Spatial neighbour sparse representation

Interface between Matrix class objects and weights lists. The as.spam.listw method converts a "listw" object to a sparse matrix as defined in the spam package.

as.spam.listw(listw)
listw2U_spam(lw)
listw2U_Matrix(lw)
as_dgRMatrix_listw(listw)
as_dsTMatrix_listw(listw)
as_dsCMatrix_I(n)
as_dsCMatrix_IrW(W, rho)
Jacobian_W(W, rho)
powerWeights(W, rho, order=250, X, tol=.Machine$double.eps^(3/5))

Arguments

listw, lw

a listw object from for example nb2listw

W

a dsTMatrix object created using as_dsTMatrix_listw from a symmetric listw object

rho

spatial regression coefficient

n

length of diagonal for identity matrix

order

Power series maximum limit

X

A numerical matrix

tol

Tolerance for convergence of power series

Author

Roger Bivand Roger.Bivand@nhh.no

See also

nb2listw

Examples

if (FALSE) {
require(sf, quietly=TRUE)
columbus <- st_read(system.file("shapes/columbus.shp", package="spData")[1], quiet=TRUE)
#require(spdep, quietly=TRUE)
col.gal.nb <- spdep::read.gal(system.file("weights/columbus.gal", package="spData")[1])
col.listw <- spdep::nb2listw(col.gal.nb)
if (require("spam", quietly=TRUE)) {
  col.sp <- as.spam.listw(col.listw)
  str(col.sp)
}
suppressMessages(nyadjmat <- as.matrix(foreign::read.dbf(system.file(
 "misc/nyadjwts.dbf", package="spData")[1])[-1]))
nyadjlw <- spdep::mat2listw(nyadjmat)
listw_NY <- spdep::nb2listw(nyadjlw$neighbours, style="B")
W_C <- as(listw_NY, "CsparseMatrix")
W_R <- as(listw_NY, "RsparseMatrix")
W_S <- as(listw_NY, "symmetricMatrix")
n <- nrow(W_S)
I <- Diagonal(n)
rho <- 0.1
c(determinant(I - rho * W_S, logarithm=TRUE)$modulus)
sum(log(1 - rho * eigenw(listw_NY)))
nW <- - W_S
nChol <- Cholesky(nW, Imult=8)
n * log(rho) + (2 * c(determinant(update(nChol, nW, 1/rho))$modulus))
}
nb7rt <- spdep::cell2nb(7, 7, torus=TRUE)
x <- matrix(sample(rnorm(500*length(nb7rt))), nrow=length(nb7rt))
lw <- spdep::nb2listw(nb7rt)
if (FALSE) {
# Only needed in some simulation settings where the input and
# output distributions must agree in all but autocorrelation
e <- eigenw(lw)
x <- apply(x, 2, scale)
st <- apply(x, 2, function(x) shapiro.test(x)$p.value)
x <- x[, (st > 0.2 & st < 0.8)]
x <- apply(x, 2, function(v) residuals(spautolm(v ~ 1, listw=lw,
 method="eigen", control=list(pre_eig=e, fdHess=FALSE))))
x <- apply(x, 2, scale)
}
W <- as(lw, "CsparseMatrix")
system.time(e <- invIrM(nb7rt, rho=0.98, method="solve", feasible=NULL) %*% x)
#>    user  system elapsed 
#>   0.003   0.000   0.002 
system.time(ee <- powerWeights(W, rho=0.98, X=x))
#> Warning: not converged within order iterations
#>    user  system elapsed 
#>   0.182   0.004   0.186 
str(attr(ee, "internal"))
#> List of 5
#>  $ series: num [1:250] 0.286 0.233 0.199 0.175 0.157 ...
#>  $ order : num 250
#>  $ tol   : num 4.05e-10
#>  $ iter  : num 250
#>  $ conv  : logi FALSE
all.equal(e, as(ee, "matrix"), check.attributes=FALSE)
#> [1] "Mean relative difference: 0.00604604"
if (FALSE) {
system.time(ee <- powerWeights(W, rho=0.9, X=x))
system.time(ee <- powerWeights(W, rho=0.98, order=1000, X=x))
all.equal(e, as(ee, "matrix"), check.attributes=FALSE)
nb60rt <- spdep::cell2nb(60, 60, torus=TRUE)
W <- as(spdep::nb2listw(nb60rt), "CsparseMatrix")
set.seed(1)
x <- matrix(rnorm(dim(W)[1]), ncol=1)
system.time(ee <- powerWeights(W, rho=0.3, X=x))
str(as(ee, "matrix"))
obj <- errorsarlm(as(ee, "matrix")[,1] ~ 1, listw=spdep::nb2listw(nb60rt), method="Matrix")
coefficients(obj)
}