are overloaded to
adapt to the LKGeometry class. This makes it easy to add new
geometries or other models to the LatticeKrig framework. The
required components of this object (see below) outline how
the latticeKrig model is structured and what should be common
features independent of the geometry. The key components are
latticeInfo that contains the information used to generate the
spatial autoregressive matrix on the lattice (see
LKrigSAR
) and the lattice centers (see
LKrigCenters
). The component basisInfo used to generate
the radial basis function (see LKrig.basis)
The function LKrigEasyDefaults is used in the top level function LattticeKrig to make the logic of different default choices more readable and reduces the clutter in this function. Its main purpose is to find a reasonable choice for NC when this is not specified.
The function LKinfoUpdate is more of a utility used for clarity that allows one to update the LKinfo object with particular components without having to recreate the entire object. This function is used in the MLE search when just values of alpha or a.wght are being varied.
An object with class "LKinfo" and also the additional class given by LKGeometry. The required components are:
Number of levels
alpha parameters as a list that has nlevel components and possibly some attributes.
a.wght parameters as a list that has nlevel components and possibly some attributes.
nu parameter
A logical indicating whether to normalize.
Value of lambda.
Value of sigma.
Value for rho.
Value for rho.object.
A list with specific multiresolution lattice information
All arguments passed in the call and any in in ...
A list with basis information.
The actual call used to create this object.
Doug Nychka
1 2 3 4 5 6 7 8 9 10 11 12  data(ozone2)
# find the ranges of the data, this is the same as passing
# the entire set of observation locations and is more compact
sDomain<apply( ozone2$lon.lat, 2,"range")
LKinfo< LKrigSetup( sDomain, NC=10, nlevel=2, alpha=c(1,.5),
a.wght = 5)
print( LKinfo)
LKinfo2< LKinfoUpdate( LKinfo, a.wght=4.1, NC=12)
LKinfo3< LKrigSetup( sDomain, NC=12, nlevel=2, alpha=c(1,.5),
a.wght=4.1)
# LKinfo2 and LKinfo3 should be the same.

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