nb2listw: Spatial weights for neighbours lists
In spdep: Spatial Dependence: Weighting Schemes, Statistics and Models

Description Usage Arguments Details Value Author(s) References See Also Examples

The nb2listw function supplements a neighbours list with spatial weights for the chosen coding scheme. The can.be.simmed helper function checks whether a spatial weights object is similar to symmetric and can be so transformed to yield real eigenvalues or for Cholesky decomposition.

1 2	nb2listw(neighbours, glist=NULL, style="W", zero.policy=NULL) can.be.simmed(listw)

`neighbours`	an object of class `nb`
`glist`	list of general weights corresponding to neighbours
`style`	`style` can take values “W”, “B”, “C”, “U”, “minmax” and “S”
`zero.policy`	default NULL, use global option value; if FALSE stop with error for any empty neighbour sets, if TRUE permit the weights list to be formed with zero-length weights vectors
`listw`	a spatial weights object

Starting from a binary neighbours list, in which regions are either listed as neighbours or are absent (thus not in the set of neighbours for some definition), the function adds a weights list with values given by the coding scheme style chosen. B is the basic binary coding, W is row standardised (sums over all links to n), C is globally standardised (sums over all links to n), U is equal to C divided by the number of neighbours (sums over all links to unity), while S is the variance-stabilizing coding scheme proposed by Tiefelsdorf et al. 1999, p. 167-168 (sums over all links to n).

If zero policy is set to TRUE, weights vectors of zero length are inserted for regions without neighbour in the neighbours list. These will in turn generate lag values of zero, equivalent to the sum of products of the zero row t(rep(0, length=length(neighbours))) %*% x, for arbitraty numerical vector x of length length(neighbours). The spatially lagged value of x for the zero-neighbour region will then be zero, which may (or may not) be a sensible choice.

If the sum of the glist vector for one or more observations is zero, a warning message is issued. The consequence for later operations will be the same as if no-neighbour observations were present and the zero.policy argument set to true.

The “minmax” style is based on Kelejian and Prucha (2010), and divides the weights by the minimum of the maximum row sums and maximum column sums of the input weights. It is similar to the C and U styles; it is also available in Stata.

A listw object with the following members:

`style`	one of W, B, C, U, S, minmax as above
`neighbours`	the input neighbours list
`weights`	the weights for the neighbours and chosen style, with attributes set to report the type of relationships (binary or general, if general the form of the glist argument), and style as above

Roger Bivand Roger.Bivand@nhh.no

Tiefelsdorf, M., Griffith, D. A., Boots, B. 1999 A variance-stabilizing coding scheme for spatial link matrices, Environment and Planning A, 31, pp. 165–180; Kelejian, H. H., and I. R. Prucha. 2010. Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances. Journal of Econometrics, 157: pp. 53–67.

summary.nb, read.gal

example(columbus)
coords <- coordinates(columbus)
cards <- card(col.gal.nb)
col.w <- nb2listw(col.gal.nb)
plot(cards, unlist(lapply(col.w$weights, sum)),xlim=c(0,10),
ylim=c(0,10), xlab="number of links", ylab="row sums of weights")
col.b <- nb2listw(col.gal.nb, style="B")
points(cards, unlist(lapply(col.b$weights, sum)), col="red")
col.c <- nb2listw(col.gal.nb, style="C")
points(cards, unlist(lapply(col.c$weights, sum)), col="green")
col.u <- nb2listw(col.gal.nb, style="U")
points(cards, unlist(lapply(col.u$weights, sum)), col="orange")
col.s <- nb2listw(col.gal.nb, style="S")
points(cards, unlist(lapply(col.s$weights, sum)), col="blue")
legend(x=c(0, 1), y=c(7, 9), legend=c("W", "B", "C", "U", "S"),
col=c("black", "red", "green", "orange", "blue"), pch=rep(1,5))
summary(nb2listw(col.gal.nb, style="minmax"))
dlist <- nbdists(col.gal.nb, coords)
dlist <- lapply(dlist, function(x) 1/x)
col.w.d <- nb2listw(col.gal.nb, glist=dlist)
summary(unlist(col.w$weights))
summary(unlist(col.w.d$weights))
# introducing other conditions into weights - only earlier sales count
# see http://sal.uiuc.edu/pipermail/openspace/2005-October/000610.html
data(baltimore)
set.seed(211)
dates <- sample(1:500, nrow(baltimore), replace=TRUE)
nb_15nn <- knn2nb(knearneigh(cbind(baltimore$X, baltimore$Y), k=15))
glist <- vector(mode="list", length=length(nb_15nn))
for (i in seq(along=nb_15nn))
  glist[[i]] <- ifelse(dates[i] > dates[nb_15nn[[i]]], 1, 0)
listw_15nn_dates <- nb2listw(nb_15nn, glist=glist, style="B")
which(lag(listw_15nn_dates, baltimore$PRICE) == 0.0)
which(sapply(glist, sum) == 0)
ex <- which(sapply(glist, sum) == 0)[1]
dates[ex]
dates[nb_15nn[[ex]]]

Loading required package: sp
Loading required package: Matrix

colmbs> require(maptools)
Loading required package: maptools
Checking rgeos availability: TRUE

colmbs> columbus <- readShapePoly(system.file("etc/shapes/columbus.shp",
colmbs+  package="spdep")[1])

colmbs> col.gal.nb <- read.gal(system.file("etc/weights/columbus.gal",
colmbs+  package="spdep")[1])
Warning message:
use rgdal::readOGR or sf::st_read 
Characteristics of weights list object:
Neighbour list object:
Number of regions: 49 
Number of nonzero links: 230 
Percentage nonzero weights: 9.579342 
Average number of links: 4.693878 
Link number distribution:

 2  3  4  5  6  7  8  9 10 
 7  7 13  4  9  6  1  1  1 
7 least connected regions:
1 6 31 39 42 46 47 with 2 links
1 most connected region:
20 with 10 links

Weights style: minmax 
Weights constants summary:
        n   nn S0  S1    S2
minmax 49 2401 23 4.6 50.48
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.1000  0.1429  0.1667  0.2130  0.2500  0.5000 
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
0.06977 0.13114 0.17710 0.21304 0.27124 0.67178 
Warning message:
In nb2listw(nb_15nn, glist = glist, style = "B") : zero sum general weights
 [1]  39  40  48  92 112 117 118 143 160 176 177 185 191 198
 [1]  39  40  48  92 112 117 118 143 160 176 177 185 191 198
[1] 13
 [1] 266  44 168 434 222  38 432 399 172 213 430  29 312 237  55