USCounties {Matrix} | R Documentation |

## Contiguity Matrix of U.S. Counties

### Description

This matrix gives the contiguities of 3111 U.S. counties,
using the queen criterion of at least one shared vertex
or edge.

### Usage

`data(USCounties)`

### Format

A `3111 \times 3111`

sparse, symmetric
matrix of class `dsCMatrix`

, with 9101
nonzero entries.

### Source

GAL lattice file ‘usc_q.GAL’
(retrieved in 2008 from
‘http://sal.uiuc.edu/weights/zips/usc.zip’
with permission from Luc Anselin for use and distribution)
was read into **R** using function `read.gal`

from package spdep.

Neighbour lists were augmented with row-standardized
(and then symmetrized) spatial weights, using functions
`nb2listw`

and `similar.listw`

from packages
spdep and spatialreg.
The resulting `listw`

object was coerced to class
`dsTMatrix`

using `as_dsTMatrix_listw`

from spatialreg,
and subsequently to class `dsCMatrix`

.

### References

Ord, J. K. (1975).
Estimation methods for models of spatial interaction.
*Journal of the American Statistical Association*,
*70*(349), 120-126.
doi:10.2307/2285387

### Examples

```
data(USCounties, package = "Matrix")
(n <- ncol(USCounties))
I <- .symDiagonal(n)
set.seed(1)
r <- 50L
rho <- 1 / runif(r, 0, 0.5)
system.time(MJ0 <- sapply(rho, function(mult)
determinant(USCounties + mult * I, logarithm = TRUE)$modulus))
## Can be done faster by updating the Cholesky factor:
C1 <- Cholesky(USCounties, Imult = 2)
system.time(MJ1 <- sapply(rho, function(mult)
determinant(update(C1, USCounties, mult), sqrt = FALSE)$modulus))
stopifnot(all.equal(MJ0, MJ1))
C2 <- Cholesky(USCounties, super = TRUE, Imult = 2)
system.time(MJ2 <- sapply(rho, function(mult)
determinant(update(C2, USCounties, mult), sqrt = FALSE)$modulus))
stopifnot(all.equal(MJ0, MJ2))
```

[Package

*Matrix* version 1.6-1.1

Index]