Fit a Spatial Linear Model (Generalized Least Squares)
DESCRIPTION:
Fits a spatial linear model (generalized least squares), returning the
bare minimum computations.
USAGE:
slm.fit.spatial(x, y, cov.family, initial, spatial.arglist=NULL,
start=NULL, ...)
REQUIRED ARGUMENTS:
x, y
numeric vectors or matrices for the predictors and the response in a
linear model. Typically, but not necessarily,
x will be the model
matrix generated by one of the fitting functions. Note that missing
values are not allowed.
cov.family
the spatial covariance family to be fit. Valid values are:
CAR
(conditional auto-regression),
SAR (simultaneous auto-regression),
or
MA (moving average). These are S-PLUS objects containing
functions required by the
slm fitting algorithm. The covariance model
is defined by argument
cov.family and is further defined by the
variables listed in argument
spatial.arglist.
initial
a list containing the quantities returned by the
cov.family$initialize function, e.g.,
a list containing arguments required by (and further defining) the
spatial model as specified by argument
cov.family. Instead of
entering these arguments individually,
spatial.arglist is used
to allow the algorithms to be generalized to different kinds of
models. For all of the models currently fit by
slm, the
spatial.arglist argument contains the following variables:
REQUIRED
neighbor - an object of class
"spatial.neighbor" containing the
neighbors and weights to be used when defining the model covariance
(see
spatial.neighbor).
OPTIONAL
region.id - when argument
subset is given and rows have been removed from
the
neighbor object, variable
region.id must be used to give the rows
currently available in the spatial neighbor object. This is described
below in the DETAILS section. Also see the help file for
spatial.subset.
weights - the
cov.family uses the
neighbor argument to
determine a covariance matrix for the residuals. It is possible to
specify a vector of observation weights to be included in the
covariance matrix. Let D denote the diagonal weight matrix, and let S
denote the part of the covariance matrix estimate which is based on
the
neighbor variable in argument
spatial.arglist. Then if
weights are specified, the residual covariance matrix is computed as
matrix expression:
sqrt(D) * S * sqrt(D).
start - vector of starting values for the optimization algorithm.
print.level - if
TRUE, then the function evaluations are printed as the
optimization algorithm proceeds. This can be quite useful for checking on
convergence of the algorithm to the maximum likelihood estimates.
start
the initial starting value of the parameters, which is
a vector with length equal to the number of weight
matrices represented by argument neighbor. If it
is not specified, the default starting value in
spatial.arglist
will be used. If that is also not provided nor valid, an
initialization procedure will be called to determine the starting
value of the parameters.
...
Additional arguments which can be passed to the function
slm.nlminb and which effect the iterative estimation algorithm.
In particular, various algorithmic control values can be passed, along
with the lower and upper bounds of the parameters.
VALUE:
A list of class
"slm". For a description of the contents of
the class, see the top level routine, function
slm.