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 1.2-17

Index]