USCounties: Contiguity Matrix of U.S. Counties

In Matrix: Sparse and Dense Matrix Classes and Methods

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. \Sexpr[results=rd]{tools:::Rd_expr_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))

Matrix documentation built on Aug. 13, 2024, 3:01 p.m.