R: USCounties Contiguity Matrix

USCounties {Matrix} | R Documentation

## USCounties Contiguity Matrix

### Description

This matrix represents the contiguities of 3111 US counties using the Queen criterion of at least a single shared boundary point. The representation is as a row standardised spatial weights matrix transformed to a symmetric matrix (see Ord (1975), p. 125).

### Usage

    data(USCounties)

### Format

A 3111 ^2 symmetric sparse matrix of class `dsCMatrix` with 9101 non-zero entries.

### Details

The data were read into R using `read.gal`, and row-standardised and transformed to symmetry using `nb2listw` and `similar.listw`. This spatial weights object was converted to class `dsCMatrix` using `as_dsTMatrix_listw` and coercion.

### Source

The data were retrieved from http://sal.uiuc.edu/weights/zips/usc.zip, files “usc.txt” and “usc\_q.GAL”, with permission for use and distribution from Luc Anselin.

### References

Ord, J. K. (1975) Estimation methods for models of spatial interaction; Journal of the American Statistical Association 70, 120–126.

### Examples

    data(USCounties)
    (n <- ncol(USCounties))
    IM <- .symDiagonal(n)
    nn <- 50
    set.seed(1)
    rho <- runif(nn, 0, 1)
    system.time(MJ <- sapply(rho, function(x)
    	determinant(IM - x * USCounties, logarithm = TRUE)$modulus))

    ## can be done faster, by update()ing the Cholesky factor:
    nWC <- -USCounties
    C1 <- Cholesky(nWC, Imult = 2)
    system.time(MJ1 <- n * log(rho) +
                sapply(rho, function(x)
                       2 * c(determinant(update(C1, nWC, 1/x))$modulus)))
    all.equal(MJ, MJ1)

    C2 <- Cholesky(nWC, super = TRUE, Imult = 2)
    system.time(MJ2 <- n * log(rho) +
                sapply(rho, function(x)
                       2 * c(determinant(update(C2, nWC, 1/x))$modulus)))
    all.equal(MJ, MJ2)
    system.time(MJ3 <- n * log(rho) + Matrix:::ldetL2up(C1, nWC, 1/rho))
    stopifnot(all.equal(MJ, MJ3))
    system.time(MJ4 <- n * log(rho) + Matrix:::ldetL2up(C2, nWC, 1/rho))
    stopifnot(all.equal(MJ, MJ4))

[Package Matrix version 1.1-4 Index]