Spatial weights for neighbours lists
Description
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.
Usage
1 2  nb2listw(neighbours, glist=NULL, style="W", zero.policy=NULL)
can.be.simmed(listw)

Arguments
neighbours 
an object of class 
glist 
list of general weights corresponding to neighbours 
style 

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 zerolength weights vectors 
listw 
a spatial weights object 
Details
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 variancestabilizing coding scheme proposed by Tiefelsdorf et al. 1999, p. 167168 (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 zeroneighbour 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 noneighbour 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.
Value
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 
Author(s)
Roger Bivand Roger.Bivand@nhh.no
References
Tiefelsdorf, M., Griffith, D. A., Boots, B. 1999 A variancestabilizing 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.
See Also
summary.nb
, read.gal
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37  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$weights))
# introducing other conditions into weights  only earlier sales count
# see http://sal.uiuc.edu/pipermail/openspace/2005October/000610.html
data(baltimore)
set.seed(211)
dates < sample(1:500, nrow(baltimore), replace=TRUE)
nb_15nn < knn2nb(knearneigh(cbind(baltimore$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]]]
