Compute a Spatial Weight Matrix

DESCRIPTION:
Given an object of class "spatial.neighbor" (and an optional set of neighbor coefficients), spatial.weights computes the spatial weight matrix.

USAGE:
spatial.weights(neighbor, parameters=NULL, region.id=NULL)

REQUIRED ARGUMENTS:
neighbor:
an object of class spatial.neighbor used (in conjunction with the elements of argument parameters) to compute a the spatial weight matrix. In situations with more than one weight matrix (see routine spatial.neighbor, and the DETAILS section below), spatial.weights computes a weighted sum of the weight matrices.

OPTIONAL ARGUMENTS:
parameters:
a vector with length equal to the number of weight matrices represented by the component matrix of argument neighbor. If parameters is not specified, a vector of all 1s is assumed.
region.id:
a vector with length equal to the number of regions in the spatial lattice. If variables row.id and col.id of argument neighbor are not integer valued variables with sequential values from 1 to the number or regions in the lattice, then argument region.id must be specified and is used to obtain a sequential coding of the lattice regions.

VALUE:
let A[i] denote the spatial weight matrix of type i, and let parameters[i] denote its corresponding parameter value. Then spatial.weights returns the linear sum over i of parameter[i]*A[i].

DETAILS:
Argument neighbor is a sparse matrix representation of one or more matrices used to indicate the strength of neighbor relationships between regions on a regular or irregular spatial lattice.

Let a[i,j] denote a non-zero element of the k-th weight matrix. This implies that regions i and j are neighbors of the k-th kind, and the strength of this relationship is given by the magnitude of a[i,j].

spatial.weights can compute a weighted sum of the matrices A, where the weights in the linear combination are given by the elements in argument parameters. In practice, you might want to use routine spatial.weights when, for example, you want to compute the spatial covariance matrix for a spatial process.


SEE ALSO:
spatial.neighbor .

EXAMPLES:
row.id <- c(1,1,2,3)
col.id <- c(2,3,3,4)
neighbor <- spatial.neighbor(row.id=row.id, col.id=col.id, symmetric=T)
spatial.weights(neighbor)