Spatial Family Object

DESCRIPTION:

Class of objects used for defining the covariance structure in a spatial regression. An object of class cov.family contains information required to optimize a profile likelihood in a spatial regression analysis, and is required input for slm.

GENERATION:

No functions for constructing objects of class "cov.family" exist. Objects of the class have already been created for the standard covariance structures, CAR , SAR, and MA. If you choose to construct a new "cov.family" object, the easiest way to proceed is to copy an existing "cov.family" object, and modify the new object.

METHODS:

The class "cov.family" has no associated methods.

INHERITANCE:

Class "cov.family" does not inherit from any other class.

STRUCTURE:

The "cov.family" object is implemented as a list with the components given below.

VALUE:

name
the name of the covariance family.
det.fun
a function for computing the determinant of the estimated spatial covariance matrix.

det.fun(parameters, spatial.arglist, initial)

ARGUMENTS

parameters - a vector containing the current values of the covariance matrix model parameters. A profile likelihood for the covariance matrix model parameters is optimized given optimal values for the parameters in the linear model.

spatial.arglist - a list of additional arguments to be used in the spatial model of the covariance matrix. See routine slm.

initial - a list containing the return value from the initialize function described below.

VALUE

the determinant of the current spatial covariance matrix.

solve.fun
a function to solve for y in the linear equation x = S y, where S is a square symmetric covariance matrix, and x is a known matrix. The solution of this equation defines the spatial covariance matrix S.

solve.fun(parameters, x, spatial.arglist, initial)

ARGUMENTS

parameters - a vector containing the current values of the spatial parameters required by the model for the covariance matrix (see above).

x - a matrix containing the right hand sides.

spatial.arglist - a list of additional arguments to be used in defining the spatial model for the covariance matrix. See routine slm .

initial - a list containing the return value from the initialize function described below. These may be used as additional variables when computing the spatial covariance matrix.

VALUE

the matrix of solutions x to the linear equations y = S x, where S is the spatial covariance matrix specified by this family of covariance matrices.

initial.parameters
a function to compute or set initial parameter estimates.

initial.parameters(spatial.arglist)

ARGUMENTS

spatial.arglist - a list of additional arguments to be used in the spatial model of the covariance matrix. See routine slm.

VALUE

a vector containing the initial parameter estimates.

initialize
a function used to compute initial statistics for use in the iterative algorithm.

initialize(spatial.arglist, subset)

ARGUMENTS

spatial.arglist - a list of additional arguments to be used in the spatial model of the covariance matrix. See routine slm.

subset - a logical vector (which is replicated to have length equal to the number of observations), a numeric vector, or a character vector of the row names. This vector is used to indicate which observation numbers are to be included in the analysis. All observations are included by default. See routine slm.

VALUE

a list to be used by the det.fun and the solve.fun to simplify and speed the computations. For many covariance models, this is the eigenvalues of the symmetric spatial neighbor matrix.

finalize
a function called at the termination of the computations for the cov.family to allow cleanup operations, should these be necessary.

finalize(spatial.arglist, initial)

ARGUMENTS

spatial.arglist - a list of additional arguments to be used in the spatial model of the covariance matrix. See routine slm.

initial - a list containing the values returned by the cov.family$initialize function. This list depends upon the cov.family.

residual.fun
a function to compute the residuals for the spatial model.

residual.fun(x, y, beta, parameters, spatial.arglist)

ARGUMENTS

x - the independent variable(s) (if any).

y - the dependent variable.

beta the estimated linear model coefficients.

parameters - the estimated covariance model parameters.

spatial.arglist - a list of additional arguments to be used in the spatial model of the covariance matrix. See routine slm.

VALUE

The return value contains an estimate of the residuals (standardized to be independent with constant variance).

DETAILS:

The six functions, det.fun, solve.fun, residual.fun, initial.parameters , initialize, and finalize are used by the spatial regression routine to define a spatial regression. Currently three models for a spatial regression can be fit: CAR, SAR, and MA.

SEE ALSO:

, , , .