Contiguity Matrix of U.S. Counties

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))
#> [1] 3111
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))
#>    user  system elapsed 
#>   0.333   0.017   0.356 

## 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))
#>    user  system elapsed 
#>   0.093   0.000   0.094 
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))
#>    user  system elapsed 
#>   0.093   0.001   0.095 
stopifnot(all.equal(MJ0, MJ2))