Contiguity Matrix of U.S. Counties — USCounties • Matrix

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

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 
#>   0.255   0.020   0.276 

## 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 
#>   0.078   0.000   0.077 
stopifnot(all.equal(MJ0, MJ1))

C2 <- Cholesky(USCounties, super = TRUE, Imult = 2)
#> Warning: CHOLMOD warning 'matrix not positive definite' at file 'Supernodal/t_cholmod_super_numeric_worker.c', line 1114
#> Error in .local(A, ...): leading principal minor of order 1550 is not positive
system.time(MJ2 <- sapply(rho, function(mult)
    determinant(update(C2, USCounties, mult), sqrt = FALSE)$modulus))
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'x' in selecting a method for function 'determinant': error in evaluating the argument 'object' in selecting a method for function 'update': object 'C2' not found
#> Timing stopped at: 0 0 0
stopifnot(all.equal(MJ0, MJ2))
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'current' in selecting a method for function 'all.equal': object 'MJ2' not found