Version:	1.3-10
Date:	2025-01-17
Title:	Spatial Dependence: Weighting Schemes, Statistics
Encoding:	UTF-8
Depends:	R (≥ 3.3.0), methods, spData (≥ 2.3.1), sf
Imports:	stats, deldir, boot (≥ 1.3-1), graphics, utils, grDevices, units, s2, e1071, sp (≥ 1.0)
Suggests:	spatialreg (≥ 1.2-1), Matrix, parallel, dbscan, RColorBrewer, lattice, xtable, foreign, igraph, RSpectra, knitr, classInt, tmap, spam, ggplot2, rmarkdown, tinytest, rgeoda (≥ 0.0.11.1)
URL:	https://github.com/r-spatial/spdep/, https://r-spatial.github.io/spdep/
BugReports:	https://github.com/r-spatial/spdep/issues/
Description:	A collection of functions to create spatial weights matrix objects from polygon 'contiguities', from point patterns by distance and tessellations, for summarizing these objects, and for permitting their use in spatial data analysis, including regional aggregation by minimum spanning tree; a collection of tests for spatial 'autocorrelation', including global 'Morans I' and 'Gearys C' proposed by 'Cliff' and 'Ord' (1973, ISBN: 0850860369) and (1981, ISBN: 0850860814), 'Hubert/Mantel' general cross product statistic, Empirical Bayes estimates and 'Assunção/Reis' (1999) <doi:10.1002/(SICI)1097-0258(19990830)18:16%3C2147::AID-SIM179%3E3.0.CO;2-I> Index, 'Getis/Ord' G ('Getis' and 'Ord' 1992) <doi:10.1111/j.1538-4632.1992.tb00261.x> and multicoloured join count statistics, 'APLE' ('Li 'et al.' ) <doi:10.1111/j.1538-4632.2007.00708.x>, local 'Moran's I', 'Gearys C' ('Anselin' 1995) <doi:10.1111/j.1538-4632.1995.tb00338.x> and 'Getis/Ord' G ('Ord' and 'Getis' 1995) <doi:10.1111/j.1538-4632.1995.tb00912.x>, 'saddlepoint' approximations ('Tiefelsdorf' 2002) <doi:10.1111/j.1538-4632.2002.tb01084.x> and exact tests for global and local 'Moran's I' ('Bivand et al.' 2009) <doi:10.1016/j.csda.2008.07.021> and 'LOSH' local indicators of spatial heteroscedasticity ('Ord' and 'Getis') <doi:10.1007/s00168-011-0492-y>. The implementation of most of these measures is described in 'Bivand' and 'Wong' (2018) <doi:10.1007/s11749-018-0599-x>, with further extensions in 'Bivand' (2022) <doi:10.1111/gean.12319>. 'Lagrange' multiplier tests for spatial dependence in linear models are provided ('Anselin et al'. 1996) <doi:10.1016/0166-0462(95)02111-6>, as are 'Rao' score tests for hypothesised spatial 'Durbin' models based on linear models ('Koley' and 'Bera' 2023) <doi:10.1080/17421772.2023.2256810>. A local indicators for categorical data (LICD) implementation based on 'Carrer et al.' (2021) <doi:10.1016/j.jas.2020.105306> and 'Bivand et al.' (2017) <doi:10.1016/j.spasta.2017.03.003> was added in 1.3-7. From 'spdep' and 'spatialreg' versions >= 1.2-1, the model fitting functions previously present in this package are defunct in 'spdep' and may be found in 'spatialreg'.
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
VignetteBuilder:	knitr
RoxygenNote:	RoxygenNote: 6.1.1
NeedsCompilation:	yes
Packaged:	2025-01-20 11:19:03 UTC; rsb
Author:	Roger Bivand [cre, aut], Micah Altman [ctb], Luc Anselin [ctb], Renato Assunção [ctb], Anil Bera [ctb], Olaf Berke [ctb], F. Guillaume Blanchet [ctb], Marilia Carvalho [ctb], Bjarke Christensen [ctb], Yongwan Chun [ctb], Carsten Dormann [ctb], Stéphane Dray [ctb], Dewey Dunnington [ctb], Virgilio Gómez-Rubio [ctb], Malabika Koley [ctb], Tomasz Kossowski [ctb], Elias Krainski [ctb], Pierre Legendre [ctb], Nicholas Lewin-Koh [ctb], Angela Li [ctb], Giovanni Millo [ctb], Werner Mueller [ctb], Hisaji Ono [ctb], Josiah Parry [ctb], Pedro Peres-Neto [ctb], Michał Pietrzak [ctb], Gianfranco Piras [ctb], Markus Reder [ctb], Jeff Sauer [ctb], Michael Tiefelsdorf [ctb], René Westerholt [ctb], Justyna Wilk [ctb], Levi Wolf [ctb], Danlin Yu [ctb]
Maintainer:	Roger Bivand <Roger.Bivand@nhh.no>
Repository:	CRAN
Date/Publication:	2025-01-20 13:00:01 UTC

Aggregate a spatial neighbours object

Description

The method aggregates a spatial neighbours object, creating a new object listing the neighbours of the aggregates.

Usage

## S3 method for class 'nb'
aggregate(x, IDs, remove.self = TRUE, ...)

Arguments

Value

an nb neighbour object, with empty aggregates dropped.

Note

Method suggested by Roberto Patuelli

Author(s)

Roger Bivand Roger.Bivand@nhh.no

Examples

data(used.cars, package="spData")
data(state)
cont_st <- match(attr(usa48.nb, "region.id"), state.abb)
cents <- as.matrix(as.data.frame(state.center))[cont_st,]
opar <- par(mfrow=c(2,1))
plot(usa48.nb, cents, xlim=c(-125, -65), ylim=c(25, 50))
IDs <- as.character(state.division[cont_st])
agg_cents <- aggregate(cents, list(IDs), mean)
agg_nb <- aggregate(usa48.nb, IDs)
plot(agg_nb, agg_cents[, 2:3], xlim=c(-125, -65), ylim=c(25, 50))
text(agg_cents[, 2:3], agg_cents[, 1], cex=0.6)
par(opar)

Measure distance from plot

Description

Measure a distance between two points on a plot using locator; the function checks par("plt") and par("usr") to try to ensure that the aspect ratio y/x is 1, that is that the units of measurement in both x and y are equivalent.

Usage

airdist(ann=FALSE)

Arguments

Value

a list with members:

Author(s)

Roger Bivand Roger.Bivand@nhh.no

See Also

locator

Distance-weighted autocovariate

Description

Calculates the autocovariate to be used in autonormal, autopoisson or autologistic regression. Three distance-weighting schemes are available.

Usage

autocov_dist(z, xy, nbs = 1, type = "inverse", zero.policy = NULL,
 style = "B", longlat=NULL)

Arguments

Value

A numeric vector of autocovariate values

Note

The validity of this approach strongly hinges on the correct choice of the neighbourhood scheme! Using style="B" ensures symmetry of the neighbourhood matrix (i.e. w_{nm} = w_{mn}). Please see Bardos et al. (2015) for details.

Author(s)

Carsten F. Dormann and Roger Bivand

References

Augustin N.H., Mugglestone M.A. and Buckland S.T. (1996) An autologistic model for the spatial distribution of wildlife. Journal of Applied Ecology, 33, 339-347; Gumpertz M.L., Graham J.M. and Ristaino J.B. (1997) Autologistic model of spatial pattern of Phytophthora epidemic in bell pepper: effects of soil variables on disease presence. Journal of Agricultural, Biological and Environmental Statistics, 2, 131-156; Bardos, D.C., Guillera-Arroita, G. and Wintle, B.A. (2015) Valid auto-models for spatially autocorrelated occupancy and abundance data. arXiv, 1501.06529.

See Also

nb2listw

Examples

columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
#xy <- cbind(columbus$X, columbus$Y)
xy <- st_coordinates(st_centroid(st_geometry(columbus),
 of_largest_polygon=TRUE))
ac1a <- autocov_dist(columbus$CRIME, xy, nbs=10, style="B",
 type="one")
acinva <- autocov_dist(columbus$CRIME, xy, nbs=10, style="B",
 type="inverse")
acinv2a <- autocov_dist(columbus$CRIME, xy, nbs=10, style="B",
 type="inverse.squared")
plot(ac1a ~ columbus$CRIME, pch=16, ylim=c(0,9000))
points(acinva ~ columbus$CRIME, pch=16, col="red")
points(acinv2a ~ columbus$CRIME, pch=16, col="blue")
legend("topleft", legend=c("one", "inverse", "inverse.squared"),
 col=c("black", "red", "blue"), bty="n", pch=16)
nb <- dnearneigh(xy, 0, 10)
lw <- nb2listw(nb, style="B")
ac1b <- lag(lw, columbus$CRIME)
all.equal(ac1b, ac1a)
nbd <- nbdists(nb, xy)
gl <- lapply(nbd, function(x) 1/x)
lw <- nb2listw(nb, glist=gl, style="B")
acinvb <- lag(lw, columbus$CRIME)
all.equal(acinvb, acinva)
gl2 <- lapply(nbd, function(x) 1/(x^2))
lw <- nb2listw(nb, glist=gl2, style="B")
acinv2b <- lag(lw, columbus$CRIME)
all.equal(acinv2b, acinv2a)
#xy <- SpatialPoints(xy)
#acinva <- autocov_dist(columbus$CRIME, xy, nbs=10, style="W",
# type="inverse")
#nb <- dnearneigh(xy, 0, 10)
#nbd <- nbdists(nb, xy)
#gl <- lapply(nbd, function(x) 1/x)
#lw <- nb2listw(nb, glist=gl)
#acinvb <- lag(lw, columbus$CRIME)
#all.equal(acinvb, acinva)
acinvc <- autocov_dist(columbus$CRIME, st_centroid(st_geometry(columbus),
 of_largest_polygon=TRUE), nbs=10, style="W", type="inverse")
all.equal(acinvc, acinva)

Data set with 4 life condition indices of Belo Horizonte region

Description

The data are collected inthe Atlas of condition indices published by the Joao Pinheiro Foundation and UNDP.

Format

A shape polygon object with seven variables:

id

The identificator

Name

Name of city

Population

The population of city

HLCI

Health Life Condition Index

ELCI

Education Life Condition Index

CLCI

Children Life Condition Index

ELCI

Economic Life Condition Index

Examples

(GDAL37 <- as.numeric_version(unname(sf_extSoftVersion()["GDAL"])) >= "3.7.0")
file <- "etc/shapes/bhicv.gpkg.zip"
zipfile <- system.file(file, package="spdep")
if (GDAL37) {
    bh <- st_read(zipfile)
} else {
    td <- tempdir()
    bn <- sub(".zip", "", basename(file), fixed=TRUE)
    target <- unzip(zipfile, files=bn, exdir=td)
    bh <- st_read(target)
}

Cardinalities for neighbours lists

Description

The function tallies the numbers of neighbours of regions in the neighbours list.

Usage

card(nb)

Arguments

Details

“nb” objects are stored as lists of integer vectors, where the vectors contain either the indices in the range 1:n for n as length(nb) of the neighbours of region i, or as.integer(0) to signal no neighbours. The function card(nb) is used to extract the numbers of neighbours from the “nb” object.

Value

An integer vector of the numbers of neighbours of regions in the neighbours list.

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

Bivand R, Pebesma EJ, Gomez-Rubio V, (2008) Applied Spatial Data Analysis with R, Springer, New York, pp. 239-251; Bivand R, Portnov B, (2004) Exploring spatial data analysis techniques using R: the case of observations with no neighbours. In: Anselin L, Florax R, Rey S, (eds.), Advances in Spatial Econometrics, Methodology, Tools and Applications. Berlin: Springer-Verlag, pp. 121-142, doi:10.1007/978-3-662-05617-2_6.

See Also

summary.nb

Examples

col.gal.nb <- read.gal(system.file("weights/columbus.gal", package="spData")[1])
table(card(col.gal.nb))

Generate neighbours list for grid cells

Description

The function generates a list of neighbours for a grid of cells. Helper functions are used to convert to and from the vector indices for row and column grid positions, and rook (shared edge) or queen (shared edge or vertex) neighbour definitions are applied by type. If torus is TRUE, the grid is mapped onto a torus, removing edge effects.

Usage

cell2nb(nrow, ncol, type="rook", torus=FALSE, legacy=FALSE, x=NULL)
vi2mrc(i, nrow, ncol)

Arguments

Value

The function returns an object of class nb with a list of integer vectors containing neighbour region number ids. See card for details of “nb” objects.

Author(s)

Roger Bivand Roger.Bivand@nhh.no

See Also

summary.nb, card

Examples

nb7rt <- cell2nb(7, 7)
summary(nb7rt)
xyc <- attr(nb7rt, "region.id")
xy <- matrix(as.integer(unlist(strsplit(xyc, ":"))), ncol=2, byrow=TRUE)
plot(nb7rt, xy)
nb7rt <- cell2nb(7, 7, torus=TRUE)
summary(nb7rt)
run <- FALSE
if (require("sp", quietly=TRUE)) run <- TRUE
if (run) {
# https://github.com/r-spatial/spdep/issues/20
GT <- GridTopology(c(1, 1), c(1, 1), c(10, 50))
SPix <- as(SpatialGrid(GT), "SpatialPixels")
nb_rook_cont <- poly2nb(as(SPix, "SpatialPolygons"), queen=FALSE)
nb_rook_dist <- dnearneigh(coordinates(SPix), 0, 1.01)
all.equal(nb_rook_cont, nb_rook_dist, check.attributes=FALSE)
## [1] TRUE
}
if (run) {
t.nb <- cell2nb(GT, type='rook', legacy=TRUE)
isTRUE(all.equal(nb_rook_cont, t.nb, check.attributes=FALSE))
## [1] FALSE
}
if (run) {
t.nb <- cell2nb(GT, type='rook')
isTRUE(all.equal(nb_rook_cont, t.nb, check.attributes=FALSE))
## [1] TRUE
}
if (run) {
# https://github.com/r-spatial/spdep/issues/55
# problem reported in issue caused by rep() cycling in unexpected order
GT <- GridTopology(c(1, 1), c(1, 1), c(22, 11))
SPix <- as(SpatialGrid(GT), "SpatialPixels")
nb_rook_cont <- poly2nb(as(SPix, "SpatialPolygons"), queen=FALSE)
nb_rook_dist <- dnearneigh(coordinates(SPix), 0, 1.01)
all.equal(nb_rook_cont, nb_rook_dist, check.attributes=FALSE)
}
if (run) {
t.nb <- cell2nb(GT, type='rook', legacy=TRUE)
isTRUE(all.equal(nb_rook_cont, t.nb, check.attributes=FALSE))
## [1] FALSE
}
if (run) {
t.nb <- cell2nb(GT, type='rook', legacy=FALSE)
isTRUE(all.equal(nb_rook_cont, t.nb, check.attributes=FALSE))
## [1] TRUE
}

Choynowski probability map values

Description

Calculates Choynowski probability map values.

Usage

choynowski(n, x, row.names=NULL, tol = .Machine$double.eps^0.5, legacy=FALSE)

Arguments

Value

A data frame with columns:

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

Choynowski, M (1959) Maps based on probabilities, Journal of the American Statistical Association, 54, 385–388; Cressie, N, Read, TRC (1985), Do sudden infant deaths come in clusters? Statistics and Decisions, Supplement Issue 2, 333–349; Bailey T, Gatrell A (1995) Interactive Spatial Data Analysis, Harlow: Longman, pp. 300–303.

See Also

probmap

Examples

auckland <- st_read(system.file("shapes/auckland.gpkg", package="spData")[1], quiet=TRUE)
auckland.nb <- poly2nb(auckland)
res <- choynowski(auckland$M77_85, 9*auckland$Und5_81)
resl <- choynowski(auckland$M77_85, 9*auckland$Und5_81, legacy=TRUE)
all.equal(res, resl)
rt <- sum(auckland$M77_85)/sum(9*auckland$Und5_81)
ch_ppois_pmap <- numeric(length(auckland$Und5_81))
side <- c("greater", "less")
for (i in seq(along=ch_ppois_pmap)) {
  ch_ppois_pmap[i] <- poisson.test(auckland$M77_85[i], r=rt,
    T=(9*auckland$Und5_81[i]), alternative=side[(res$type[i]+1)])$p.value
}
all.equal(ch_ppois_pmap, res$pmap)
res1 <- probmap(auckland$M77_85, 9*auckland$Und5_81)
table(abs(res$pmap - res1$pmap) < 0.00001, res$type)
lt005 <- (res$pmap < 0.05) & (res$type)
ge005 <- (res$pmap < 0.05) & (!res$type)
cols <- rep("nonsig", length(lt005))
cols[lt005] <- "low"
cols[ge005] <- "high"
auckland$cols <- factor(cols)
plot(auckland[,"cols"], main="Probability map")

Columbus OH spatial analysis data set

Description

The data set is now part of the spData package

Usage

data(columbus)

Examples

columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
col.gal.nb <- read.gal(system.file("weights/columbus.gal", package="spData")[1])

Differences between neighbours lists

Description

The function finds symmetric differences between lists of neighbours (ordering of objects does not matter), returning a nb neighbour list of those found

Usage

diffnb(x, y, verbose=NULL, legacy=TRUE)

Arguments

Value

A neighbours list with class nb

Author(s)

Roger Bivand Roger.Bivand@nhh.no

Examples

columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE)
rn <- row.names(columbus)
knn1 <- knearneigh(coords, 1)
knn2 <- knearneigh(coords, 2)
nb1 <- knn2nb(knn1, row.names=rn)
nb2 <- knn2nb(knn2, row.names=rn)
diffs <- diffnb(nb2, nb1, legacy=TRUE)
diffsl <- diffnb(nb2, nb1, legacy=FALSE)
all.equal(diffs, diffsl)
# call attribute fifference expected
diffsd <- union.nb(setdiff.nb(nb1, nb2), setdiff.nb(nb2, nb1))
all.equal(diffs, diffsd)
# call attribute fifference expected
opar <- par(no.readonly=TRUE)
plot(st_geometry(columbus), border="grey", reset=FALSE,
 main="Plot of first (black) and second (red)\nnearest neighbours")
plot(nb1, coords, add=TRUE)
plot(diffs, coords, add=TRUE, col="red", lty=2)
par(opar)

Neighbourhood contiguity by distance

Description

The function identifies neighbours of region points by Euclidean distance in the metric of the points between lower (greater than or equal to (changed from version 1.1-7)) and upper (less than or equal to) bounds, or with longlat = TRUE, by Great Circle distance in kilometers. If x is an "sf" object and use_s2= is TRUE, spherical distances in km are used.

Usage

dnearneigh(x, d1, d2, row.names = NULL, longlat = NULL, bounds=c("GE", "LE"),
 use_kd_tree=TRUE, symtest=FALSE, use_s2=packageVersion("s2") > "1.0.7", k=200,
 dwithin=TRUE)

Arguments

Value

The function returns a list of integer vectors giving the region id numbers for neighbours satisfying the distance criteria. See card for details of “nb” objects.

Author(s)

Roger Bivand Roger.Bivand@nhh.no

See Also

knearneigh, card

Examples

columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE)
rn <- row.names(columbus)
k1 <- knn2nb(knearneigh(coords))
all.linked <- max(unlist(nbdists(k1, coords)))
col.nb.0.all <- dnearneigh(coords, 0, all.linked, row.names=rn)
summary(col.nb.0.all, coords)
opar <- par(no.readonly=TRUE)
plot(st_geometry(columbus), border="grey", reset=FALSE,
 main=paste("Distance based neighbours 0-",  format(all.linked), sep=""))
plot(col.nb.0.all, coords, add=TRUE)
par(opar)
(sfc_obj <- st_centroid(st_geometry(columbus)))
col.nb.0.all_sf <- dnearneigh(sfc_obj, 0, all.linked, row.names=rn)
all.equal(col.nb.0.all, col.nb.0.all_sf, check.attributes=FALSE)
data(state)
us48.fipsno <- read.geoda(system.file("etc/weights/us48.txt",
 package="spdep")[1])
if (as.numeric(paste(version$major, version$minor, sep="")) < 19) {
 m50.48 <- match(us48.fipsno$"State.name", state.name)
} else {
 m50.48 <- match(us48.fipsno$"State_name", state.name)
}
xy <- as.matrix(as.data.frame(state.center))[m50.48,]
llk1 <- knn2nb(knearneigh(xy, k=1, longlat=FALSE))
(all.linked <- max(unlist(nbdists(llk1, xy, longlat=FALSE))))
ll.nb <- dnearneigh(xy, 0, all.linked, longlat=FALSE)
summary(ll.nb, xy, longlat=TRUE, scale=0.5)
gck1 <- knn2nb(knearneigh(xy, k=1, longlat=TRUE))
(all.linked <- max(unlist(nbdists(gck1, xy, longlat=TRUE))))
gc.nb <- dnearneigh(xy, 0, all.linked, longlat=TRUE)
summary(gc.nb, xy, longlat=TRUE, scale=0.5)
plot(ll.nb, xy)
plot(diffnb(ll.nb, gc.nb), xy, add=TRUE, col="red", lty=2)
title(main="Differences Euclidean/Great Circle")

#xy1 <- SpatialPoints((as.data.frame(state.center))[m50.48,],
#  proj4string=CRS("+proj=longlat +ellps=GRS80"))
#gck1a <- knn2nb(knearneigh(xy1, k=1))
#(all.linked <- max(unlist(nbdists(gck1a, xy1))))
#gc.nb <- dnearneigh(xy1, 0, all.linked)
#summary(gc.nb, xy1, scale=0.5)

xy1 <- st_as_sf((as.data.frame(state.center))[m50.48,], coords=1:2,
  crs=st_crs("OGC:CRS84"))
old_use_s2 <- sf_use_s2()
sf_use_s2(TRUE)
gck1b <- knn2nb(knearneigh(xy1, k=1))
system.time(o <- nbdists(gck1b, xy1))
(all.linked <- max(unlist(o)))
# use s2 brute-force dwithin_matrix approach for s2 <= 1.0.7
system.time(gc.nb.dwithin <- dnearneigh(xy1, 0, all.linked, use_s2=TRUE, dwithin=TRUE))
summary(gc.nb, xy1, scale=0.5)
# use s2 closest_edges approach s2 > 1.0.7
if (packageVersion("s2") > "1.0.7") {
(system.time(gc.nb.closest <- dnearneigh(xy1, 0, all.linked, dwithin=FALSE)))
}
if (packageVersion("s2") > "1.0.7") {
system.time(gc.nb.dwithin <- dnearneigh(xy1, 0, all.linked, use_s2=TRUE, dwithin=TRUE))
}
if (packageVersion("s2") > "1.0.7") {
summary(gc.nb.dwithin, xy1, scale=0.5)
}
if (packageVersion("s2") > "1.0.7") {
summary(gc.nb.closest, xy1, scale=0.5)
}
# use legacy symmetric brute-force approach
system.time(gc.nb.legacy <- dnearneigh(xy1, 0, all.linked, use_s2=FALSE))
summary(gc.nb, xy1, scale=0.5)
if (packageVersion("s2") > "1.0.7") all.equal(gc.nb.closest, gc.nb.dwithin, check.attributes=FALSE)
# legacy is ellipsoidal, s2 spherical, so minor differences expected
if (packageVersion("s2") > "1.0.7") all.equal(gc.nb, gc.nb.closest, check.attributes=FALSE)
all.equal(gc.nb, gc.nb.dwithin, check.attributes=FALSE)
sf_use_s2(old_use_s2)
# example of reading points with readr::read_csv() yielding a tibble
load(system.file("etc/misc/coords.rda", package="spdep"))
class(coords)
k1 <- knn2nb(knearneigh(coords, k=1))
all.linked <- max(unlist(nbdists(k1, coords)))
dnearneigh(coords, 0, all.linked)

Drop and add links in a neighbours list

Description

droplinks drops links to and from or just to a region from a neighbours list. The example corresponds to Fingleton's Table 1, (1999) p. 6, for lattices 5 to 19. addlinks1 adds links from a single region to specified regions.

Usage

droplinks(nb, drop, sym=TRUE)
addlinks1(nb, from, to, sym=TRUE)

Arguments

Value

The function returns an object of class nb with a list of integer vectors containing neighbour region number ids.

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

B. Fingleton (1999) Spurious spatial regression: some Monte Carlo results with a spatial unit root and spatial cointegration, Journal of Regional Science 39, pp. 1–19.

See Also

is.symmetric.nb

Examples

rho <- c(0.2, 0.5, 0.95, 0.999, 1.0)
ns <- c(5, 7, 9, 11, 13, 15, 17, 19)
mns <- matrix(0, nrow=length(ns), ncol=length(rho))
rownames(mns) <- ns
colnames(mns) <- rho
mxs <- matrix(0, nrow=length(ns), ncol=length(rho))
rownames(mxs) <- ns
colnames(mxs) <- rho
for (i in 1:length(ns)) {
  nblist <- cell2nb(ns[i], ns[i])
  nbdropped <- droplinks(nblist, ((ns[i]*ns[i])+1)/2, sym=FALSE)
  listw <- nb2listw(nbdropped, style="W", zero.policy=TRUE)
  wmat <- listw2mat(listw)
  for (j in 1:length(rho)) {
    mat <- diag(ns[i]*ns[i]) - rho[j] * wmat
    res <- diag(solve(t(mat) %*% mat))
    mns[i,j] <- mean(res)
    mxs[i,j] <- max(res)
  }
}
print(mns)
print(mxs)

Global Empirical Bayes estimator

Description

The function computes global empirical Bayes estimates for rates "shrunk" to the overall mean.

Usage

EBest(n, x, family="poisson")

Arguments

Details

Details of the implementation for the "poisson" family are to be found in Marshall, p. 284–5, and Bailey and Gatrell p. 303–306 and exercise 8.2, pp. 328–330. For the "binomial" family, see Martuzzi and Elliott (implementation by Olaf Berke).

Value

A data frame with two columns:

and a parameters attribute list with components:

Author(s)

Roger Bivand Roger.Bivand@nhh.no and Olaf Berke, Population Medicine, OVC, University of Guelph, CANADA

References

Marshall R M (1991) Mapping disease and mortality rates using Empirical Bayes Estimators, Applied Statistics, 40, 283–294; Bailey T, Gatrell A (1995) Interactive Spatial Data Analysis, Harlow: Longman, pp. 303–306, Martuzzi M, Elliott P (1996) Empirical Bayes estimation of small area prevalence of non-rare conditions, Statistics in Medicine 15, 1867–1873.

See Also

EBlocal, probmap, EBImoran.mc

Examples

auckland <- st_read(system.file("shapes/auckland.gpkg", package="spData")[1], quiet=TRUE)
res <- EBest(auckland$M77_85, 9*auckland$Und5_81)
attr(res, "parameters")
auckland$estmm000 <- res$estmm*1000
plot(auckland[,"estmm000"], breaks=c(0,2,2.5,3,3.5,5),
 main="Infant mortality per 1000 per year")
data(huddersfield, package="spData")
res <- EBest(huddersfield$cases, huddersfield$total, family="binomial")
round(res[,1:2],4)*100

Permutation test for empirical Bayes index

Description

An empirical Bayes index modification of Moran's I for testing for spatial autocorrelation in a rate, typically the number of observed cases in a population at risk. The index value is tested by using nsim random permutations of the index for the given spatial weighting scheme, to establish the rank of the observed statistic in relation to the nsim simulated values.

Usage

EBImoran.mc(n, x, listw, nsim, zero.policy = attr(listw, "zero.policy"), 
 alternative = "greater", spChk=NULL, return_boot=FALSE,
 subtract_mean_in_numerator=TRUE)

Arguments

Details

The statistic used is (m is the number of observations):

EBI = \frac{m}{\sum_{i=1}^{m}\sum_{j=1}^{m}w_{ij}} \frac{\sum_{i=1}^{m}\sum_{j=1}^{m}w_{ij}z_i z_j}{\sum_{i=1}^{m}(z_i - \bar{z})^2}

where:

z_i = \frac{p_i - b}{\sqrt{v_i}}

and:

p_i = n_i / x_i

v_i = a + (b / x_i)

b = \sum_{i=1}^{m} n_i / \sum_{i=1}^{m} x_i

a = s^2 - b / (\sum_{i=1}^{m} x_i / m)

s^2 = \sum_{i=1}^{m} x_i (p_i - b)^2 / \sum_{i=1}^{m} x_i

Value

A list with class htest and mc.sim containing the following components:

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

Assunção RM, Reis EA 1999 A new proposal to adjust Moran's I for population density. Statistics in Medicine 18, pp. 2147–2162; Bivand RS, Wong DWS 2018 Comparing implementations of global and local indicators of spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x

See Also

moran, moran.mc, EBest

Examples

nc.sids <- st_read(system.file("shapes/sids.gpkg", package="spData")[1], quiet=TRUE)
rn <- as.character(nc.sids$FIPS)
ncCC89_nb <- read.gal(system.file("weights/ncCC89.gal", package="spData")[1],
 region.id=rn)
EBImoran.mc(nc.sids$SID74, nc.sids$BIR74,
 nb2listw(ncCC89_nb, style="B", zero.policy=TRUE), nsim=999,
 alternative="two.sided", zero.policy=TRUE)
sids.p <- nc.sids$SID74 / nc.sids$BIR74
moran.mc(sids.p, nb2listw(ncCC89_nb, style="B", zero.policy=TRUE),
 nsim=999, alternative="two.sided", zero.policy=TRUE)

Local Empirical Bayes estimator

Description

The function computes local empirical Bayes estimates for rates "shrunk" to a neighbourhood mean for neighbourhoods given by the nb neighbourhood list.

Usage

EBlocal(ri, ni, nb, zero.policy = NULL, spChk = NULL, geoda=FALSE)

Arguments

Details

Details of the implementation are to be found in Marshall, p. 286, and Bailey and Gatrell p. 307 and exercise 8.2, pp. 328–330. The example results do not fully correspond to the sources because of slightly differing neighbourhoods, but are generally close. If there are many zero counts, some estimates may be affected by division by zero, see https://stat.ethz.ch/pipermail/r-sig-geo/2022-January/028882.html.

Value

A data frame with two columns:

and a parameters attribute list with components (if both are zero, the estimate will be NaN, https://stat.ethz.ch/pipermail/r-sig-geo/2022-January/028882.html):

Author(s)

Roger Bivand Roger.Bivand@nhh.no, based on contributions by Marilia Carvalho

References

Marshall R M (1991) Mapping disease and mortality rates using Empirical Bayes Estimators, Applied Statistics, 40, 283–294; Bailey T, Gatrell A (1995) Interactive Spatial Data Analysis, Harlow: Longman, pp. 303–306.

See Also

EBest, probmap

Examples

auckland <- st_read(system.file("shapes/auckland.gpkg", package="spData")[1], quiet=TRUE)
auckland.nb <- poly2nb(auckland)
res <- EBlocal(auckland$M77_85,  9*auckland$Und5_81, auckland.nb)
auckland$est000 <- res$est*1000
plot(auckland[,"est000"], breaks=c(0,2,2.5,3,3.5,8),
 main="Infant mortality per 1000 per year")

Interactive editing of neighbours lists

Description

The function provides simple interactive editing of neighbours lists to allow unneeded links to be deleted, and missing links to be inserted. It uses identify to pick the endpoints of the link to be deleted or added, and asks for confirmation before committing. If the result is not assigned to a new object, the editing will be lost - as in edit.

This method relies on direct contact with the graphics device. Do not use in RStudio.

Usage

## S3 method for class 'nb'
edit(name, coords, polys=NULL, ..., use_region.id=FALSE)

Arguments

Value

The function returns an object of class nb with the edited list of integer vectors containing neighbour region number ids, with added attributes tallying the added and deleted links.

Author(s)

Roger Bivand Roger.Bivand@nhh.no

See Also

summary.nb, plot.nb

Examples

## Not run: 
columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
class(columbus)
if (FALSE) nnb1 <- edit.nb(col.gal.nb, polys=as(columbus, "Spatial"))

## End(Not run)

Eire data sets

Description

The data set is now part of the spData package

Usage

data(eire)

Compute Geary's C

Description

A simple function to compute Geary's C, called by geary.test and geary.mc;

C = \frac{(n-1)}{2\sum_{i=1}^{n}\sum_{j=1}^{n}w_{ij}} \frac{\sum_{i=1}^{n}\sum_{j=1}^{n}w_{ij}(x_i-x_j)^2}{\sum_{i=1}^{n}(x_i - \bar{x})^2}

geary.intern is an internal function used to vary the similarity criterion.

Usage

geary(x, listw, n, n1, S0, zero.policy=attr(listw, "zero.policy"), scale=TRUE)

Arguments

Value

a list with

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 17.

See Also

geary.test, geary.mc, sp.mantel.mc

Examples

data(oldcol)
col.W <- nb2listw(COL.nb, style="W")
str(geary(COL.OLD$CRIME, col.W, length(COL.nb), length(COL.nb)-1,
 Szero(col.W)))

Permutation test for Geary's C statistic

Description

A permutation test for Geary's C statistic calculated by using nsim random permutations of x for the given spatial weighting scheme, to establish the rank of the observed statistic in relation to the nsim simulated values.

Usage

geary.mc(x, listw, nsim, zero.policy=attr(listw, "zero.policy"), alternative="greater",
 spChk=NULL, adjust.n=TRUE, return_boot=FALSE, na.action=na.fail, scale=TRUE)

Arguments

Value

A list with class htest and mc.sim containing the following components:

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 63-5.

See Also

geary, geary.test

Examples

data(oldcol)
set.seed(1)
sim1 <- geary.mc(COL.OLD$CRIME, nb2listw(COL.nb, style="W"),
 nsim=99, alternative="less")
sim1
mean(sim1$res)
var(sim1$res)
summary(sim1$res)
colold.lags <- nblag(COL.nb, 3)
sim2 <- geary.mc(COL.OLD$CRIME, nb2listw(colold.lags[[2]],
 style="W"), nsim=99)
sim2
summary(sim2$res)
sim3 <- geary.mc(COL.OLD$CRIME, nb2listw(colold.lags[[3]],
 style="W"), nsim=99)
sim3
summary(sim3$res)
crime <- COL.OLD$CRIME
is.na(crime) <- sample(1:length(crime), 10)
try(geary.mc(crime, nb2listw(COL.nb, style="W"), nsim=99,
 na.action=na.fail))
geary.mc(crime, nb2listw(COL.nb, style="W"), nsim=99, zero.policy=TRUE,
 na.action=na.omit)
geary.mc(crime, nb2listw(COL.nb, style="W"), nsim=99, zero.policy=TRUE,
 return_boot=TRUE, na.action=na.omit)
geary.mc(crime, nb2listw(COL.nb, style="W"), nsim=99, zero.policy=TRUE,
 na.action=na.exclude)
geary.mc(crime, nb2listw(COL.nb, style="W"), nsim=99, zero.policy=TRUE,
 return_boot=TRUE, na.action=na.exclude)
try(geary.mc(crime, nb2listw(COL.nb, style="W"), nsim=99, na.action=na.pass))

Geary's C test for spatial autocorrelation

Description

Geary's test for spatial autocorrelation using a spatial weights matrix in weights list form. The assumptions underlying the test are sensitive to the form of the graph of neighbour relationships and other factors, and results may be checked against those of geary.mc permutations.

Usage

geary.test(x, listw, randomisation=TRUE, zero.policy=attr(listw, "zero.policy"),
    alternative="greater", spChk=NULL, adjust.n=TRUE, na.action=na.fail,
    scale=TRUE)

Arguments

Value

A list with class htest containing the following components:

Note

The derivation of the test (Cliff and Ord, 1981, p. 18) assumes that the weights matrix is symmetric. For inherently non-symmetric matrices, such as k-nearest neighbour matrices, listw2U() can be used to make the matrix symmetric. In non-symmetric weights matrix cases, the variance of the test statistic may be negative (thanks to Franz Munoz I for a well documented bug report). Geary's C is affected by non-symmetric weights under normality much more than Moran's I. From 0.4-35, the sign of the standard deviate of C is changed to match Cliff and Ord (1973, p. 21).

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 21, Cliff, A. D., Ord, J. K. 1973 Spatial Autocorrelation, Pion, pp. 15-16, 21; Bivand RS, Wong DWS 2018 Comparing implementations of global and local indicators of spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x

See Also

geary, geary.mc, listw2U

Examples

data(oldcol)
geary.test(COL.OLD$CRIME, nb2listw(COL.nb, style="W"))
geary.test(COL.OLD$CRIME, nb2listw(COL.nb, style="W"),
 randomisation=FALSE)
colold.lags <- nblag(COL.nb, 3)
geary.test(COL.OLD$CRIME, nb2listw(colold.lags[[2]],
 style="W"))
geary.test(COL.OLD$CRIME, nb2listw(colold.lags[[3]],
 style="W"), alternative="greater")
print(is.symmetric.nb(COL.nb))
coords.OLD <- cbind(COL.OLD$X, COL.OLD$Y)
COL.k4.nb <- knn2nb(knearneigh(coords.OLD, 4))
print(is.symmetric.nb(COL.k4.nb))
geary.test(COL.OLD$CRIME, nb2listw(COL.k4.nb, style="W"))
geary.test(COL.OLD$CRIME, nb2listw(COL.k4.nb, style="W"),
 randomisation=FALSE)
cat("Note non-symmetric weights matrix - use listw2U()\n")
geary.test(COL.OLD$CRIME, listw2U(nb2listw(COL.k4.nb,
 style="W")))
geary.test(COL.OLD$CRIME, listw2U(nb2listw(COL.k4.nb,
 style="W")), randomisation=FALSE)
crime <- COL.OLD$CRIME
is.na(crime) <- sample(1:length(crime), 10)
try(geary.test(crime, nb2listw(COL.nb, style="W"), na.action=na.fail))
geary.test(crime, nb2listw(COL.nb, style="W"), zero.policy=TRUE,
 na.action=na.omit)
geary.test(crime, nb2listw(COL.nb, style="W"), zero.policy=TRUE,
 na.action=na.exclude)
try(geary.test(crime, nb2listw(COL.nb, style="W"), na.action=na.pass))

Global G test for spatial autocorrelation

Description

The global G statistic for spatial autocorrelation, complementing the local Gi LISA measures: localG.

Usage

globalG.test(x, listw, zero.policy=attr(listw, "zero.policy"), alternative="greater",
 spChk=NULL, adjust.n=TRUE, B1correct=TRUE, adjust.x=TRUE, Arc_all_x=FALSE,
 na.action=na.fail)

Arguments

Value

A list with class htest containing the following components:

Author(s)

Hisaji ONO hi-ono@mn.xdsl.ne.jp and Roger Bivand Roger.Bivand@nhh.no

References

Getis. A, Ord, J. K. 1992 The analysis of spatial association by use of distance statistics, Geographical Analysis, 24, p. 195; see also Getis. A, Ord, J. K. 1993 Erratum, Geographical Analysis, 25, p. 276; Bivand RS, Wong DWS 2018 Comparing implementations of global and local indicators of spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x

See Also

localG

Examples

nc.sids <- st_read(system.file("shapes/sids.gpkg", package="spData")[1], quiet=TRUE)
sidsrate79 <- (1000*nc.sids$SID79)/nc.sids$BIR79
dists <- c(10, 20, 30, 33, 40, 50, 60, 70, 80, 90, 100)
ndists <- length(dists)
ZG <- vector(mode="list", length=ndists)
names(ZG) <- as.character(dists)
milesxy <- cbind(nc.sids$east, nc.sids$north)
for (i in 1:ndists) {
  thisnb <- dnearneigh(milesxy, 0, dists[i])
  thislw <- nb2listw(thisnb, style="B", zero.policy=TRUE)
  ZG[[i]] <- globalG.test(sidsrate79, thislw, zero.policy=TRUE)
}
t(sapply(ZG, function(x) c(x$estimate[1], x$statistic, p.value=unname(x$p.value))))
for (i in 1:ndists) {
  thisnb <- dnearneigh(milesxy, 0, dists[i])
  thislw <- nb2listw(thisnb, style="B", zero.policy=TRUE)
  ZG[[i]] <- globalG.test(sidsrate79, thislw, zero.policy=TRUE, alternative="two.sided")
}
t(sapply(ZG, function(x) c(x$estimate[1], x$statistic, p.value=unname(x$p.value))))
data(oldcol)
crime <- COL.OLD$CRIME
is.na(crime) <- sample(1:length(crime), 10)
res <- try(globalG.test(crime, nb2listw(COL.nb, style="B"),
 na.action=na.fail))
globalG.test(crime, nb2listw(COL.nb, style="B"), zero.policy=TRUE,
 na.action=na.omit)
globalG.test(crime, nb2listw(COL.nb, style="B"), zero.policy=TRUE,
 na.action=na.exclude)
try(globalG.test(crime, nb2listw(COL.nb, style="B"), na.action=na.pass))

Depth First Search on Neighbor Lists

Description

n.comp.nb() finds the number of disjoint connected subgraphs in the graph depicted by nb.obj - a spatial neighbours list object.

Usage

n.comp.nb(nb.obj)

Arguments

Details

If attr(nb.obj, "sym") is FALSE and igraph::components is available, the components of the directed graph will be found by a simple breadth-first search; if igraph::components is not available, the object will be made symmetric (which may be time-consuming with large numbers of neighbours) and the components found by depth-first search. If attr(nb.obj, "sym") is TRUE, the components of the directed graph will be found by depth-first search. The time complexity of algorithms used in native code and through igraph::components is linear in the sum of the number of nodes and the number of edges in the graph, see https://github.com/r-spatial/spdep/issues/160 for details; very dense neighbour objects will have large numbers of edges.

Value

A list of:

Author(s)

Nicholas Lewin-Koh nikko@hailmail.net

See Also

plot.nb

Examples

columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
col.gal.nb <- read.gal(system.file("weights/columbus.gal", package="spData")[1])
coords <- st_coordinates(st_centroid(st_geometry(columbus)))
plot(col.gal.nb, coords, col="grey")
col2 <- droplinks(col.gal.nb, 21)
res <- n.comp.nb(col2)
table(res$comp.id)
plot(col2, coords, add=TRUE)
points(coords, col=res$comp.id, pch=16)
run <- FALSE
if (require("igraph", quietly=TRUE) && require("spatialreg", quietly=TRUE)) run <- TRUE
if (run) {
B <- as(nb2listw(col2, style="B", zero.policy=TRUE), "CsparseMatrix")
g1 <- graph_from_adjacency_matrix(B, mode="undirected")
c1 <- components(g1)
print(c1$no == res$nc)
}
if (run) {
print(all.equal(c1$membership, res$comp.id))
}
if (run) {
print(all.equal(c1$csize, c(table(res$comp.id)), check.attributes=FALSE))
}
if (run) {
W <- as(nb2listw(col2, style="W", zero.policy=TRUE), "CsparseMatrix")
g1W <- graph_from_adjacency_matrix(W, mode="directed", weighted="W")
c1W <- components(g1W, mode="weak")
print(all.equal(c1W$membership, res$comp.id, check.attributes=FALSE))
}

if (run) {
data(house, package="spData")
house <- sf::st_as_sf(house)
k6 <- knn2nb(knearneigh(house, k=6))
is.symmetric.nb(k6)
}
if (run) {
print(k6)
}
if (run) {
length(k6) + sum(card(k6))
}
if (run) {
# no pre-computed graph components
str(attr(k6, "ncomp"))
}
if (run) {
# raising the subgraph compute ceiling to above |N|+|E| computes and stores the
# object in the neighbour object
set.SubgraphCeiling(180000L)
k6 <- knn2nb(knearneigh(house, k=6))
str(attr(k6, "ncomp"))
}
if (run) {
print(k6)
}
if (run) {
system.time(udir <- n.comp.nb(make.sym.nb(k6)))
}
if (run) {
system.time(dir <- n.comp.nb(k6))
}
if (run) {
udir$nc
}
if (run) {
dir$nc
}
if (run) {
all.equal(dir, udir)
}

Graph based spatial weights

Description

Functions return a graph object containing a list with the vertex coordinates and the to and from indices defining the edges. Some/all of these functions assume that the coordinates are not exactly regularly spaced. The helper function graph2nb converts a graph object into a neighbour list. The plot functions plot the graph objects.

Usage

gabrielneigh(coords, nnmult=3)
relativeneigh(coords, nnmult=3)
soi.graph(tri.nb, coords, quadsegs=10)
graph2nb(gob, row.names=NULL,sym=FALSE)
## S3 method for class 'Gabriel'
plot(x, show.points=FALSE, add=FALSE, linecol=par(col), ...)
## S3 method for class 'relative'
plot(x, show.points=FALSE, add=FALSE, linecol=par(col),...)

Arguments

Details

The graph functions produce graphs on a 2d point set that are all subgraphs of the Delaunay triangulation. The relative neighbor graph is defined by the relation, x and y are neighbors if

d(x,y) \le min(max(d(x,z),d(y,z))| z \in S)

where d() is the distance, S is the set of points and z is an arbitrary point in S. The Gabriel graph is a subgraph of the delaunay triangulation and has the relative neighbor graph as a sub-graph. The relative neighbor graph is defined by the relation x and y are Gabriel neighbors if

d(x,y) \le min((d(x,z)^2 + d(y,z)^2)^{1/2} |z \in S)

where x,y,z and S are as before. The sphere of influence graph is defined for a finite point set S, let r_x be the distance from point x to its nearest neighbor in S, and C_x is the circle centered on x. Then x and y are SOI neigbors iff C_x and C_y intersect in at least 2 places. From 2016-05-31, Computational Geometry in C code replaced by calls to functions in dbscan and sf; with a large quadsegs= argument, the behaviour of the function is the same, otherwise buffer intersections only closely approximate the original function.

See card for details of “nb” objects.

Value

A list of class Graph with the following elements

The helper functions return an nb object with a list of integer vectors containing neighbour region number ids.

Author(s)

Nicholas Lewin-Koh nikko@hailmail.net

References

Matula, D. W. and Sokal R. R. 1980, Properties of Gabriel graphs relevant to geographic variation research and the clustering of points in the plane, Geographic Analysis, 12(3), pp. 205-222.

Toussaint, G. T. 1980, The relative neighborhood graph of a finite planar set, Pattern Recognition, 12(4), pp. 261-268.

Kirkpatrick, D. G. and Radke, J. D. 1985, A framework for computational morphology. In Computational Geometry, Ed. G. T. Toussaint, North Holland.

See Also

knearneigh, dnearneigh, knn2nb, card

Examples

columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
sf_obj <- st_centroid(st_geometry(columbus), of_largest_polygon)
sp_obj <- as(sf_obj, "Spatial")
coords <- st_coordinates(sf_obj)
suppressMessages(col.tri.nb <- tri2nb(coords))
col.gab.nb <- graph2nb(gabrielneigh(coords), sym=TRUE)
col.rel.nb <- graph2nb(relativeneigh(coords), sym=TRUE)
par(mfrow=c(2,2))
plot(st_geometry(columbus), border="grey")
plot(col.tri.nb,coords,add=TRUE)
title(main="Delaunay Triangulation", cex.main=0.6)
plot(st_geometry(columbus), border="grey")
plot(col.gab.nb, coords, add=TRUE)
title(main="Gabriel Graph", cex.main=0.6)
plot(st_geometry(columbus), border="grey")
plot(col.rel.nb, coords, add=TRUE)
title(main="Relative Neighbor Graph", cex.main=0.6)
plot(st_geometry(columbus), border="grey")
if (require("dbscan", quietly=TRUE)) {
  col.soi.nb <- graph2nb(soi.graph(col.tri.nb,coords), sym=TRUE)
  plot(col.soi.nb, coords, add=TRUE)
  title(main="Sphere of Influence Graph", cex.main=0.6)
}
par(mfrow=c(1,1))
col.tri.nb_sf <- tri2nb(sf_obj)
all.equal(col.tri.nb, col.tri.nb_sf, check.attributes=FALSE)
col.tri.nb_sp <- tri2nb(sp_obj)
all.equal(col.tri.nb, col.tri.nb_sp, check.attributes=FALSE)
if (require("dbscan", quietly=TRUE)) {
  col.soi.nb_sf <- graph2nb(soi.graph(col.tri.nb, sf_obj), sym=TRUE)
  all.equal(col.soi.nb, col.soi.nb_sf, check.attributes=FALSE)
  col.soi.nb_sp <- graph2nb(soi.graph(col.tri.nb, sp_obj), sym=TRUE)
  all.equal(col.soi.nb, col.soi.nb_sp, check.attributes=FALSE)
}
col.gab.nb_sp <- graph2nb(gabrielneigh(sp_obj), sym=TRUE)
all.equal(col.gab.nb, col.gab.nb_sp, check.attributes=FALSE)
col.gab.nb_sf <- graph2nb(gabrielneigh(sf_obj), sym=TRUE)
all.equal(col.gab.nb, col.gab.nb_sf, check.attributes=FALSE)
col.rel.nb_sp <- graph2nb(relativeneigh(sp_obj), sym=TRUE)
all.equal(col.rel.nb, col.rel.nb_sp, check.attributes=FALSE)
col.rel.nb_sf <- graph2nb(relativeneigh(sf_obj), sym=TRUE)
all.equal(col.rel.nb, col.rel.nb_sf, check.attributes=FALSE)
dx <- rep(0.25*0:4,5)
dy <- c(rep(0,5),rep(0.25,5),rep(0.5,5), rep(0.75,5),rep(1,5))
m <- cbind(c(dx, dx, 3+dx, 3+dx), c(dy, 3+dy, dy, 3+dy))
cat(try(res <- gabrielneigh(m), silent=TRUE), "\n")
res <- gabrielneigh(m, nnmult=4)
summary(graph2nb(res))
grd <- as.matrix(expand.grid(x=1:5, y=1:5)) #gridded data
r2 <- gabrielneigh(grd)
set.seed(1)
grd1 <- as.matrix(expand.grid(x=1:5, y=1:5)) + matrix(runif(50, .0001, .0006), nrow=25)
r3 <- gabrielneigh(grd1)
opar <- par(mfrow=c(1,2))
plot(r2, show=TRUE, linecol=2)
plot(r3, show=TRUE, linecol=2)
par(opar)
# example of reading points with readr::read_csv() yielding a tibble
load(system.file("etc/misc/coords.rda", package="spdep"))
class(coords)
graph2nb(gabrielneigh(coords))
graph2nb(relativeneigh(coords))

Construct neighbours for a GridTopology

Description

The function builds a neighbours list for a grid topology. It works for a k-dimentional grid topology, k>=1.

Usage

grid2nb(grid, d = grid@cells.dim,
        queen = TRUE, nb = TRUE, self = FALSE)

Arguments

Value

Either a matrix, if “nb” is FALSE or a neighbours list with class nb. See card for details of “nb” objects.

Note

This applies to a k-dimentional grid topology.

Author(s)

Elias T Krainski eliaskrainski@gmail.com

See Also

poly2nb, summary.nb, card

Examples

nb <- grid2nb(d = c(5L, 5L, 5L))
nb
summary(nb)
if (require("sp", quietly=TRUE)) {
gt <- GridTopology(c(.125,.1), c(.25,.2), c(4L, 5L))
nb1 <- grid2nb(gt, queen = FALSE)
nb2 <- grid2nb(gt)

sg <- SpatialGrid(gt)
plot(sg, lwd=3)
plot(nb1, coordinates(sg), add=TRUE, lty=2, col=2, lwd=2)
plot(nb2, coordinates(sg), add=TRUE, lty=3, col=4)

str(grid2nb(d=5))
}

Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data

Description

Used to return a factor showing so-called cluster classification for local indicators of spatial association for local Moran's I, local Geary's C (and its multivariate variant) and local Getis-Ord G. This factor vector can be added to a spatial object for mapping. When obj is of class licd, a list of up to six factors for measures of local composition (analytical and permutation), local configuration (analytical and permutation), and combined measures, both the interaction of composition and configuration, and a simplified recoding of these.

Usage

hotspot(obj, ...)

## Default S3 method:
hotspot(obj, ...)

## S3 method for class 'localmoran'
hotspot(obj, Prname, cutoff=0.005, quadrant.type="mean",
 p.adjust="fdr", droplevels=TRUE, ...)
## S3 method for class 'summary.localmoransad'
hotspot(obj, Prname, cutoff=0.005,
 quadrant.type="mean", p.adjust="fdr", droplevels=TRUE, ...)
## S3 method for class 'data.frame.localmoranex'
hotspot(obj, Prname, cutoff=0.005,
 quadrant.type="mean", p.adjust="fdr", droplevels=TRUE, ...)

## S3 method for class 'localG'
hotspot(obj, Prname, cutoff=0.005, p.adjust="fdr", droplevels=TRUE, ...)

## S3 method for class 'localC'
hotspot(obj, Prname, cutoff=0.005, p.adjust="fdr", droplevels=TRUE, ...)
## S3 method for class 'licd'
hotspot(obj, type = "both", cutoff = 0.05, p.adjust = "none", 
 droplevels = TRUE, control = list(), ...)

Arguments

Value

A factor showing so-called cluster classification for local indicators of spatial association. When obj is of class licd, a list of up to six factors for measures of local composition (analytical and permutation), local configuration (analytical and permutation), and combined measures, both the interaction of composition and configuration, and a simplified recoding of these.

Author(s)

Roger Bivand

See Also

licd_multi

Examples

orig <- spData::africa.rook.nb
listw <- nb2listw(orig)
x <- spData::afcon$totcon

set.seed(1)
C <- localC_perm(x, listw)
Ch <- hotspot(C, Prname="Pr(z != E(Ci)) Sim", cutoff=0.05, p.adjust="none")
table(addNA(Ch))
set.seed(1)
I <- localmoran_perm(x, listw)
Ih <- hotspot(I, Prname="Pr(z != E(Ii)) Sim", cutoff=0.05, p.adjust="none")
table(addNA(Ih))
Is <- summary(localmoran.sad(lm(x ~ 1), nb=orig))
Ish <- hotspot(Is, Prname="Pr. (Sad)", cutoff=0.05, p.adjust="none")
table(addNA(Ish))
Ie <- as.data.frame(localmoran.exact(lm(x ~ 1), nb=orig))
Ieh <- hotspot(Ie, Prname="Pr. (exact)", cutoff=0.05, p.adjust="none")
table(addNA(Ieh))
set.seed(1)
G <- localG_perm(x, listw)
Gh <- hotspot(G, Prname="Pr(z != E(Gi)) Sim", cutoff=0.05, p.adjust="none")
table(addNA(Gh))

Include self in neighbours list

Description

The function includes the region itself in its own list of neighbours, and sets attribute "self.included" to TRUE; remove.self reverts the effects of include.self.

Usage

include.self(nb)
remove.self(nb)

Arguments

Value

The function returns an object of class nb with a list of integer vectors containing neighbour region number ids; attribute "self.included" is set to TRUE.

Author(s)

Roger Bivand Roger.Bivand@nhh.no

See Also

summary.nb

Examples

columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
col.gal.nb <- read.gal(system.file("weights/columbus.gal", package="spData")[1])
coords <- st_coordinates(st_centroid(columbus))
summary(col.gal.nb, coords)
summary(include.self(col.gal.nb), coords)
summary(remove.self(include.self(col.gal.nb)), coords)

Test a neighbours list for symmetry

Description

Checks a neighbours list for symmetry/transitivity (if i is a neighbour of j, then j is a neighbour of i). This holds for distance and contiguity based neighbours, but not for k-nearest neighbours. The helper function sym.attr.nb() calls is.symmetric.nb() to set the sym attribute if needed, and make.sym.nb makes a non-symmetric list symmetric by adding neighbors. is.symmetric.glist checks a list of general weights corresponding to neighbours for symmetry for symmetric neighbours.

Usage

is.symmetric.nb(nb, verbose = NULL, force = FALSE)
sym.attr.nb(nb)
make.sym.nb(nb)
old.make.sym.nb(nb)
is.symmetric.glist(nb, glist)

Arguments

Value

TRUE if symmetric, FALSE if not; is.symmetric.glist returns a value with an attribute, "d", indicating for failed symmetry the largest failing value.

Note

A new version of make.sym.nb by Bjarke Christensen is now included. The older version has been renamed old.make.sym.nb, and their comparison constitutes a nice demonstration of vectorising speedup using sapply and lapply rather than loops. When any no-neighbour observations are present, old.make.sym.nb is used.

Author(s)

Roger Bivand Roger.Bivand@nhh.no

See Also

read.gal

Examples

columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
col.gal.nb <- read.gal(system.file("weights/columbus.gal", package="spData")[1])
coords <- st_coordinates(st_centroid(columbus))
ind <- row.names(as(columbus, "Spatial"))
print(is.symmetric.nb(col.gal.nb, verbose=TRUE, force=TRUE))
k4 <- knn2nb(knearneigh(coords, k=4), row.names=ind)
k4 <- sym.attr.nb(k4)
print(is.symmetric.nb(k4))
k4.sym <- make.sym.nb(k4)
print(is.symmetric.nb(k4.sym))

Permutation test for same colour join count statistics

Description

A permutation test for same colour join count statistics calculated by using nsim random permutations of fx for the given spatial weighting scheme, to establish the ranks of the observed statistics (for each colour) in relation to the nsim simulated values.

Usage

joincount.mc(fx, listw, nsim, zero.policy=attr(listw, "zero.policy"),
 alternative="greater", spChk=NULL)

Arguments

Value

A list with class jclist of lists with class htest and mc.sim for each of the k colours containing the following components:

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 63-5.

See Also

joincount.test

Examples

data(oldcol)
HICRIME <- cut(COL.OLD$CRIME, breaks=c(0,35,80), labels=c("low","high"))
names(HICRIME) <- rownames(COL.OLD)
joincount.mc(HICRIME, nb2listw(COL.nb, style="B"), nsim=99, alternative="two.sided")
joincount.test(HICRIME, nb2listw(COL.nb, style="B"), alternative="two.sided")

BB, BW and Jtot join count statistic for k-coloured factors

Description

A function for tallying join counts between same-colour and different colour spatial objects, where neighbour relations are defined by a weights list. Given the global counts in each colour, expected counts and variances are calculated under non-free sampling, and a z-value reported. Since multiple tests are reported, no p-values are given, allowing the user to adjust the significance level applied. Jtot is the count of all different-colour joins.

Usage

joincount.multi(fx, listw, zero.policy = attr(listw, "zero.policy"),
 spChk = NULL, adjust.n=TRUE)
## S3 method for class 'jcmulti'
print(x, ...)

Arguments

Value

A matrix with class jcmulti with row and column names for observed and expected counts, variance, and z-value.

Note

The derivation of the test (Cliff and Ord, 1981, p. 18) assumes that the weights matrix is symmetric. For inherently non-symmetric matrices, such as k-nearest neighbour matrices, listw2U() can be used to make the matrix symmetric. In non-symmetric weights matrix cases, the variance of the test statistic may be negative.

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 20; Upton, G., Fingleton, B. 1985 Spatial data analysis by example: point pattern and qualitative data, Wiley, pp. 158–170.

See Also

joincount.test

Examples

columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
HICRIME <- cut(columbus$CRIME, breaks=c(0,35,80), labels=c("low","high"))
(nb <- poly2nb(columbus))
lw <- nb2listw(nb, style="B")
joincount.multi(HICRIME, lw)
col_geoms <- st_geometry(columbus)
col_geoms[21] <- st_buffer(col_geoms[21], dist=-0.05)
st_geometry(columbus) <- col_geoms
(nb <- poly2nb(columbus))
lw <- nb2listw(nb, style="B", zero.policy=TRUE)
joincount.multi(HICRIME, lw)
## Not run: 
data(oldcol)
HICRIME <- cut(COL.OLD$CRIME, breaks=c(0,35,80), labels=c("low","high"))
names(HICRIME) <- rownames(COL.OLD)
joincount.multi(HICRIME, nb2listw(COL.nb, style="B"))
data(hopkins, package="spData")
image(1:32, 1:32, hopkins[5:36,36:5], breaks=c(-0.5, 3.5, 20),
 col=c("white", "black"))
box()
hopkins.rook.nb <- cell2nb(32, 32, type="rook")
unlist(spweights.constants(nb2listw(hopkins.rook.nb, style="B")))
hopkins.queen.nb <- cell2nb(32, 32, type="queen")
hopkins.bishop.nb <- diffnb(hopkins.rook.nb, hopkins.queen.nb, verbose=FALSE)
hopkins4 <- hopkins[5:36,36:5]
hopkins4[which(hopkins4 > 3, arr.ind=TRUE)] <- 4
hopkins4.f <- factor(hopkins4)
table(hopkins4.f)
joincount.multi(hopkins4.f, nb2listw(hopkins.rook.nb, style="B"))
cat("replicates Upton & Fingleton table 3.4 (p. 166)\n")
joincount.multi(hopkins4.f, nb2listw(hopkins.bishop.nb, style="B"))
cat("replicates Upton & Fingleton table 3.6 (p. 168)\n")
joincount.multi(hopkins4.f, nb2listw(hopkins.queen.nb, style="B"))
cat("replicates Upton & Fingleton table 3.7 (p. 169)\n")

## End(Not run)
GDAL37 <- as.numeric_version(unname(sf_extSoftVersion()["GDAL"])) >= "3.7.0"
file <- "etc/shapes/GB_2024_southcoast_50m.gpkg.zip"
zipfile <- system.file(file, package="spdep")
if (GDAL37) {
    sc50m <- st_read(zipfile)
} else {
    td <- tempdir()
    bn <- sub(".zip", "", basename(file), fixed=TRUE)
    target <- unzip(zipfile, files=bn, exdir=td)
    sc50m <- st_read(target)
}
sc50m$Winner <- factor(sc50m$Winner, levels=c("Con", "Green", "Lab", "LD"))
plot(sc50m[,"Winner"], pal=c("#2297E6", "#61D04F", "#DF536B", "#F5C710"))
nb_sc_50m <- poly2nb(sc50m, row.names=as.character(sc50m$Constituency))
sub2 <- attr(nb_sc_50m, "region.id")[attr(nb_sc_50m, "ncomp")$comp.id == 2L]
iowe <- match(sub2[1], attr(nb_sc_50m, "region.id"))
diowe <- c(st_distance(sc50m[iowe,], sc50m))
meet_criterion <- sum(diowe <= units::set_units(5000, "m"))
cands <- attr(nb_sc_50m, "region.id")[order(diowe)[1:meet_criterion]]
nb_sc_50m_iowe <- addlinks1(nb_sc_50m, from = cands[1],
 to = cands[3:meet_criterion])
ioww <- match(sub2[2], attr(nb_sc_50m, "region.id"))
dioww <- c(st_distance(sc50m[ioww,], sc50m))
meet_criterion <- sum(dioww <= units::set_units(5000, "m"))
cands <- attr(nb_sc_50m, "region.id")[order(dioww)[1:meet_criterion]]
nb_sc_50m_iow <- addlinks1(nb_sc_50m_iowe, from = cands[2], to = cands[3:meet_criterion])
nb_sc_1_2 <- nblag_cumul(nblag(nb_sc_50m_iow, 2))
joincount.multi(sc50m$Winner, nb2listw(nb_sc_1_2, style="B"))

BB join count statistic for k-coloured factors

Description

The BB join count test for spatial autocorrelation using a spatial weights matrix in weights list form for testing whether same-colour joins occur more frequently than would be expected if the zones were labelled in a spatially random way. The assumptions underlying the test are sensitive to the form of the graph of neighbour relationships and other factors, and results may be checked against those of joincount.mc permutations.

Usage

joincount.test(fx, listw, zero.policy=attr(listw, "zero.policy"), alternative="greater",
 sampling="nonfree", spChk=NULL, adjust.n=TRUE)
## S3 method for class 'jclist'
print(x, ...)

Arguments

Value

A list with class jclist of lists with class htest for each of the k colours containing the following components:

Note

The derivation of the test (Cliff and Ord, 1981, p. 18) assumes that the weights matrix is symmetric. For inherently non-symmetric matrices, such as k-nearest neighbour matrices, listw2U() can be used to make the matrix symmetric. In non-symmetric weights matrix cases, the variance of the test statistic may be negative.

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, pp. 19-20.

See Also

joincount.mc, joincount.multi, listw2U

Examples

data(oldcol)
HICRIME <- cut(COL.OLD$CRIME, breaks=c(0,35,80), labels=c("low","high"))
names(HICRIME) <- rownames(COL.OLD)
joincount.test(HICRIME, nb2listw(COL.nb, style="B"))
joincount.test(HICRIME, nb2listw(COL.nb, style="B"), sampling="free")
joincount.test(HICRIME, nb2listw(COL.nb, style="C"))
joincount.test(HICRIME, nb2listw(COL.nb, style="S"))
joincount.test(HICRIME, nb2listw(COL.nb, style="W"))
by(card(COL.nb), HICRIME, summary)
print(is.symmetric.nb(COL.nb))
coords.OLD <- cbind(COL.OLD$X, COL.OLD$Y)
COL.k4.nb <- knn2nb(knearneigh(coords.OLD, 4))
print(is.symmetric.nb(COL.k4.nb))
joincount.test(HICRIME, nb2listw(COL.k4.nb, style="B"))
cat("Note non-symmetric weights matrix - use listw2U()\n")
joincount.test(HICRIME, listw2U(nb2listw(COL.k4.nb, style="B")))
columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
HICRIME <- cut(columbus$CRIME, breaks=c(0,35,80), labels=c("low","high"))
(nb <- poly2nb(columbus))
lw <- nb2listw(nb, style="B")
joincount.test(HICRIME, lw)
col_geoms <- st_geometry(columbus)
col_geoms[21] <- st_buffer(col_geoms[21], dist=-0.05)
st_geometry(columbus) <- col_geoms
(nb <- poly2nb(columbus))
lw <- nb2listw(nb, style="B", zero.policy=TRUE)
joincount.test(HICRIME, lw)

K nearest neighbours for spatial weights

Description

The function returns a matrix with the indices of points belonging to the set of the k nearest neighbours of each other. If longlat = TRUE, Great Circle distances are used. A warning will be given if identical points are found.

Usage

knearneigh(x, k=1, longlat = NULL, use_kd_tree=TRUE)

Arguments

Details

The underlying legacy C code is based on the knn function in the class package.

Value

A list of class knn

Author(s)

Roger Bivand Roger.Bivand@nhh.no

See Also

knn, dnearneigh, knn2nb, kNN

Examples

columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE)
col.knn <- knearneigh(coords, k=4)
plot(st_geometry(columbus), border="grey")
plot(knn2nb(col.knn), coords, add=TRUE)
title(main="K nearest neighbours, k = 4")
data(state)
us48.fipsno <- read.geoda(system.file("etc/weights/us48.txt",
 package="spdep")[1])
if (as.numeric(paste(version$major, version$minor, sep="")) < 19) {
 m50.48 <- match(us48.fipsno$"State.name", state.name)
} else {
 m50.48 <- match(us48.fipsno$"State_name", state.name)
}
xy <- as.matrix(as.data.frame(state.center))[m50.48,]
llk4.nb <- knn2nb(knearneigh(xy, k=4, longlat=FALSE))
gck4.nb <- knn2nb(knearneigh(xy, k=4, longlat=TRUE))
plot(llk4.nb, xy)
plot(diffnb(llk4.nb, gck4.nb), xy, add=TRUE, col="red", lty=2)
title(main="Differences between Euclidean and Great Circle k=4 neighbours")
summary(llk4.nb, xy, longlat=TRUE, scale=0.5)
summary(gck4.nb, xy, longlat=TRUE, scale=0.5)

#xy1 <- SpatialPoints((as.data.frame(state.center))[m50.48,],
#  proj4string=CRS("+proj=longlat +ellps=GRS80"))
#gck4a.nb <- knn2nb(knearneigh(xy1, k=4))
#summary(gck4a.nb, xy1, scale=0.5)

xy1 <- st_as_sf((as.data.frame(state.center))[m50.48,], coords=1:2,
  crs=st_crs("OGC:CRS84"))
old_use_s2 <- sf_use_s2()
sf_use_s2(TRUE)
system.time(gck4a.nb <- knn2nb(knearneigh(xy1, k=4)))
summary(gck4a.nb, xy1, scale=0.5)
sf_use_s2(FALSE)
system.time(gck4a.nb <- knn2nb(knearneigh(xy1, k=4)))
summary(gck4a.nb, xy1, scale=0.5)
sf_use_s2(old_use_s2)

# https://github.com/r-spatial/spdep/issues/38
run <- FALSE
if (require("dbscan", quietly=TRUE)) run <- TRUE
if (run) {
  set.seed(1)
  x <- cbind(runif(50), runif(50), runif(50))
  out <- knearneigh(x, k=5)
  knn2nb(out)
}
if (run) {
# fails because dbscan works with > 2 dimensions but does 
# not work with duplicate points
  try(out <- knearneigh(rbind(x, x[1:10,]), k=5))
}

Neighbours list from knn object

Description

The function converts a knn object returned by knearneigh into a neighbours list of class nb with a list of integer vectors containing neighbour region number ids.

Usage

knn2nb(knn, row.names = NULL, sym = FALSE)

Arguments

Value

The function returns an object of class nb with a list of integer vectors containing neighbour region number ids. See card for details of “nb” objects.

Author(s)

Roger Bivand Roger.Bivand@nhh.no

See Also

knearneigh, card

Examples

columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
coords <- st_coordinates(st_centroid(columbus))
col.knn <- knearneigh(coords, k=4)
plot(st_geometry(columbus), border="grey")
plot(knn2nb(col.knn), coords, add=TRUE)
title(main="K nearest neighbours, k = 4")
# example of reading points with readr::read_csv() yielding a tibble
load(system.file("etc/misc/coords.rda", package="spdep"))
class(coords)
knn2nb(knearneigh(coords, k=4))

Spatial lag of a numeric vector

Description

Using a listw sparse representation of a spatial weights matrix, compute the lag vector V x

Usage

## S3 method for class 'listw'
lag(x, var, zero.policy=attr(listw, "zero.policy"), NAOK=FALSE, ...)

Arguments

Value

a numeric vector the same length as var

Author(s)

Roger Bivand Roger.Bivand@nhh.no

See Also

nb2listw

Examples

data(oldcol)
Vx <- lag.listw(nb2listw(COL.nb, style="W"), COL.OLD$CRIME)
plot(Vx, COL.OLD$CRIME)
plot(ecdf(COL.OLD$CRIME))
plot(ecdf(Vx), add=TRUE, col.points="red", col.hor="red")
is.na(COL.OLD$CRIME[5]) <- TRUE
VxNA <- lag.listw(nb2listw(COL.nb, style="W"), COL.OLD$CRIME, NAOK=TRUE)

Compute Lee's statistic

Description

A simple function to compute Lee's L statistic for bivariate spatial data;

L(x,y) = \frac{n}{\sum_{i=1}^{n}(\sum_{j=1}^{n}w_{ij})^2} \frac{\sum_{i=1}^{n}(\sum_{j=1}^{n}w_{ij}(x_i-\bar{x})) ((\sum_{j=1}^{n}w_{ij}(y_j-\bar{y}))}{\sqrt{\sum_{i=1}^{n}(x_i - \bar{x})^2} \sqrt{\sum_{i=1}^{n}(y_i - \bar{y})^2}}

Usage

lee(x, y, listw, n, S2, zero.policy=attr(listw, "zero.policy"), NAOK=FALSE)

Arguments

Value

a list of

Author(s)

Roger Bivand and Virgiio Gómez-Rubio Virgilio.Gomez@uclm.es

References

Lee (2001). Developing a bivariate spatial association measure: An integration of Pearson's r and Moran's I. J Geograph Syst 3: 369-385

See Also

lee.mc

Examples

data(boston, package="spData")
lw<-nb2listw(boston.soi)

x<-boston.c$CMEDV
y<-boston.c$CRIM
z<-boston.c$RAD

Lxy<-lee(x, y, lw, length(x), zero.policy=TRUE)
Lxz<-lee(x, z, lw, length(x), zero.policy=TRUE)

Permutation test for Lee's L statistic

Description

A permutation test for Lee's L statistic calculated by using nsim random permutations of x and y for the given spatial weighting scheme, to establish the rank of the observed statistic in relation to the nsim simulated values.

Usage

lee.mc(x, y, listw, nsim, zero.policy=attr(listw, "zero.policy"), alternative="greater",
 na.action=na.fail, spChk=NULL, return_boot=FALSE)

Arguments

Value

A list with class htest and mc.sim containing the following components:

Author(s)

Roger Bivand, Virgilio Gómez-Rubio Virgilio.Gomez@uclm.es

References

Lee (2001). Developing a bivariate spatial association measure: An integration of Pearson's r and Moran's I. J Geograph Syst 3: 369-385

See Also

lee

Examples

data(boston, package="spData")
lw<-nb2listw(boston.soi)

x<-boston.c$CMEDV
y<-boston.c$CRIM

lee.mc(x, y, nsim=99, lw, zero.policy=TRUE, alternative="two.sided")

#Test with missing values
x[1:5]<-NA
y[3:7]<-NA

lee.mc(x, y, nsim=99, lw, zero.policy=TRUE, alternative="two.sided", 
   na.action=na.omit)

Lee's L test for spatial autocorrelation

Description

Lee's L test for spatial autocorrelation using a spatial weights matrix in weights list form. The assumptions underlying the test are sensitive to the form of the graph of neighbour relationships and other factors, and results may be checked against those of lee.mc permutations.

Usage

lee.test(x, y, listw, zero.policy=attr(listw, "zero.policy"),
 alternative="greater", na.action=na.fail, spChk=NULL)

Arguments

Value

A list with class htest containing the following components:

Note

See Lee (2004) for details on how the asymptotic expectation and variance of Lee's L is computed. In particular, check Lee (2004), table 1, page 1690.

This test may fail for large datasets as the computation of the asymptotic expectation and variance requires the use of dense matrices.

Author(s)

Roger Bivand and Virgilio Gómez-Rubio Virgilio.Gomez@uclm.es

References

Lee (2004). A generalized significance testing method for global measures of spatial association: an extension of the Mantel test. Environment and Planning A 2004, volume 36, pages 1687 - 1703

See Also

lee, lee.mc, listw2U

Examples

data(oldcol)
col.W <- nb2listw(COL.nb, style="W")
crime <- COL.OLD$CRIME

lee.test(crime, crime, col.W, zero.policy=TRUE)

#Test with missing values
x<-crime
y<-crime
x[1:5]<-NA
y[3:7]<-NA

lee.test(x, y, col.W, zero.policy=TRUE, na.action=na.omit)
#  lee.test(x, y, col.W, zero.policy=TRUE)#Stops with an error



data(boston, package="spData")
lw<-nb2listw(boston.soi)

x<-boston.c$CMEDV
y<-boston.c$CRIM

lee.test(x, y, lw, zero.policy=TRUE, alternative="less")

#Test with missing values
x[1:5]<-NA
y[3:7]<-NA

lee.test(x, y, lw, zero.policy=TRUE, alternative="less", na.action=na.omit)

Local Indicators for Categorical Data

Description

Local indicators for categorical data combine a measure of local composition in a window given by the per-observation set of neighbouring observations, with a local multi-category joincount test simplified to neighbours with the same or different categories compared to the focal observation

Usage

licd_multi(fx, listw, zero.policy = attr(listw, "zero.policy"), adjust.n = TRUE,
 nsim = 0L, iseed = NULL, no_repeat_in_row = FALSE, control = list())

Arguments

Details

The original code may be found at doi:10.5281/zenodo.4283766

Value

Note

In order to increase the numbers of neighbours using nblag and nblag_cumul is advisable; use of binary weights is advised and are in any case used for the composition measure

Author(s)

Roger Bivand Roger.Bivand@nhh.no based on earlier code by Tomasz M. Kossowski, Justyna Wilk and Michał B. Pietrzak

References

Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 20;

Upton, G., Fingleton, B. 1985 Spatial data analysis by example: point pattern and qualitative data, Wiley, pp. 158–170;

Boots, B., 2003. Developing local measures of spatial association for categorical data. Journal of Geographical Systems 5, 139–160;

Boots, B., 2006. Local configuration measures for categorical spatial data: binary regular lattices. Journal of Geographical Systems 8 (1), 1–24;

Pietrzak, M.B., Wilk, J., Kossowski, T., Bivand, R.S., 2014. The application of local indicators for categorical data (LICD) in the spatial analysis of economic development. Comparative Economic Research 17 (4), 203–220 doi:10.2478/cer-2014-0041;

Bivand, R.S., Wilk, J., Kossowski, T., 2017. Spatial association of population pyramids across Europe: The application of symbolic data, cluster analysis and join-count tests. Spatial Statistics 21 (B), 339–361 doi:10.1016/j.spasta.2017.03.003;

Francesco Carrer, Tomasz M. Kossowski, Justyna Wilk, Michał B. Pietrzak, Roger S. Bivand, The application of Local Indicators for Categorical Data (LICD) to explore spatial dependence in archaeological spaces, Journal of Archaeological Science, 126, 2021, doi:10.1016/j.jas.2020.105306

See Also

joincount.multi

Examples

columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
HICRIME <- cut(columbus$CRIME, breaks=c(0,35,80), labels=c("low","high"))
(nb <- poly2nb(columbus))
lw <- nb2listw(nblag_cumul(nblag(nb, 2)), style="B")
obj <- licd_multi(HICRIME, lw)
str(obj)
h_obj <- hotspot(obj)
str(h_obj)
table(h_obj$both_recode)
columbus$both <- h_obj$both_recode
plot(columbus[, "both"])
GDAL37 <- as.numeric_version(unname(sf_extSoftVersion()["GDAL"])) >= "3.7.0"
file <- "etc/shapes/GB_2024_southcoast_50m.gpkg.zip"
zipfile <- system.file(file, package="spdep")
if (GDAL37) {
    sc50m <- st_read(zipfile)
} else {
    td <- tempdir()
    bn <- sub(".zip", "", basename(file), fixed=TRUE)
    target <- unzip(zipfile, files=bn, exdir=td)
    sc50m <- st_read(target)
}
sc50m$Winner <- factor(sc50m$Winner, levels=c("Con", "Green", "Lab", "LD"))
plot(sc50m[,"Winner"], pal=c("#2297E6", "#61D04F", "#DF536B", "#F5C710"))
nb_sc_50m <- poly2nb(sc50m, row.names=as.character(sc50m$Constituency))
sub2 <- attr(nb_sc_50m, "region.id")[attr(nb_sc_50m, "ncomp")$comp.id == 2L]
iowe <- match(sub2[1], attr(nb_sc_50m, "region.id"))
diowe <- c(st_distance(sc50m[iowe,], sc50m))
meet_criterion <- sum(diowe <= units::set_units(5000, "m"))
cands <- attr(nb_sc_50m, "region.id")[order(diowe)[1:meet_criterion]]
nb_sc_50m_iowe <- addlinks1(nb_sc_50m, from = cands[1],
 to = cands[3:meet_criterion])
ioww <- match(sub2[2], attr(nb_sc_50m, "region.id"))
dioww <- c(st_distance(sc50m[ioww,], sc50m))
meet_criterion <- sum(dioww <= units::set_units(5000, "m"))
cands <- attr(nb_sc_50m, "region.id")[order(dioww)[1:meet_criterion]]
nb_sc_50m_iow <- addlinks1(nb_sc_50m_iowe, from = cands[2], to = cands[3:meet_criterion])
nb_sc_1_2 <- nblag_cumul(nblag(nb_sc_50m_iow, 2))
lw <- nb2listw(nb_sc_1_2, style="B")
licd_obj <- licd_multi(sc50m$Winner, lw)
h_obj <- hotspot(licd_obj)
sc50m$both <- h_obj$both_recode
plot(sc50m[, "both"])
ljc <- local_joincount_uni(factor(sc50m$Winner == "LD"), chosen="TRUE", lw)
sc50m$LD_pv <- ljc[, 2]
plot(sc50m[, "LD_pv"], breaks=c(0, 0.025, 0.05, 0.1, 0.5, 1))

Spatial neighbour sparse representation

Description

The function makes a "spatial neighbour" object representation (similar to the S-PLUS spatial statististics module representation of a "listw" spatial weights object. sn2listw() is the inverse function to listw2sn(), creating a "listw" object from a "spatial neighbour" object.

Usage

listw2sn(listw)
sn2listw(sn, style = NULL, zero.policy = NULL, from_mat2listw=FALSE)

Arguments

Value

listw2sn()returns a data frame with three columns, and with class spatial.neighbour:

Author(s)

Roger Bivand Roger.Bivand@nhh.no

See Also

nb2listw

Examples

columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
col.gal.nb <- read.gal(system.file("weights/columbus.gal", package="spData")[1])
col.listw <- nb2listw(col.gal.nb)
col.listw$neighbours[[1]]
col.listw$weights[[1]]
col.sn <- listw2sn(col.listw)
str(col.sn)

Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models

Description

The function reports the estimates of tests chosen among five statistics for testing for spatial dependence in linear models. The statistics are the simple RS test for error dependence (“RSerr”), the simple RS test for a missing spatially lagged dependent variable (“RSlag”), variants of these adjusted for the presence of the other (“adjRSerr” tests for error dependence in the possible presence of a missing lagged dependent variable, “adjRSlag” the other way round), and a portmanteau test (“SARMA”, in fact “RSerr” + “adjRSlag”). Note: from spdep 1.3-2, the tests are re-named “RS” - Rao's score tests, rather than “LM” - Lagrange multiplier tests to match the naming of tests from the same family in SDM.RStests.

Usage

lm.RStests(model, listw, zero.policy=attr(listw, "zero.policy"), test="RSerr",
 spChk=NULL, naSubset=TRUE)
lm.LMtests(model, listw, zero.policy=attr(listw, "zero.policy"), test="LMerr",
 spChk=NULL, naSubset=TRUE)
## S3 method for class 'RStestlist'
print(x, ...)
## S3 method for class 'RStestlist'
summary(object, p.adjust.method="none", ...)
## S3 method for class 'RStestlist.summary'
print(x, digits=max(3, getOption("digits") - 2), ...)

Arguments

Details

The two types of dependence are for spatial lag \rho and spatial error \lambda:

\mathbf{y} = \mathbf{X \beta} + \rho \mathbf{W_{(1)} y} + \mathbf{u},

\mathbf{u} = \lambda \mathbf{W_{(2)} u} + \mathbf{e}

where \mathbf{e} is a well-behaved, uncorrelated error term. Tests for a missing spatially lagged dependent variable test that \rho = 0, tests for spatial autocorrelation of the error \mathbf{u} test whether \lambda = 0. \mathbf{W} is a spatial weights matrix; for the tests used here they are identical.

Value

A list of class RStestlist of htest objects, each with:

Author(s)

Roger Bivand Roger.Bivand@nhh.no and Andrew Bernat

References

Anselin, L. 1988 Spatial econometrics: methods and models. (Dordrecht: Kluwer); Anselin, L., Bera, A. K., Florax, R. and Yoon, M. J. 1996 Simple diagnostic tests for spatial dependence. Regional Science and Urban Economics, 26, 77–104 doi:10.1016/0166-0462(95)02111-6; Malabika Koley (2024) Specification Testing under General Nesting Spatial Model, https://sites.google.com/view/malabikakoley/research.

See Also

lm, SD.RStests

Examples

data(oldcol)
oldcrime.lm <- lm(CRIME ~ HOVAL + INC, data = COL.OLD)
summary(oldcrime.lm)
lw <- nb2listw(COL.nb)
res <- lm.RStests(oldcrime.lm, listw=lw, test="all")
summary(res)
if (require("spatialreg", quietly=TRUE)) {
  oldcrime.slx <- lmSLX(CRIME ~ HOVAL + INC, data = COL.OLD, listw=lw)
  summary(lm.RStests(oldcrime.slx, listw=lw, test=c("adjRSerr", "adjRSlag")))
}

Moran's I test for residual spatial autocorrelation

Description

Moran's I test for spatial autocorrelation in residuals from an estimated linear model (lm()).

Usage

lm.morantest(model, listw, zero.policy=attr(listw, "zero.policy"),
 alternative = "greater", spChk=NULL, resfun=weighted.residuals, naSubset=TRUE)

Arguments

Value

A list with class htest containing the following components:

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 203,

See Also

lm.LMtests, lm

Examples

data(oldcol)
oldcrime1.lm <- lm(CRIME ~ 1, data = COL.OLD)
oldcrime.lm <- lm(CRIME ~ HOVAL + INC, data = COL.OLD)
lm.morantest(oldcrime.lm, nb2listw(COL.nb, style="W"))
lm.LMtests(oldcrime.lm, nb2listw(COL.nb, style="W"))
lm.morantest(oldcrime.lm, nb2listw(COL.nb, style="S"))
lm.morantest(oldcrime1.lm, nb2listw(COL.nb, style="W"))
moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style="W"),
 randomisation=FALSE)
oldcrime.wlm <- lm(CRIME ~ HOVAL + INC, data = COL.OLD,
 weights = I(1/AREA_PL))
lm.morantest(oldcrime.wlm, nb2listw(COL.nb, style="W"),
 resfun=weighted.residuals)
lm.morantest(oldcrime.wlm, nb2listw(COL.nb, style="W"),
 resfun=rstudent)

Exact global Moran's I test

Description

The function implements Tiefelsdorf's exact global Moran's I test.

Usage

lm.morantest.exact(model, listw, zero.policy = attr(listw, "zero.policy"),
 alternative = "greater", spChk = NULL, resfun = weighted.residuals,
 zero.tol = 1e-07, Omega=NULL, save.M=NULL, save.U=NULL, useTP=FALSE,
 truncErr=1e-6, zeroTreat=0.1)
## S3 method for class 'moranex'
print(x, ...)

Arguments

Value

A list of class moranex with the following components:

Author(s)

Markus Reder and Roger Bivand

References

Roger Bivand, Werner G. Müller and Markus Reder (2009) "Power calculations for global and local Moran's I." Computational Statistics & Data Analysis 53, 2859-2872.

See Also

lm.morantest.sad

Examples

eire <- st_read(system.file("shapes/eire.gpkg", package="spData")[1])
row.names(eire) <- as.character(eire$names)
eire.nb <- poly2nb(eire)
e.lm <- lm(OWNCONS ~ ROADACC, data=eire)
lm.morantest(e.lm, nb2listw(eire.nb))
lm.morantest.sad(e.lm, nb2listw(eire.nb))
lm.morantest.exact(e.lm, nb2listw(eire.nb))
lm.morantest.exact(e.lm, nb2listw(eire.nb), useTP=TRUE)

Saddlepoint approximation of global Moran's I test

Description

The function implements Tiefelsdorf's application of the Saddlepoint approximation to global Moran's I's reference distribution.

Usage

lm.morantest.sad(model, listw, zero.policy=attr(listw, "zero.policy"),
  alternative="greater", spChk=NULL, resfun=weighted.residuals,
  tol=.Machine$double.eps^0.5, maxiter=1000, tol.bounds=0.0001,
  zero.tol = 1e-07, Omega=NULL, save.M=NULL, save.U=NULL)
## S3 method for class 'moransad'
print(x, ...)
## S3 method for class 'moransad'
summary(object, ...)
## S3 method for class 'summary.moransad'
print(x, ...) 

Arguments

Details

The function involves finding the eigenvalues of an n by n matrix, and numerically finding the root for the Saddlepoint approximation, and should therefore only be used with care when n is large.

Value

A list of class moransad with the following components:

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

Tiefelsdorf, M. 2002 The Saddlepoint approximation of Moran's I and local Moran's Ii reference distributions and their numerical evaluation. Geographical Analysis, 34, pp. 187–206; Bivand RS, Wong DWS 2018 Comparing implementations of global and local indicators of spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x

See Also

lm.morantest

Examples

eire <- st_read(system.file("shapes/eire.gpkg", package="spData")[1])
row.names(eire) <- as.character(eire$names)
eire.nb <- poly2nb(eire)
e.lm <- lm(OWNCONS ~ ROADACC, data=eire)
lm.morantest(e.lm, nb2listw(eire.nb))
lm.morantest.sad(e.lm, nb2listw(eire.nb))
summary(lm.morantest.sad(e.lm, nb2listw(eire.nb)))
e.wlm <- lm(OWNCONS ~ ROADACC, data=eire, weights=RETSALE)
lm.morantest(e.wlm, nb2listw(eire.nb), resfun=rstudent)
lm.morantest.sad(e.wlm, nb2listw(eire.nb), resfun=rstudent)

Calculate the local bivariate join count

Description

The bivariate join count (BJC) evaluates event occurrences in predefined regions and tests if the co-occurrence of events deviates from complete spatial randomness.

Usage

local_joincount_bv(
  x,
  z,
  listw,
  nsim = 199,
  alternative = "two.sided"
)

Arguments

Details

There are two cases that are evaluated in the bivariate join count. The first being in-situ colocation (CLC) where xi = 1 and zi = 1. The second is the general form of the bivariate join count (BJC) that is used when there is no in-situ colocation.

The BJC case "is useful when x and z cannot occur in the same location, such as when x and z correspond to two different values of a single categorical variable" or "when x and z can co-locate, but do not" (Anselin and Li, 2019). Whereas the CLC case is useful in evaluating simultaneous occurrences of events.

The local bivariate join count statistic requires a binary weights list which can be generated with nb2listw(nb, style = "B").

P-values are only reported for those regions that match the CLC or BJC criteria. Others will not have an associated p-value.

P-values are estimated using a conditional permutation approach. This creates a reference distribution from which the observed statistic is compared.

Value

a data.frame with two columns join_count and p_sim and number of rows equal to the length of arguments x.

Author(s)

Josiah Parry josiah.parry@gmail.com

References

Anselin, L., & Li, X. (2019). Operational Local Join Count Statistics for Cluster Detection. Journal of geographical systems, 21(2), 189–210. doi:10.1007/s10109-019-00299-x

Examples

data("oldcol")
listw <- nb2listw(COL.nb, style = "B")
# Colocation case
x <- COL.OLD[["CP"]]
z <- COL.OLD[["EW"]]
set.seed(1)
res <- local_joincount_bv(x, z, listw)
na.omit(res)
# no colocation case
z <- 1 - x
set.seed(1)
res <- local_joincount_bv(x, z, listw)
na.omit(res)

Calculate the local univariate join count

Description

The univariate local join count statistic is used to identify clusters of rarely occurring binary variables. The binary variable of interest should occur less than half of the time.

Usage

local_joincount_uni(
  fx,
  chosen,
  listw,
  alternative = "two.sided",
  nsim = 199,
  iseed = NULL,
  no_repeat_in_row=FALSE
)

Arguments

Details

The local join count statistic requires a binary weights list which can be generated with nb2listw(nb, style = "B"). Additionally, ensure that the binary variable of interest is rarely occurring in no more than half of observations.

P-values are estimated using a conditional permutation approach. This creates a reference distribution from which the observed statistic is compared. For more see Geoda Glossary.

Value

a data.frame with two columns BB and Pr() and number of rows equal to the length of x.

Author(s)

Josiah Parry josiah.parry@gmail.com

References

Anselin, L., & Li, X. (2019). Operational Local Join Count Statistics for Cluster Detection. Journal of geographical systems, 21(2), 189–210. doi:10.1007/s10109-019-00299-x

Examples

data(oldcol)
fx <- as.factor(ifelse(COL.OLD$CRIME < 35, "low-crime", "high-crime"))
listw <- nb2listw(COL.nb, style = "B")
set.seed(1)
(res <- local_joincount_uni(fx, chosen = "high-crime", listw))

Compute Local Geary statistic

Description

The Local Geary is a local adaptation of Geary's C statistic of spatial autocorrelation. The Local Geary uses squared differences to measure dissimilarity unlike the Local Moran. Low values of the Local Geary indicate positive spatial autocorrelation and large refers to negative spatial autocorrelation.

Inference for the Local Geary is based on a permutation approach which compares the observed value to the reference distribution under spatial randomness. localC_perm() returns a pseudo p-value. This is not an analytical p-value and is based on the number of permutations and as such should be used with care.

Usage

localC(x, ..., zero.policy=NULL)

## Default S3 method:
localC(x, listw, ..., zero.policy=attr(listw, "zero.policy"))

## S3 method for class 'formula'
localC(formula, data, listw, ..., zero.policy=attr(listw, "zero.policy"))

## S3 method for class 'list'
localC(x, listw, ..., zero.policy=attr(listw, "zero.policy"))

## S3 method for class 'matrix'
localC(x, listw, ..., zero.policy=attr(listw, "zero.policy"))

## S3 method for class 'data.frame'
localC(x, listw, ..., zero.policy=attr(listw, "zero.policy"))

localC_perm(x, ..., zero.policy=NULL, iseed=NULL, no_repeat_in_row=FALSE)

## Default S3 method:
localC_perm(x, listw, nsim = 499, alternative = "two.sided", ...,
 zero.policy=attr(listw, "zero.policy"), iseed=NULL, no_repeat_in_row=FALSE)

## S3 method for class 'formula'
localC_perm(formula, data, listw, nsim = 499,
 alternative = "two.sided", ..., zero.policy=attr(listw, "zero.policy"), iseed=NULL,
 no_repeat_in_row=FALSE)

Arguments

Details

The Local Geary can be extended to a multivariate context. When x is a numeric vector, the univariate Local Geary will be calculated. To calculate the multivariate Local Moran provide either a list or a matrix. When x is a list, each element must be a numeric vector of the same length and of the same length as the neighbours in listw. In the case that x is a matrix the number of rows must be the same as the length of the neighbours in listw.

While not required in the univariate context, the standardized Local Geary is calculated. The multivariate Local Geary is always standardized.

The univariate Local Geary is calculated as c_i = \sum_j w_{ij}(x_i - x_j)^2 and the multivariate Local Geary is calculated as c_{k,i} = \sum_{v=1}^{k} c_{v,i} as described in Anselin (2019).

Value

A numeric vector containing Local Geary statistic with attribute pseudo-p when localC_perm() is used. pseudo-p is an 8 column matrix containing

Author(s)

Josiah Parry josiah.parry@gmail.com and Roger Bivand

References

Anselin, L. (1995), Local Indicators of Spatial Association—LISA. Geographical Analysis, 27: 93-115. doi:10.1111/j.1538-4632.1995.tb00338.x

Anselin, L. (2019), A Local Indicator of Multivariate Spatial Association: Extending Gearys c. Geogr Anal, 51: 133-150. doi:10.1111/gean.12164

Examples

orig <- spData::africa.rook.nb
listw <- nb2listw(orig)
x <- spData::afcon$totcon

(A <- localC(x, listw))
listw1 <- nb2listw(droplinks(sym.attr.nb(orig), 3, sym=TRUE), zero.policy=TRUE)
(A1 <- localC(x, listw1, zero.policy=FALSE))
(A2 <- localC(x, listw1, zero.policy=TRUE))
run <- FALSE
if (require(rgeoda, quietly=TRUE)) run <- TRUE
if (run) {
  W <- create_weights(as.numeric(length(x)))
  for (i in 1:length(listw$neighbours)) {
    set_neighbors_with_weights(W, i, listw$neighbours[[i]], listw$weights[[i]])
    update_weights(W)
  }
  set.seed(1)
  B <- local_geary(W, data.frame(x))
  all.equal(A, lisa_values(B))
}
if (run) {
  set.seed(1)
  C <- localC_perm(x, listw, nsim = 499, conditional=TRUE,
    alternative="two.sided")
  cor(ifelse(lisa_pvalues(B) < 0.5, lisa_pvalues(B), 1-lisa_pvalues(B)),
    attr(C, "pseudo-p")[,6])
}
# pseudo-p values probably wrongly folded https://github.com/GeoDaCenter/rgeoda/issues/28

tmap_ok <- FALSE
if (require(tmap, quietly=TRUE)) tmap_ok <- TRUE
if (run) {
  # doi: 10.1111/gean.12164
  guerry_path <- system.file("extdata", "Guerry.shp", package = "rgeoda")
  g <- st_read(guerry_path)[, 7:12]
  cor(st_drop_geometry(g)) #(Tab. 1)
  lw <- nb2listw(poly2nb(g))
  moran(g$Crm_prs, lw, n=nrow(g), S0=Szero(lw))$I
  moran(g$Crm_prp, lw, n=nrow(g), S0=Szero(lw))$I
  moran(g$Litercy, lw, n=nrow(g), S0=Szero(lw))$I
  moran(g$Donatns, lw, n=nrow(g), S0=Szero(lw))$I
  moran(g$Infants, lw, n=nrow(g), S0=Szero(lw))$I
  moran(g$Suicids, lw, n=nrow(g), S0=Szero(lw))$I
}
if (run) {
  o <- prcomp(st_drop_geometry(g), scale.=TRUE)
  cor(st_drop_geometry(g), o$x[,1:2])^2 #(Tab. 2)
}
if (run) {
  g$PC1 <- o$x[, "PC1"]
  brks <- c(min(g$PC1), natural_breaks(k=6, g["PC1"]), max(g$PC1))
  if (tmap_ok) {
    tmap4 <- packageVersion("tmap") >= "3.99"
    if (tmap4) {
      tm_shape(g) + tm_polygons(fill="PC1", 
        fill.scale=tm_scale(values="brewer.rd_yl_gn", breaks=brks,
        midpoint=0), fill.legend=tm_legend(position=tm_pos_in("left", "bottom"),
        frame=FALSE, item.r=0))
    } else {
      tm_shape(g) + tm_fill("PC1", breaks=brks, midpoint=0) + 
      tm_borders() # Fig. 1
    }
  } else {
    pplot(g["PC1"], breaks=brks)
  }
}
if (run) {
  g$PC2 <- -1*o$x[, "PC2"] # eigenvalue sign arbitrary
  brks <- c(min(g$PC2), natural_breaks(k=6, g["PC2"]), max(g$PC2))
  if (tmap_ok) {
    if (tmap4) {
      tm_shape(g) + tm_polygons(fill="PC2", 
        fill.scale=tm_scale(values="brewer.rd_yl_gn", breaks=brks,
        midpoint=0), fill.legend=tm_legend(position=tm_pos_in("left", "bottom"),
        frame=FALSE, item.r=0))
    } else {
      tm_shape(g) + tm_fill("PC2", breaks=brks, midpoint=0) + 
      tm_borders() # Fig. 2
    }
  } else {
    plot(g["PC2"], breaks=brks)
  }
}
if (run) {
  w <- queen_weights(g)
  lm_PC1 <- local_moran(w, g["PC1"], significance_cutoff=0.01,
    permutations=99999)
  g$lm_PC1 <- factor(lisa_clusters(lm_PC1), levels=0:4,
    labels=lisa_labels(lm_PC1)[1:5])
  is.na(g$lm_PC1) <- g$lm_PC1 == "Not significant"
  g$lm_PC1 <- droplevels(g$lm_PC1)
  if (tmap_ok) {
    if (tmap4) {
      tm_shape(g) + tm_polygons(fill="lm_PC1",
        fill.scale=tm_scale(values="brewer.set3", value.na="gray95",
          label.na="Insignificant"),
        fill.legend=tm_legend(position=tm_pos_in("left", "bottom"),
          frame=FALSE, item.r=0))
    } else {
      tm_shape(g) + tm_fill("lm_PC1", textNA="Insignificant",
        colorNA="gray95") + tm_borders() # Fig. 3
    }
  } else {
    plot(g["lm_PC1"])
  }
}
if (run) {
  set.seed(1)
  lm_PC1_spdep <- localmoran_perm(g$PC1, lw, nsim=9999)
  q <- attr(lm_PC1_spdep, "quadr")$pysal
  g$lm_PC1_spdep <- q
  is.na(g$lm_PC1_spdep) <- lm_PC1_spdep[,6] > 0.02 # note folded p-values
  g$lm_PC1_spdep <- droplevels(g$lm_PC1_spdep)
  if (tmap_ok) {
    if (tmap4) {
      tm_shape(g) + tm_polygons(fill="lm_PC1_spdep",
        fill.scale=tm_scale(values="brewer.set3", value.na="gray95",
          label.na="Insignificant"),
        fill.legend=tm_legend(position=tm_pos_in("left", "bottom"),
          frame=FALSE, item.r=0))
    } else {
      tm_shape(g) + tm_fill("lm_PC1_spdep", textNA="Insignificant",
        colorNA="gray95") + tm_borders() # rep. Fig. 3
    }
  } else {
    plot(g["lm_PC1_spdep"])
  }
}
if (run) {
  lg_PC1 <- local_g(w, g["PC1"], significance_cutoff=0.01,
    permutations=99999)
  g$lg_PC1 <- factor(lisa_clusters(lg_PC1), levels=0:2,
    labels=lisa_labels(lg_PC1)[0:3])
  is.na(g$lg_PC1) <- g$lg_PC1 == "Not significant"
  g$lg_PC1 <- droplevels(g$lg_PC1)
  if (tmap_ok) {
    if (tmap4) {
      tm_shape(g) + tm_polygons(fill="lg_PC1",
        fill.scale=tm_scale(values="brewer.set3", value.na="gray95",
          label.na="Insignificant"),
        fill.legend=tm_legend(position=tm_pos_in("left", "bottom"),
          frame=FALSE, item.r=0))
    } else {
      tm_shape(g) + tm_fill("lg_PC1", textNA="Insignificant",
        colorNA="gray95") + tm_borders() # Fig. 4 (wrong)
    }
  } else {
    plot(g["lg_PC1"])
  }
  g$lg_PC1a <- cut(g$PC1, c(-Inf, mean(g$PC1), Inf), labels=c("Low", "High"))
  is.na(g$lg_PC1a) <- lisa_pvalues(lg_PC1) >= 0.01
  g$lg_PC1a <- droplevels(g$lg_PC1a)
  if (tmap_ok) {
    if (tmap4) {
      tm_shape(g) + tm_polygons(fill="lg_PC1a",
        fill.scale=tm_scale(values="brewer.set3", value.na="gray95",
          label.na="Insignificant"),
        fill.legend=tm_legend(position=tm_pos_in("left", "bottom"),
          frame=FALSE, item.r=0))
    } else {
      tm_shape(g) + tm_fill("lg_PC1a", textNA="Insignificant",
        colorNA="gray95") + tm_borders() # Fig. 4 (guess)
    }
  } else {
    plot(g["lg_PC1"])
  }
}
if (run) {
  lc_PC1 <- local_geary(w, g["PC1"], significance_cutoff=0.01,
    permutations=99999)
  g$lc_PC1 <- factor(lisa_clusters(lc_PC1), levels=0:4,
    labels=lisa_labels(lc_PC1)[1:5])
  is.na(g$lc_PC1) <- g$lc_PC1 == "Not significant"
  g$lc_PC1 <- droplevels(g$lc_PC1)
  if (tmap_ok) {
    if (tmap4) {
      tm_shape(g) + tm_polygons(fill="lc_PC1",
        fill.scale=tm_scale(values="brewer.set3", value.na="gray95",
          label.na="Insignificant"),
        fill.legend=tm_legend(position=tm_pos_in("left", "bottom"),
          frame=FALSE, item.r=0))
    } else {
      tm_shape(g) + tm_fill("lc_PC1", textNA="Insignificant",
        colorNA="gray95") + tm_borders() # Fig. 5
    }
  } else {
    plot(g["lc_PC1"])
  }
}
if (run) {
  set.seed(1)
  system.time(lc_PC1_spdep <- localC_perm(g$PC1, lw, nsim=9999,
    alternative="two.sided"))
}
if (run) {
  if (require(parallel, quietly=TRUE)) {
    ncpus <- max(2L, detectCores(logical=FALSE), na.rm = TRUE)-1L
# test with single core
    if (ncpus > 1L) ncpus <- 1L
    cores <- get.coresOption()
    set.coresOption(ncpus)
    system.time(lmc_PC1_spdep1 <- localC_perm(g$PC1, lw, nsim=9999,
      alternative="two.sided", iseed=1))
    set.coresOption(cores)
  }
}
if (run) {
  g$lc_PC1_spdep <- attr(lc_PC1_spdep, "cluster")
  is.na(g$lc_PC1_spdep) <- attr(lc_PC1_spdep, "pseudo-p")[,6] > 0.01
  g$lc_PC1_spdep <- droplevels(g$lc_PC1_spdep)
  if (tmap_ok) {
    if (tmap4) {
      tm_shape(g) + tm_polygons(fill="lc_PC1_spdep",
        fill.scale=tm_scale(values="brewer.set3", value.na="gray95",
          label.na="Insignificant"),
        fill.legend=tm_legend(position=tm_pos_in("left", "bottom"),
          frame=FALSE, item.r=0))
    } else {
      tm_shape(g) + tm_fill("lc_PC1_spdep", textNA="Insignificant",
        colorNA="gray95") + tm_borders() # rep. Fig. 5
    }
  } else {
    plot(g["lc_PC1_spdep"])
  }
}
if (run) {
  g$both_PC1 <- interaction(g$lc_PC1, g$lm_PC1)
  g$both_PC1 <- droplevels(g$both_PC1)
  if (tmap_ok) {
    if (tmap4) {
      tm_shape(g) + tm_polygons(fill="both_PC1",
        fill.scale=tm_scale(values="brewer.set3", value.na="gray95",
          label.na="Insignificant"),
        fill.legend=tm_legend(position=tm_pos_in("left", "bottom"),
          frame=FALSE, item.r=0))
    } else {
      tm_shape(g) + tm_fill("both_PC1", textNA="Insignificant",
        colorNA="gray95") + tm_borders() # Fig. 6
    }
  } else {
    plot(g["both_PC1"])
  }
}
if (run) {
  lc005_PC1 <- local_geary(w, g["PC1"], significance_cutoff=0.005,
    permutations=99999)
  g$lc005_PC1 <- factor(lisa_clusters(lc005_PC1), levels=0:4,
    labels=lisa_labels(lc005_PC1)[1:5])
  is.na(g$lc005_PC1) <- g$lc005_PC1 == "Not significant"
  g$lc005_PC1 <- droplevels(g$lc005_PC1)
  if (tmap_ok) {
    if (tmap4) {
      tm_shape(g) + tm_polygons(fill="lc005_PC1",
        fill.scale=tm_scale(values="brewer.set3", value.na="gray95",
          label.na="Insignificant"),
        fill.legend=tm_legend(position=tm_pos_in("left", "bottom"),
          frame=FALSE, item.r=0))
    } else {
      tm_shape(g) + tm_fill("lc005_PC1", textNA="Insignificant",
        colorNA="gray95") + tm_borders() # Fig. 7
    }
  } else {
    plot(g["lc005_PC1"])
}
if (run) {
  g$lc005_PC1_spdep <- attr(lc_PC1_spdep, "cluster")
  is.na(g$lc005_PC1_spdep) <- attr(lc_PC1_spdep, "pseudo-p")[,6] > 0.005
  g$lc005_PC1_spdep <- droplevels(g$lc005_PC1_spdep)
  if (tmap_ok) {
    if (tmap4) {
      tm_shape(g) + tm_polygons(fill="lc005_PC1_spdep",
        fill.scale=tm_scale(values="brewer.set3", value.na="gray95",
          label.na="Insignificant"),
        fill.legend=tm_legend(position=tm_pos_in("left", "bottom"),
          frame=FALSE, item.r=0))
    } else {
      tm_shape(g) + tm_fill("lc005_PC1_spdep", textNA="Insignificant",
        colorNA="gray95") + tm_borders() # rep. Fig. 7
    }
  } else {
    plot(g["lc005_PC1_spdep"])
  }
}
if (run) {
  lc001_PC1 <- local_geary(w, g["PC1"], significance_cutoff=0.001,
    permutations=99999)
  g$lc001_PC1 <- factor(lisa_clusters(lc001_PC1), levels=0:4,
    labels=lisa_labels(lc001_PC1)[1:5])
  is.na(g$lc001_PC1) <- g$lc001_PC1 == "Not significant"
  g$lc001_PC1 <- droplevels(g$lc001_PC1)
  if (tmap_ok) {
    if (tmap4) {
      tm_shape(g) + tm_polygons(fill="lc005_PC1",
        fill.scale=tm_scale(values="brewer.set3", value.na="gray95",
          label.na="Insignificant"),
        fill.legend=tm_legend(position=tm_pos_in("left", "bottom"),
          frame=FALSE, item.r=0))
    } else {
      tm_shape(g) + tm_fill("lc001_PC1", textNA="Insignificant",
        colorNA="gray95") + tm_borders() # Fig. 8
    }
  } else {
    plot(g["lc001_PC1"])
  }
}
if (run) {
  g$lc001_PC1_spdep <- attr(lc_PC1_spdep, "cluster")
  is.na(g$lc001_PC1_spdep) <- attr(lc_PC1_spdep, "pseudo-p")[,6] > 0.001
  g$lc001_PC1_spdep <- droplevels(g$lc001_PC1_spdep)
  if (tmap_ok) {
    if (tmap4) {
      tm_shape(g) + tm_polygons(fill="lc005_PC1_spdep",
        fill.scale=tm_scale(values="brewer.set3", value.na="gray95",
          label.na="Insignificant"),
        fill.legend=tm_legend(position=tm_pos_in("left", "bottom"),
          frame=FALSE, item.r=0))
    } else {
      tm_shape(g) + tm_fill("lc001_PC1_spdep", textNA="Insignificant",
        colorNA="gray95") + tm_borders() # rep. Fig. 8
    }
  } else {
    plot(g["lc001_PC1_spdep"])
  }
}
}
if (run) {
  lc_PC2 <- local_geary(w, g["PC2"], significance_cutoff=0.01,
    permutations=99999)
  g$lc_PC2 <- factor(lisa_clusters(lc_PC2), levels=0:4,
    labels=lisa_labels(lc_PC2)[1:5])
  is.na(g$lc_PC2) <- g$lc_PC2 == "Not significant"
  g$lc_PC2 <- droplevels(g$lc_PC2)
  if (tmap_ok) {
    if (tmap4) {
      tm_shape(g) + tm_polygons(fill="lc_PC2",
        fill.scale=tm_scale(values="brewer.set3", value.na="gray95",
          label.na="Insignificant"),
        fill.legend=tm_legend(position=tm_pos_in("left", "bottom"),
          frame=FALSE, item.r=0))
    } else {
      tm_shape(g) + tm_fill("lc_PC2", textNA="Insignificant",
        colorNA="gray95") + tm_borders() # Fig. 9
    }
  } else {
    plot(g["lc_PC2"])
  }
}
if (run) {
  lmc_PC <- local_multigeary(w, g[c("PC1","PC2")], significance_cutoff=0.00247,
    permutations=99999)
  g$lmc_PC <- factor(lisa_clusters(lmc_PC), levels=0:1,
    labels=lisa_labels(lmc_PC)[1:2])
  is.na(g$lmc_PC) <- g$lmc_PC == "Not significant"
  g$lmc_PC <- droplevels(g$lmc_PC)
  table(interaction((p.adjust(lisa_pvalues(lmc_PC), "fdr") < 0.01), g$lmc_PC))
}
if (run) {
  if (tmap_ok) {
    if (tmap4) {
      tm_shape(g) + tm_polygons(fill="lmc_PC",
        fill.scale=tm_scale(values="brewer.set3", value.na="gray95",
          label.na="Insignificant"),
        fill.legend=tm_legend(position=tm_pos_in("left", "bottom"),
          frame=FALSE, item.r=0))
    } else {
      tm_shape(g) + tm_fill("lmc_PC", textNA="Insignificant",
        colorNA="gray95") + tm_borders() # Fig. 10
    }
  } else {
    plot(g["lmc_PC"])
  }
}
if (run) {
  set.seed(1)
  lmc_PC_spdep <- localC_perm(g[c("PC1","PC2")], lw, nsim=9999, alternative="two.sided")
  all.equal(lisa_values(lmc_PC), c(lmc_PC_spdep))
}
if (run) {
  cor(attr(lmc_PC_spdep, "pseudo-p")[,6], lisa_pvalues(lmc_PC))
}
if (run) {
  g$lmc_PC_spdep <- attr(lmc_PC_spdep, "cluster")
  is.na(g$lmc_PC_spdep) <- p.adjust(attr(lmc_PC_spdep, "pseudo-p")[,6], "fdr") > 0.01
  g$lmc_PC_spdep <- droplevels(g$lmc_PC_spdep)
  if (tmap_ok) {
    if (tmap4) {
      tm_shape(g) + tm_polygons(fill="lmc_PC_spdep",
        fill.scale=tm_scale(values="brewer.set3", value.na="gray95",
          label.na="Insignificant"),
        fill.legend=tm_legend(position=tm_pos_in("left", "bottom"),
          frame=FALSE, item.r=0))
    } else {
      tm_shape(g) + tm_fill("lmc_PC_spdep", textNA="Insignificant",
        colorNA="gray95") + tm_borders() # rep. Fig. 10
    }
  } else {
    plot(g["lmc_PC_spdep"])
  }
}
if (run) {
  lmc_vars <- local_multigeary(w, st_drop_geometry(g)[, 1:6],
    significance_cutoff=0.00247, permutations=99999)
  g$lmc_vars <- factor(lisa_clusters(lmc_vars), levels=0:1,
    labels=lisa_labels(lmc_vars)[1:2])
  is.na(g$lmc_vars) <- g$lmc_vars == "Not significant"
  g$lmc_vars <- droplevels(g$lmc_vars)
  table(interaction((p.adjust(lisa_pvalues(lmc_vars), "fdr") < 0.01),
    g$lmc_vars))
}
if (run) {
  if (tmap_ok) {
    if (tmap4) {
      tm_shape(g) + tm_polygons(fill="lmc_vars",
        fill.scale=tm_scale(values="brewer.set3", value.na="gray95",
          label.na="Insignificant"),
        fill.legend=tm_legend(position=tm_pos_in("left", "bottom"),
          frame=FALSE, item.r=0))
    } else {
      tm_shape(g) + tm_fill("lmc_vars", textNA="Insignificant",
        colorNA="gray95") + tm_borders() # Fig. 11
    }
  } else {
    plot(g["lmc_vars"])
  }
}
if (run) {
  set.seed(1)
  system.time(lmc_vars_spdep <- localC_perm(st_drop_geometry(g)[, 1:6], lw,
    nsim=9999, alternative="two.sided"))
}
if (run) {
  all.equal(lisa_values(lmc_vars), c(lmc_vars_spdep))
}
if (run) {
  cor(attr(lmc_vars_spdep, "pseudo-p")[,6], lisa_pvalues(lmc_vars))
}
if (run) {
  if (require(parallel, quietly=TRUE)) {
    ncpus <- max(2L, detectCores(logical=FALSE), na.rm = TRUE)-1L
# test with single core
    if (ncpus > 1L) ncpus <- 1L
    cores <- get.coresOption()
    set.coresOption(ncpus)
    system.time(lmc_vars_spdep1 <- localC_perm(st_drop_geometry(g)[, 1:6], lw,
      nsim=9999, alternative="two.sided", iseed=1))
    set.coresOption(cores)
  }
}
if (run) {
  all.equal(lisa_values(lmc_vars), c(lmc_vars_spdep1))
}
if (run) {
  cor(attr(lmc_vars_spdep1, "pseudo-p")[,6], lisa_pvalues(lmc_vars))
}
if (run) {
  g$lmc_vars_spdep <- attr(lmc_vars_spdep1, "cluster")
  is.na(g$lmc_vars_spdep) <- p.adjust(attr(lmc_vars_spdep1, "pseudo-p")[,6], "fdr") > 0.01
  g$lmc_vars_spdep <- droplevels(g$lmc_vars_spdep)
  if (tmap_ok) {
    if (tmap4) {
      tm_shape(g) + tm_polygons(fill="lmc_vars_spdep",
        fill.scale=tm_scale(values="brewer.set3", value.na="gray95",
          label.na="Insignificant"),
        fill.legend=tm_legend(position=tm_pos_in("left", "bottom"),
          frame=FALSE, item.r=0))
    } else {
      tm_shape(g) + tm_fill("lmc_vars_spdep", textNA="Insignificant",
        colorNA="gray95") + tm_borders() # rep. Fig. 11
    }
  } else {
    plot(g["lmc_vars_spdep"])
  }
}


## Not run: 
library(reticulate)
use_python("/usr/bin/python", required = TRUE)
gp <- import("geopandas")
ps <- import("libpysal")
W <- listw2mat(listw)
w <- ps$weights$full2W(W, rownames(W))
w$transform <- "R"
esda <- import("esda")
lM <- esda$Moran_Local(x, w)
all.equal(unname(localmoran(x, listw, mlvar=FALSE)[,1]), c(lM$Is))
# confirm x and w the same
lC <- esda$Geary_Local(connectivity=w)$fit(scale(x))
# np$std missing ddof=1
n <- length(x)
D0 <- spdep:::geary.intern((x - mean(x)) / sqrt(var(x)*(n-1)/n), listw, n=n)
# lC components probably wrongly ordered https://github.com/pysal/esda/issues/192
o <- match(round(D0, 6), round(lC$localG, 6))
all.equal(c(lC$localG)[o], D0)
# simulation order not retained
lC$p_sim[o]
attr(C, "pseudo-p")[,6]

## End(Not run)

G and Gstar local spatial statistics

Description

The local spatial statistic G is calculated for each zone based on the spatial weights object used. The value returned is a Z-value, and may be used as a diagnostic tool. High positive values indicate the posibility of a local cluster of high values of the variable being analysed, very low relative values a similar cluster of low values. For inference, a Bonferroni-type test is suggested in the references, where tables of critical values may be found (see also details below).

Usage

localG(x, listw, zero.policy=attr(listw, "zero.policy"), spChk=NULL, GeoDa=FALSE,
 alternative = "two.sided", return_internals=TRUE)
localG_perm(x, listw, nsim=499, zero.policy=attr(listw, "zero.policy"), spChk=NULL,
 alternative = "two.sided", iseed=NULL, fix_i_in_Gstar_permutations=TRUE,
 no_repeat_in_row=FALSE)

Arguments

Details

If the neighbours member of listw has a "self.included" attribute set to TRUE, the Gstar variant, including the self-weight w_{ii} > 0, is calculated and returned. The returned vector will have a "gstari" attribute set to TRUE. Self-weights must be included by using the include.self function before converting the neighbour list to a spatial weights list with nb2listw as shown below in the example.

The critical values of the statistic under assumptions given in the references for the 95th percentile are for n=1: 1.645, n=50: 3.083, n=100: 3.289, n=1000: 3.886.

Value

A vector of G or Gstar standard deviate values, with attributes "gstari" set to TRUE or FALSE, "call" set to the function call, and class "localG". For conditional permutation, the returned value is the same as for localG(), and the simulated standard deviate is returned as column "StdDev.Gi" in attr(., "internals").

Note

Conditional permutations added for comparative purposes; permutations are over the whole data vector omitting the observation itself, and from 1.2-8 fixing the observation itself as its own neighbour for local G-star.

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

Ord, J. K. and Getis, A. 1995 Local spatial autocorrelation statistics: distributional issues and an application. Geographical Analysis, 27, 286–306; Getis, A. and Ord, J. K. 1996 Local spatial statistics: an overview. In P. Longley and M. Batty (eds) Spatial analysis: modelling in a GIS environment (Cambridge: Geoinformation International), 261–277; Bivand RS, Wong DWS 2018 Comparing implementations of global and local indicators of spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x

Examples

data(getisord, package="spData")
# spData 0.3.2 changes x, y, xyz object names to go_x, go_y, go_xyz to
# avoid putting these objects into the global environment via lazy loading
if (exists("go_xyz") && packageVersion("spData") >= "0.3.2") {
  xyz <- go_xyz
  x <- go_x
  y <- go_y
}
xycoords <- cbind(xyz$x, xyz$y)
nb30 <- dnearneigh(xycoords, 0, 30)
G30 <- localG(xyz$val, nb2listw(nb30, style="B"))
G30[length(xyz$val)-136]
set.seed(1)
G30_sim <- localG_perm(xyz$val, nb2listw(nb30, style="B"))
G30_sim[length(xyz$val)-136]
nb60 <- dnearneigh(xycoords, 0, 60)
G60 <- localG(xyz$val, nb2listw(nb60, style="B"))
G60[length(xyz$val)-136]
nb90 <- dnearneigh(xycoords, 0, 90)
G90 <- localG(xyz$val, nb2listw(nb90, style="B"))
G90[length(xyz$val)-136]
nb120 <- dnearneigh(xycoords, 0, 120)
G120 <- localG(xyz$val, nb2listw(nb120, style="B"))
G120[length(xyz$val)-136]
nb150 <- dnearneigh(xycoords, 0, 150)
G150 <- localG(xyz$val, nb2listw(nb150, style="B"))
G150[length(xyz$val)-136]
brks <- seq(-5,5,1)
cm.col <- cm.colors(length(brks)-1)
image(x, y, t(matrix(G30, nrow=16, ncol=16, byrow=TRUE)),
  breaks=brks, col=cm.col, asp=1)
text(xyz$x, xyz$y, round(G30, digits=1), cex=0.7)
polygon(c(195,225,225,195), c(195,195,225,225), lwd=2)
title(main=expression(paste("Values of the ", G[i], " statistic")))
G30s <- localG(xyz$val, nb2listw(include.self(nb30),
 style="B"))
cat("value according to Getis and Ord's eq. 14.2, p. 263 (1996)\n")
G30s[length(xyz$val)-136]
cat(paste("value given by Getis and Ord (1996), p. 267",
  "(division by n-1 rather than n \n in variance)\n"))
G30s[length(xyz$val)-136] *
  (sqrt(sum(scale(xyz$val, scale=FALSE)^2)/length(xyz$val)) /
  sqrt(var(xyz$val)))
image(x, y, t(matrix(G30s, nrow=16, ncol=16, byrow=TRUE)),
  breaks=brks, col=cm.col, asp=1)
text(xyz$x, xyz$y, round(G30s, digits=1), cex=0.7)
polygon(c(195,225,225,195), c(195,195,225,225), lwd=2)
title(main=expression(paste("Values of the ", G[i]^"*", " statistic")))

A local hotspot statistic for analysing multiscale datasets

Description

The function implements the GS_i test statistic for local hotspots on specific pairwise evaluated distance bands, as proposed by Westerholt et al. (2015). Like the hotspot estimator G_i^*, the GS_i statistic is given as z-scores that can be evaluated accordingly. The idea of the method is to identify hotspots in datasets that comprise several, difficult-to-separate processes operating at different scales. This is often the case in complex user-generated datasets such as those from Twitter feeds. For example, a football match could be reflected in tweets from pubs, homes, and the stadium vicinity. These exemplified phenomena represent different processes that may be detected at different geometric scales. The GS_i method enables this identification by specifying a geometric scale band and strictly calculating all statistical quantities such as mean and variance solely from respective relevant observations that interact on the range of the adjusted scale band. In addition, in each neighbourhood not only the relationships to the respective central unit, but all scale-relevant relationships are considered. In this way, hotspots can be detected on specific scale ranges independently of other scales. The statistic is given as:

GS_i = \frac{\displaystyle\sum_{j; k < j}{w_{ij}w_{ik}\phi_{jk}a_{jk}} - \frac{W_i}{\Phi} \displaystyle\sum_{j; k < j}{\phi_{jk}a_{jk}}}{\sqrt{\frac{W_i}{\Phi}\displaystyle\sum_{j; k < j}{\phi_{jk}a_{jk}^2} + \frac{W_i\left(W_i-1\right)}{\Phi\left(\Phi-1\right)}\left(\Gamma^2 -\!\! \displaystyle\sum_{j; k < j}{\left(\phi_{jk}a_{jk}\right)^2}\right) - \left(\frac{W_i}{\Phi}\displaystyle\sum_{j; k < j}{\phi_{jk}a_{jk}}\right)^2}}

with

a_{jk} = x_j + x_k,\;\;\; W_i = \displaystyle\sum_{j; k < j}{w_{ij}w_{ik}\phi_{jk}},\;\;\; \Phi = \displaystyle\sum_{j; k < j}{\phi_{jk}},\;\;\; \textrm{and} \;\;\; \Gamma = \displaystyle\sum_{j; k < j}{\phi_{jk}a_{jk}}.

Usage

localGS(x, listw, dmin, dmax, attr, longlat = NULL)

Arguments

Details

Only pairs of observations with a shared distance (in map units) on the interval [dmin, dmax] that are within a maximum radius of dmax around a corresponding output observation are considered. Thereby, also the mean values and variance terms estimated within the measure are adjusted to the scale range under consideration. For application examples of the method see Westerholt et al. (2015) (applied to tweets) and Sonea & Westerholt (2021) (applied in an access to banking scenario).

Value

A vector of GS_i values that are given as z-scores.

Author(s)

René Westerholt rene.westerholt@tu-dortmund.de

References

Westerholt, R., Resch, B. & Zipf, A. 2015. A local scale-sensitive indicator of spatial autocorrelation for assessing high-and low-value clusters in multiscale datasets. International Journal of Geographical Information Science, 29(5), 868–887, doi:10.1080/13658816.2014.1002499.

Sonea, A. and Westerholt, R. (2021): Geographic and temporal access to basic banking services in Wales. Applied Spatial Analysis and Policy, 14 (4), 879–905, doi:10.1007/s12061-021-09386-3.

See Also

localG

Examples

boston.tr <- sf::st_read(system.file("shapes/boston_tracts.gpkg", package="spData")[1])
boston.tr_utm <- st_transform(boston.tr, 32619) #26786

boston_listw1 <- nb2listwdist(dnearneigh(st_centroid(boston.tr_utm), 1, 2000),
    boston.tr_utm, type = "dpd", alpha = 2, zero.policy = TRUE, dmax = 9500)

boston_listw2 <- nb2listwdist(dnearneigh(st_centroid(boston.tr_utm), 5000, 9500), 
    boston.tr_utm, type = "dpd", alpha = 2, zero.policy = TRUE, dmax = 9500)

boston_RM_gsi_1 <- localGS(boston.tr_utm, boston_listw1, 1, 2000, "RM", FALSE)
boston_RM_gsi_2 <- localGS(boston.tr_utm, boston_listw2, 2000, 9500, "RM", FALSE)

Local Moran's I statistic

Description

The local spatial statistic Moran's I is calculated for each zone based on the spatial weights object used. The values returned include a Z-value, and may be used as a diagnostic tool. The statistic is:

I_i = \frac{(x_i-\bar{x})}{{\sum_{k=1}^{n}(x_k-\bar{x})^2}/(n-1)}{\sum_{j=1}^{n}w_{ij}(x_j-\bar{x})}

, and its expectation and variance were given in Anselin (1995), but those from Sokal et al. (1998) are implemented here.

Usage

localmoran(x, listw, zero.policy=attr(listw, "zero.policy"), na.action=na.fail,
        conditional=TRUE, alternative = "two.sided", mlvar=TRUE,
        spChk=NULL, adjust.x=FALSE)
localmoran_perm(x, listw, nsim=499, zero.policy=attr(listw, "zero.policy"), 
        na.action=na.fail, alternative = "two.sided", mlvar=TRUE,
        spChk=NULL, adjust.x=FALSE, sample_Ei=TRUE, iseed=NULL,
        no_repeat_in_row=FALSE)

Arguments

Details

The values of local Moran's I are divided by the variance (or sample variance) of the variable of interest to accord with Table 1, p. 103, and formula (12), p. 99, in Anselin (1995), rather than his formula (7), p. 98. The variance of the local Moran statistic is taken from Sokal et al. (1998) p. 334, equations 4 & 5 or equations 7 & 8 located depending on user specification. By default, the implementation divides by n, not (n-1) in calculating the variance and higher moments. Conditional code contributed by Jeff Sauer and Levi Wolf.

Value

In addition, an attribute data frame "quadr" with mean and median quadrant columns, and a column splitting on the demeaned variable and lagged demeaned variable at zero.

Note

Conditional permutations added for comparative purposes; permutations are over the whole data vector omitting the observation itself. For p-value adjustment, use p.adjust() or p.adjustSP() on the output vector.

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

Anselin, L. 1995. Local indicators of spatial association, Geographical Analysis, 27, 93–115; Getis, A. and Ord, J. K. 1996 Local spatial statistics: an overview. In P. Longley and M. Batty (eds) Spatial analysis: modelling in a GIS environment (Cambridge: Geoinformation International), 261–277; Sokal, R. R, Oden, N. L. and Thomson, B. A. 1998. Local Spatial Autocorrelation in a Biological Model. Geographical Analysis, 30. 331–354; Bivand RS, Wong DWS 2018 Comparing implementations of global and local indicators of spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x; Sauer, J., Oshan, T. M., Rey, S., & Wolf, L. J. 2021. The Importance of Null Hypotheses: Understanding Differences in Local Moran’s under Heteroskedasticity. Geographical Analysis. doi:10.1111/gean.12304

Bivand, R. (2022), R Packages for Analyzing Spatial Data: A Comparative Case Study with Areal Data. Geographical Analysis, 54(3), 488-518. doi:10.1111/gean.12319

See Also

localG

Examples

data(afcon, package="spData")
oid <- order(afcon$id)
resI <- localmoran(afcon$totcon, nb2listw(paper.nb))
printCoefmat(data.frame(resI[oid,], row.names=afcon$name[oid]),
 check.names=FALSE)
hist(resI[,5])
mean(resI[,1])
sum(resI[,1])/Szero(nb2listw(paper.nb))
moran.test(afcon$totcon, nb2listw(paper.nb))
# note equality for mean() only when the sum of weights equals
# the number of observations (thanks to Juergen Symanzik)
resI <- localmoran(afcon$totcon, nb2listw(paper.nb))
printCoefmat(data.frame(resI[oid,], row.names=afcon$name[oid]),
 check.names=FALSE)
hist(p.adjust(resI[,5], method="bonferroni"))
totcon <-afcon$totcon
is.na(totcon) <- sample(1:length(totcon), 5)
totcon
resI.na <- localmoran(totcon, nb2listw(paper.nb), na.action=na.exclude,
 zero.policy=TRUE)
if (class(attr(resI.na, "na.action")) == "exclude") {
 print(data.frame(resI.na[oid,], row.names=afcon$name[oid]), digits=2)
} else print(resI.na, digits=2)
resG <- localG(afcon$totcon, nb2listw(include.self(paper.nb)))
print(data.frame(resG[oid], row.names=afcon$name[oid]), digits=2)
set.seed(1)
resI_p <- localmoran_perm(afcon$totcon, nb2listw(paper.nb))
printCoefmat(data.frame(resI_p[oid,], row.names=afcon$name[oid]),
 check.names=FALSE)

Compute the Local Bivariate Moran's I Statistic

Description

Given two continuous numeric variables, calculate the bivariate Local Moran's I.

Usage

localmoran_bv(x, y, listw, nsim = 199, scale = TRUE, alternative="two.sided",
 iseed=1L, no_repeat_in_row=FALSE, zero.policy=attr(listw, "zero.policy"))

Arguments

Details

The Bivariate Local Moran, like its global counterpart, evaluates the value of x at observation i with its spatial neighbors' value of y. The value of I_i^B is xi * Wyi. Or, in simpler words, the local bivariate Moran is the result of multiplying x by the spatial lag of y. Formally it is defined as

I_i^B= cx_i\Sigma_j{w_{ij}y_j}

Value

a data.frame containing two columns Ib and p_sim containing the local bivariate Moran's I and simulated p-values respectively.

Author(s)

Josiah Parry josiah.parry@gmail.com

References

Anselin, Luc, Ibnu Syabri, and Oleg Smirnov. 2002. “Visualizing Multivariate Spatial Correlation with Dynamically Linked Windows.” In New Tools for Spatial Data Analysis: Proceedings of the Specialist Meeting, edited by Luc Anselin and Sergio Rey. University of California, Santa Barbara: Center for Spatially Integrated Social Science (CSISS).

Examples

# load columbus datay
columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData"))
nb <- poly2nb(columbus)
listw <- nb2listw(nb)
set.seed(1)
(res <- localmoran_bv(columbus$CRIME, columbus$INC, listw, nsim = 499))
columbus$hs <- hotspot(res, Prname="Pr(folded) Sim", cutoff=0.05,
 quadrant.type="pysal", p.adjust="none")

if (require("tmap", quietly=TRUE)) {
tmap4 <- packageVersion("tmap") >= "3.99"
if (tmap4) {
  tm_shape(columbus) + tm_polygons(fill="hs",
    fill.scale=tm_scale(values="brewer.set3"),
    fill.legend=tm_legend(position=tm_pos_in("left", "top"),
      frame=FALSE, item.r=0), lwd=0.01)
} else {
  tm_shape(columbus) + tm_fill("hs")
}
}

moran.plot(x=columbus$CRIME, y=columbus$INC, listw=listw)

Exact local Moran's Ii tests

Description

localmoran.exact provides exact local Moran's Ii tests under the null hypothesis, while localmoran.exact.alt provides exact local Moran's Ii tests under the alternative hypothesis. In this case, the model may be a fitted model derived from a model fitted by spatialreg::errorsarlm, with the covariance matrix can be passed through the Omega= argument.

Usage

localmoran.exact(model, select, nb, glist = NULL, style = "W", 
 zero.policy = NULL, alternative = "two.sided", spChk = NULL, 
 resfun = weighted.residuals, save.Vi = FALSE, useTP=FALSE, truncErr=1e-6, 
 zeroTreat=0.1)
localmoran.exact.alt(model, select, nb, glist = NULL, style = "W",
 zero.policy = NULL, alternative = "two.sided", spChk = NULL,
 resfun = weighted.residuals, Omega = NULL, save.Vi = FALSE,
 save.M = FALSE, useTP=FALSE, truncErr=1e-6, zeroTreat=0.1)
## S3 method for class 'localmoranex'
print(x, ...)
## S3 method for class 'localmoranex'
as.data.frame(x, row.names=NULL, optional=FALSE, ...)

Arguments

Value

A list with class localmoranex containing "select" lists, each with class moranex with the following components:

When the alternative is being tested, a list of left and right M products in attribute M.

Author(s)

Markus Reder and Roger Bivand

References

Bivand RS, Müller W, Reder M (2009) Power calculations for global and local Moran’s I. Comput Stat Data Anal 53:2859–2872; Bivand RS, Wong DWS 2018 Comparing implementations of global and local indicators of spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x

See Also

lm.morantest.exact, localmoran.sad

Examples

eire <- st_read(system.file("shapes/eire.gpkg", package="spData")[1])
row.names(eire) <- as.character(eire$names)
eire.nb <- poly2nb(eire)
e.lm <- lm(OWNCONS ~ ROADACC, data=eire)
localmoran.sad(e.lm, nb=eire.nb)
localmoran.exact(e.lm, nb=eire.nb)
localmoran.exact(e.lm, nb=eire.nb, useTP=TRUE)
run <- FALSE
if (requireNamespace("spatialreg", quietly=TRUE)) run <- TRUE
if (run) {
e.errorsar <- spatialreg::errorsarlm(OWNCONS ~ ROADACC, data=eire,
 listw=nb2listw(eire.nb))
lm.target <- lm(e.errorsar$tary ~ e.errorsar$tarX - 1)
localmoran.exact.alt(lm.target, nb=eire.nb)
}
if (run) {
Omega <- spatialreg::invIrW(nb2listw(eire.nb), rho=e.errorsar$lambda)
Omega1 <- tcrossprod(Omega)
localmoran.exact.alt(lm.target, nb=eire.nb, Omega=Omega1)
}
if (run) {
localmoran.exact.alt(lm.target, nb=eire.nb, Omega=Omega1, useTP=TRUE)
}

Saddlepoint approximation of local Moran's Ii tests

Description

The function implements Tiefelsdorf's application of the Saddlepoint approximation to local Moran's Ii's reference distribution. If the model object is of class "lm", global independence is assumed; if of class "sarlm", global dependence is assumed to be represented by the spatial parameter of that model. Tests are reported separately for each zone selected, and may be summarised using summary.localmoransad. Values of local Moran's Ii agree with those from localmoran(), but in that function, the standard deviate - here the Saddlepoint approximation - is based on the randomisation assumption.

Usage

localmoran.sad(model, select, nb, glist=NULL, style="W",
 zero.policy=NULL, alternative="two.sided", spChk=NULL,
 resfun=weighted.residuals, save.Vi=FALSE,
 tol = .Machine$double.eps^0.5, maxiter = 1000, tol.bounds=0.0001,
 save.M=FALSE, Omega = NULL)
## S3 method for class 'localmoransad'
print(x, ...)
## S3 method for class 'localmoransad'
summary(object, ...)
## S3 method for class 'summary.localmoransad'
print(x, ...)
listw2star(listw, ireg, style, n, D, a, zero.policy=attr(listw, "zero.policy"))

Arguments

Details

The function implements the analytical eigenvalue calculation together with trace shortcuts given or suggested in Tiefelsdorf (2002), partly following remarks by J. Keith Ord, and uses the Saddlepoint analytical solution from Tiefelsdorf's SPSS code.

If a histogram of the probability values of the saddlepoint estimate for the assumption of global independence is not approximately flat, the assumption is probably unjustified, and re-estimation with global dependence is recommended.

No n by n matrices are needed at any point for the test assuming no global dependence, the star-shaped weights matrices being handled as listw lists. When the test is made on residuals from a spatial regression, taking a global process into account. n by n matrices are necessary, and memory constraints may be reached for large lattices.

Value

A list with class localmoransad containing "select" lists, each with class moransad with the following components:

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

Tiefelsdorf, M. 2002 The Saddlepoint approximation of Moran's I and local Moran's Ii reference distributions and their numerical evaluation. Geographical Analysis, 34, pp. 187–206.

See Also

localmoran, lm.morantest, lm.morantest.sad, errorsarlm

Examples

eire <- st_read(system.file("shapes/eire.gpkg", package="spData")[1])
row.names(eire) <- as.character(eire$names)
eire.nb <- poly2nb(eire)
lw <- nb2listw(eire.nb)
e.lm <- lm(OWNCONS ~ ROADACC, data=eire)
e.locmor <- summary(localmoran.sad(e.lm, nb=eire.nb))
e.locmor
mean(e.locmor[,1])
sum(e.locmor[,1])/Szero(lw)
lm.morantest(e.lm, lw)
# note equality for mean() only when the sum of weights equals
# the number of observations (thanks to Juergen Symanzik)
hist(e.locmor[,"Pr. (Sad)"])
e.wlm <- lm(OWNCONS ~ ROADACC, data=eire, weights=RETSALE)
e.locmorw1 <- summary(localmoran.sad(e.wlm, nb=eire.nb, resfun=weighted.residuals))
e.locmorw1
e.locmorw2 <- summary(localmoran.sad(e.wlm, nb=eire.nb, resfun=rstudent))
e.locmorw2
run <- FALSE
if (requireNamespace("spatialreg", quietly=TRUE)) run <- TRUE
if (run) {
e.errorsar <- spatialreg::errorsarlm(OWNCONS ~ ROADACC, data=eire,
  listw=lw)
if (packageVersion("spatialreg") < "1.1.7")
  spatialreg::print.sarlm(e.errorsar)
else
  print(e.errorsar)
}
if (run) {
lm.target <- lm(e.errorsar$tary ~ e.errorsar$tarX - 1)
Omega <- tcrossprod(spatialreg::invIrW(lw, rho=e.errorsar$lambda))
e.clocmor <- summary(localmoran.sad(lm.target, nb=eire.nb, Omega=Omega))
e.clocmor
}
if (run) {
hist(e.clocmor[,"Pr. (Sad)"])
}

Local spatial heteroscedasticity

Description

Local spatial heteroscedasticity is calculated for each location based on the spatial weights object used. The statistic is:

H_i = \frac{\sum_j^n w_{ij} \cdot |e_j|^a}{h_1 \cdot \sum_j^n w_{ij}}

with

e_j = x_j - \bar{x}_j

and

\bar{x}_j = \frac{\sum_k^n w_{jk} \cdot x_k}{\sum_k^n w_{jk}}

Its expectation and variance are given in Ord & Getis (2012). The exponent a allows for investigating different types of mean dispersal.

Usage

  LOSH(x, listw, a=2, var_hi=TRUE, zero.policy=attr(listw, "zero.policy"),
 na.action=na.fail, spChk=NULL)

Arguments

Details

In addition to the LOSH measure, the values returned include local spatially weighted mean values \bar{x}_i and local residuals e_i estimated about these means. These values facilitate the interpretation of LOSH values. Further, if specified through var_hi, the statistical moments and the test statistics as proposed by Ord & Getis (2012) are also calculated and returned.

Value

Author(s)

René Westerholt rene.westerholt@tu-dortmund.de

References

Ord, J. K., & Getis, A. 2012. Local spatial heteroscedasticity (LOSH), The Annals of Regional Science, 48 (2), 529–539.

See Also

LOSH.cs, LOSH.mc

Examples

    data(boston, package="spData")
    resLOSH <- LOSH(boston.c$NOX, nb2listw(boston.soi))
    hist(resLOSH[,"Hi"])
    mean(resLOSH[,"Hi"])
  

Chi-square based test for local spatial heteroscedasticity

Description

The function implements the chi-square based test statistic for local spatial heteroscedasticity (LOSH) as proposed by Ord & Getis (2012).

Usage

LOSH.cs(x, listw, zero.policy = attr(listw, "zero.policy"), na.action = na.fail, 
                 p.adjust.method = "none", spChk = NULL)

Arguments

Details

The test uses a = 2 (see LOSH) because chi-square based inference is not applicable with other exponents. The function makes use of LOSH in its calculations.

Value

Author(s)

René Westerholt rene.westerholt@tu-dortmund.de

References

Ord, J. K., & Getis, A. 2012. Local spatial heteroscedasticity (LOSH), The Annals of Regional Science, 48 (2), 529–539.

See Also

LOSH, LOSH.mc

Examples

    data(boston, package="spData")
    resLOSH <- LOSH.cs(boston.c$NOX, nb2listw(boston.soi))
    hist(resLOSH[,"Hi"])
    mean(resLOSH[,"Hi"])

Bootstrapping-based test for local spatial heteroscedasticity

Description

The function draws inferences about local spatial heteroscedasticity (LOSH) by means of the randomisation-based Monte-Carlo bootstrap proposed by Xu et al. (2014).

Usage

LOSH.mc(x, listw, a = 2, nsim = 99, zero.policy = attr(listw, "zero.policy"),
 na.action = na.fail, spChk = NULL, adjust.n = TRUE, p.adjust.method = "none")

Arguments

Details

The test calculates LOSH (see LOSH) and estimates pseudo p-values from a conditional bootstrap. Thereby, the i-th value in each location is held fixed, whereas all other values are permuted nsim times over all other spatial units.

Value

Author(s)

René Westerholt rene.westerholt@tu-dortmund.de

References

Ord, J. K., & Getis, A. 2012. Local spatial heteroscedasticity (LOSH), The Annals of Regional Science, 48 (2), 529–539; Xu, M., Mei, C. L., & Yan, N. 2014. A note on the null distribution of the local spatial heteroscedasticity (LOSH) statistic. The Annals of Regional Science, 52 (3), 697–710.

See Also

LOSH, LOSH.mc

Examples

    data(columbus, package="spData")
    resLOSH_mc <- LOSH.mc(columbus$CRIME, nb2listw(col.gal.nb), 2, 100)
    summary(resLOSH_mc)
    resLOSH_cs <- LOSH.cs(columbus$CRIME, nb2listw(col.gal.nb))
    summary(resLOSH_cs)
    plot(resLOSH_mc[,"Pr()"], resLOSH_cs[,"Pr()"])

Convert a square spatial weights matrix to a weights list object

Description

The function converts a square spatial weights matrix, optionally a sparse matrix to a weights list object, optionally adding region IDs from the row names of the matrix, as a sequence of numbers 1:nrow(x), or as given as an argument. The style can be imposed by rebuilting the weights list object internally.

Usage

mat2listw(x, row.names = NULL, style=NULL, zero.policy = NULL)

Arguments

Value

A listw object with the following members:

Author(s)

Roger Bivand Roger.Bivand@nhh.no

See Also

nb2listw, nb2mat

Examples

columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
col005 <- dnearneigh(st_coordinates(st_centroid(st_geometry(columbus),
 of_largest_polygon=TRUE)), 0, 0.5, as.character(columbus$NEIGNO))
summary(col005)
col005.w.mat <- nb2mat(col005, style="W", zero.policy=TRUE)
try(col005.w.b <- mat2listw(col005.w.mat, style="W"))
col005.w.b <- mat2listw(col005.w.mat, style="W", zero.policy=TRUE)
summary(col005.w.b$neighbours)
diffnb(col005, col005.w.b$neighbours)
col005.w.mat.3T <- kronecker(diag(3), col005.w.mat)
col005.w.b.3T <- mat2listw(col005.w.mat.3T, style="W", zero.policy=TRUE)
summary(col005.w.b.3T$neighbours)
run <- FALSE
if (require("spatialreg", quiet=TRUE)) run <- TRUE
if (run) {
W <- as(nb2listw(col005, style="W", zero.policy=TRUE), "CsparseMatrix")
try(col005.spM <- mat2listw(W))
col005.spM <- mat2listw(W, style="W", zero.policy=TRUE)
summary(col005.spM$neighbours)
}
if (run) {
diffnb(col005, col005.spM$neighbours)
}
if (run && require("Matrix", quiet=TRUE)) {
IW <- kronecker(Diagonal(3), W)
col005.spM.3T <- mat2listw(as(IW, "CsparseMatrix"), style="W", zero.policy=TRUE)
summary(col005.spM.3T$neighbours)
}

Compute Moran's I

Description

A simple function to compute Moran's I, called by moran.test and moran.mc;

I = \frac{n}{\sum_{i=1}^{n}\sum_{j=1}^{n}w_{ij}} \frac{\sum_{i=1}^{n}\sum_{j=1}^{n}w_{ij}(x_i-\bar{x})(x_j-\bar{x})}{\sum_{i=1}^{n}(x_i - \bar{x})^2}

Usage

moran(x, listw, n, S0, zero.policy=attr(listw, "zero.policy"), NAOK=FALSE)

Arguments

Value

a list of

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 17.

See Also

moran.test, moran.mc

Examples

data(oldcol)
col.W <- nb2listw(COL.nb, style="W")
crime <- COL.OLD$CRIME
str(moran(crime, col.W, length(COL.nb), Szero(col.W)))
is.na(crime) <- sample(1:length(crime), 10)
str(moran(crime, col.W, length(COL.nb), Szero(col.W), NAOK=TRUE))

Compute the Global Bivariate Moran's I

Description

Given two continuous numeric variables, calculate the bivariate Moran's I. See details for more.

Usage

moran_bv(x, y, listw, nsim = 499, scale = TRUE)

Arguments

Details

The Global Bivariate Moran is defined as

I_B = \frac{\Sigma_i(\Sigma_j{w_{ij}y_j\times x_i})}{\Sigma_i{x_i^2}}

It is important to note that this is a measure of autocorrelation of X with the spatial lag of Y. As such, the resultant measure may overestimate the amount of spatial autocorrelation which may be a product of the inherent correlation of X and Y. The output object is of class "boot", so that plots and confidence intervals are available using appropriate methods.

Value

An object of class "boot", with the observed statistic in component t0.

Author(s)

Josiah Parry josiah.parry@gmail.com

References

Wartenberg, D. (1985), Multivariate Spatial Correlation: A Method for Exploratory Geographical Analysis. Geographical Analysis, 17: 263-283. doi:10.1111/j.1538-4632.1985.tb00849.x

Examples

data(boston, package = "spData")
x <- boston.c$CRIM
y <- boston.c$NOX
listw <- nb2listw(boston.soi)
set.seed(1)
res_xy <- moran_bv(x, y, listw, nsim=499)
res_xy$t0
boot::boot.ci(res_xy, conf=c(0.99, 0.95, 0.9), type="basic")
plot(res_xy)
set.seed(1)
lee_xy <- lee.mc(x, y, listw, nsim=499, return_boot=TRUE)
lee_xy$t0
boot::boot.ci(lee_xy, conf=c(0.99, 0.95, 0.9), type="basic")
plot(lee_xy)
set.seed(1)
res_yx <- moran_bv(y, x, listw, nsim=499)
res_yx$t0
boot::boot.ci(res_yx, conf=c(0.99, 0.95, 0.9), type="basic")
plot(res_yx)
set.seed(1)
lee_yx <- lee.mc(y, x, listw, nsim=499, return_boot=TRUE)
lee_yx$t0
boot::boot.ci(lee_yx, conf=c(0.99, 0.95, 0.9), type="basic")
plot(lee_yx)

Permutation test for Moran's I statistic

Description

A permutation test for Moran's I statistic calculated by using nsim random permutations of x for the given spatial weighting scheme, to establish the rank of the observed statistic in relation to the nsim simulated values.

Usage

moran.mc(x, listw, nsim, zero.policy=attr(listw, "zero.policy"),
 alternative="greater", na.action=na.fail, spChk=NULL, return_boot=FALSE,
 adjust.n=TRUE)

Arguments

Value

A list with class htest and mc.sim containing the following components:

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 63-5.

See Also

moran, moran.test

Examples

data(oldcol)
colw <- nb2listw(COL.nb, style="W")
nsim <- 99
set.seed(1234)
sim1 <- moran.mc(COL.OLD$CRIME, listw=colw, nsim=nsim)
sim1
mean(sim1$res[1:nsim])
var(sim1$res[1:nsim])
summary(sim1$res[1:nsim])
colold.lags <- nblag(COL.nb, 3)
set.seed(1234)
sim2 <- moran.mc(COL.OLD$CRIME, nb2listw(colold.lags[[2]],
 style="W"), nsim=nsim)
summary(sim2$res[1:nsim])
sim3 <- moran.mc(COL.OLD$CRIME, nb2listw(colold.lags[[3]],
 style="W"), nsim=nsim)
summary(sim3$res[1:nsim])
crime <- COL.OLD$CRIME
is.na(crime) <- sample(1:length(crime), 10)
try(moran.mc(crime, nb2listw(COL.nb, style="W"), nsim=99,
 na.action=na.fail))
moran.mc(crime, nb2listw(COL.nb, style="W"), nsim=99, zero.policy=TRUE,
 na.action=na.omit)
moran.mc(crime, nb2listw(COL.nb, style="W"), nsim=99, zero.policy=TRUE,
 return_boot=TRUE, na.action=na.omit)
moran.mc(crime, nb2listw(COL.nb, style="W"), nsim=99, zero.policy=TRUE,
 na.action=na.exclude)
moran.mc(crime, nb2listw(COL.nb, style="W"), nsim=99, zero.policy=TRUE,
 return_boot=TRUE, na.action=na.exclude)
try(moran.mc(crime, nb2listw(COL.nb, style="W"), nsim=99, na.action=na.pass))

Moran scatterplot

Description

A plot of spatial data against its spatially lagged values, augmented by reporting the summary of influence measures for the linear relationship between the data and the lag. If zero policy is TRUE, such observations are also marked if they occur.

Usage

moran.plot(x, listw, y=NULL, zero.policy=attr(listw, "zero.policy"), spChk=NULL,
 labels=NULL, xlab=NULL, ylab=NULL, quiet=NULL, plot=TRUE, return_df=TRUE, ...)

Arguments

Value

The function returns a data.frame object with coordinates and influence measures if return_df is TRUE, or an influence object from influence.measures.

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

Anselin, L. 1996. The Moran scatterplot as an ESDA tool to assess local instability in spatial association. pp. 111–125 in M. M. Fischer, H. J. Scholten and D. Unwin (eds) Spatial analytical perspectives on GIS, London, Taylor and Francis; Anselin, L. 1995. Local indicators of spatial association, Geographical Analysis, 27, 93–115

See Also

localmoran, influence.measures

Examples

data(afcon, package="spData")
mp <- moran.plot(afcon$totcon, nb2listw(paper.nb),
 labels=as.character(afcon$name), pch=19)
moran.plot(as.vector(scale(afcon$totcon)), nb2listw(paper.nb),
 labels=as.character(afcon$name), xlim=c(-2, 4), ylim=c(-2,4), pch=19)
if (require(ggplot2, quietly=TRUE)) {
  xname <- attr(mp, "xname")
  ggplot(mp, aes(x=x, y=wx)) + geom_point(shape=1) + 
    geom_smooth(formula=y ~ x, method="lm") + 
    geom_hline(yintercept=mean(mp$wx), lty=2) + 
    geom_vline(xintercept=mean(mp$x), lty=2) + theme_minimal() + 
    geom_point(data=mp[mp$is_inf,], aes(x=x, y=wx), shape=9) +
    geom_text(data=mp[mp$is_inf,], aes(x=x, y=wx, label=labels, vjust=1.5)) +
    xlab(xname) + ylab(paste0("Spatially lagged ", xname))
}
columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData"))
nb <- poly2nb(columbus)
listw <- nb2listw(nb)
moran.plot(x=columbus$CRIME, y=columbus$INC, listw=listw)
moran.plot(x=columbus$INC, y=columbus$CRIME, listw=listw)

Moran's I test for spatial autocorrelation

Description

Moran's test for spatial autocorrelation using a spatial weights matrix in weights list form. The assumptions underlying the test are sensitive to the form of the graph of neighbour relationships and other factors, and results may be checked against those of moran.mc permutations.

Usage

moran.test(x, listw, randomisation=TRUE, zero.policy=attr(listw, "zero.policy"),
 alternative="greater", rank = FALSE, na.action=na.fail, spChk=NULL,
 adjust.n=TRUE, drop.EI2=FALSE)

Arguments

Value

A list with class htest containing the following components:

Note

Var(I) is taken from Cliff and Ord (1969, p. 28), and Goodchild's CATMOG 47 (1986), see also Upton & Fingleton (1985) p. 171; it agrees with SpaceStat, see Tutorial workbook Chapter 22; VI is the second crude moment minus the square of the first crude moment. The derivation of the test (Cliff and Ord, 1981, p. 18) assumes that the weights matrix is symmetric. For inherently non-symmetric matrices, such as k-nearest neighbour matrices, listw2U() can be used to make the matrix symmetric.

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 21; Bivand RS, Wong DWS 2018 Comparing implementations of global and local indicators of spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x

See Also

moran, moran.mc, listw2U

Examples

data(oldcol)
coords.OLD <- cbind(COL.OLD$X, COL.OLD$Y)
moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style="W"))
moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style="B"))
moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style="C"))
moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style="S"))
moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style="W"),
 randomisation=FALSE)
colold.lags <- nblag(COL.nb, 3)
moran.test(COL.OLD$CRIME, nb2listw(colold.lags[[2]],
 style="W"))
moran.test(COL.OLD$CRIME, nb2listw(colold.lags[[3]],
 style="W"))
print(is.symmetric.nb(COL.nb))
COL.k4.nb <- knn2nb(knearneigh(coords.OLD, 4))
print(is.symmetric.nb(COL.k4.nb))
moran.test(COL.OLD$CRIME, nb2listw(COL.k4.nb, style="W"))
moran.test(COL.OLD$CRIME, nb2listw(COL.k4.nb, style="W"),
 randomisation=FALSE)
cat("Note: non-symmetric weights matrix, use listw2U()")
moran.test(COL.OLD$CRIME, listw2U(nb2listw(COL.k4.nb,
 style="W")))
moran.test(COL.OLD$CRIME, listw2U(nb2listw(COL.k4.nb,
 style="W")), randomisation=FALSE)
ranks <- rank(COL.OLD$CRIME)
names(ranks) <- rownames(COL.OLD)
moran.test(ranks, nb2listw(COL.nb, style="W"), rank=TRUE)
crime <- COL.OLD$CRIME
is.na(crime) <- sample(1:length(crime), 10)
res <- try(moran.test(crime, nb2listw(COL.nb, style="W"),
 na.action=na.fail))
moran.test(crime, nb2listw(COL.nb, style="W"), zero.policy=TRUE,
 na.action=na.omit)
moran.test(crime, nb2listw(COL.nb, style="W"), zero.policy=TRUE,
 na.action=na.exclude)
moran.test(crime, nb2listw(COL.nb, style="W"), na.action=na.pass)
columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
col_geoms <- st_geometry(columbus)
col_geoms[1] <- st_buffer(col_geoms[1], dist=-0.05)
st_geometry(columbus) <- col_geoms
(nb1 <- poly2nb(columbus))
try(lw <- nb2listw(nb1, style="W"))
(lw <- nb2listw(nb1, style="W", zero.policy=TRUE))
moran.test(COL.OLD$CRIME, lw)

Find the minimal spanning tree

Description

The minimal spanning tree is a connected graph with n nodes and n-1 edges. This is a smaller class of possible partitions of a graph by pruning edges with high dissimilarity. If one edge is removed, the graph is partioned in two unconnected subgraphs. This function implements the algorithm due to Prim (1987).

Usage

mstree(nbw, ini = NULL)

Arguments

Details

The minimum spanning tree algorithm.

Input a connected graph.

Begin a empty set of nodes.

Add an arbitrary note in this set.

While are nodes not in the set, find a minimum cost edge connecting a node in the set and a node out of the set and add this node in the set.

The set of edges is a minimum spanning tree.

Value

A matrix with n-1 rows and tree columns. Each row is two nodes and the cost, i. e. the edge and it cost.

Author(s)

Renato M. Assuncao and Elias T. Krainski

References

R. C. Prim (1957) Shortest connection networks and some generalisations. In: Bell System Technical Journal, 36, pp. 1389-1401

Examples

### loading data
(GDAL37 <- as.numeric_version(unname(sf_extSoftVersion()["GDAL"])) >= "3.7.0")
file <- "etc/shapes/bhicv.gpkg.zip"
zipfile <- system.file(file, package="spdep")
if (GDAL37) {
    bh <- st_read(zipfile)
} else {
    td <- tempdir()
    bn <- sub(".zip", "", basename(file), fixed=TRUE)
    target <- unzip(zipfile, files=bn, exdir=td)
    bh <- st_read(target)
}
### data padronized
dpad <- data.frame(scale(as.data.frame(bh)[,5:8]))

### neighboorhod list 
bh.nb <- poly2nb(bh)

### calculing costs
lcosts <- nbcosts(bh.nb, dpad)

### making listw
nb.w <- nb2listw(bh.nb, lcosts, style="B")

### find a minimum spanning tree
system.time(mst.bh <- mstree(nb.w,5))
dim(mst.bh)
head(mst.bh)
tail(mst.bh)
### the mstree plot
par(mar=c(0,0,0,0))
plot(st_geometry(bh), border=gray(.5))
plot(mst.bh, st_coordinates(st_centroid(bh)), col=2, 
     cex.lab=.6, cex.circles=0.035, fg="blue", add=TRUE)

Set operations on neighborhood objects

Description

Performs set operations on neighbors list objects union, intersection, (asymmetric!) difference and complement; note that from 1.3-9, setdiff.nb behaves like setdiff, where the ordering of the objects being compared matters - (asymmetric!) difference.

Usage

intersect.nb(nb.obj1,nb.obj2)
union.nb(nb.obj1,nb.obj2)
setdiff.nb(nb.obj1,nb.obj2)
complement.nb(nb.obj)

Arguments

Details

These functions perform set operations on each element of a neighborlist. The arguments must be neighbor lists created from the same spatial objects, checked by the region.id attributes being required to be identical.

Value

A new neighborlist created from the set operations on the input neighbor list(s)

Author(s)

Nicholas Lewin-Koh nikko@hailmail.net

See Also

intersect.nb, union.nb, setdiff.nb

Examples

columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
col.gal.nb <- read.gal(system.file("weights/columbus.gal", package="spData")[1])
coords <- st_coordinates(st_centroid(columbus))
col.tri.nb <- tri2nb(coords)
oldpar <- par(mfrow=c(1,2))
if (require("dbscan", quietly=TRUE)) {
  col.soi.nb <- graph2nb(soi.graph(col.tri.nb, coords))
  plot(st_geometry(columbus), border="grey")
  plot(col.soi.nb, coords, add=TRUE)
  title(main="Sphere of Influence Graph", cex.main=0.7)
  plot(st_geometry(columbus), border="grey")
  plot(complement.nb(col.soi.nb), coords, add=TRUE)
  title(main="Complement of Sphere of Influence Graph", cex.main=0.7)
}
par(mfrow=c(2,2))
col2 <- droplinks(col.gal.nb, 21)
plot(intersect.nb(col.gal.nb, col2), coords)
title(main="Intersect", cex.main=0.7)
plot(union.nb(col.gal.nb, col2), coords)
title(main="Union", cex.main=0.7)
plot(setdiff.nb(col.gal.nb, col2), coords)
title(main="Set diff", cex.main=0.7)
par(oldpar)

Block up neighbour list for location-less observations

Description

The function blocks up a neighbour list for known spatial locations to create a new neighbour list for multiple location-less observations know to belong to the spatial locations, using the identification tags of the locations as the key.

Usage

nb2blocknb(nb=NULL, ID, row.names = NULL)

Arguments

Details

Assume that there is a list of unique locations, then a neighbour list can build for that, to create an input neighbour list. This needs to be "unfolded", so that observations belonging to each unique location are observation neighbours, and observations belonging to the location neighbours of the unique location in question are also observation neighbours, finally removing the observation itself (because it should not be its own neighbour). This scenario also arises when say only post codes are available, and some post codes contain multiple observations, where all that is known is that they belong to a specific post code, not where they are located within it (given that the post code locations are known).

Value

The function returns an object of class nb with a list of integer vectors containing neighbour observation number ids.

Author(s)

Roger Bivand Roger.Bivand@nhh.no

See Also

knn2nb, dnearneigh, cell2nb, tri2nb, poly2nb

Examples

## Not run: 
data(boston, package="spData")
summary(as.vector(table(boston.c$TOWN)))
townaggr <- aggregate(boston.utm, list(town=boston.c$TOWN), mean)
block.rel <- graph2nb(relativeneigh(as.matrix(townaggr[,2:3])),
 as.character(townaggr[,1]), sym=TRUE)
block.rel
print(is.symmetric.nb(block.rel))
plot(block.rel, as.matrix(townaggr[,2:3]))
points(boston.utm, pch=18, col="lightgreen")
block.nb <- nb2blocknb(block.rel, as.character(boston.c$TOWN))
block.nb
print(is.symmetric.nb(block.nb))
plot(block.nb, boston.utm)
points(boston.utm, pch=18, col="lightgreen")
n.comp.nb(block.nb)$nc
moran.test(boston.c$CMEDV, nb2listw(boston.soi))
moran.test(boston.c$CMEDV, nb2listw(block.nb))
block.nb <- nb2blocknb(NULL, as.character(boston.c$TOWN))
block.nb
print(is.symmetric.nb(block.nb))
plot(block.nb, boston.utm)
n.comp.nb(block.nb)$nc
moran.test(boston.c$CMEDV, nb2listw(block.nb, zero.policy=TRUE), zero.policy=TRUE)

## End(Not run)

Output spatial neighbours for INLA

Description

Output spatial neighbours for INLA

Usage

nb2INLA(file, nb)

Arguments

Value

Nothing is returned but a file will be created with the representation of the adjacency matrix as required by INLA for its spatial models.

Author(s)

Virgilio Gomez-Rubio

References

http://www.r-inla.org

Examples

col.gal.nb <- read.gal(system.file("weights/columbus.gal", package="spData")[1])
td <- tempdir()
x <- nb2INLA(paste(td, "columbus-INLA.adj", sep="/"), col.gal.nb)
readLines(paste(td, "columbus-INLA.adj", sep="/"), n=10)

Use vector files for import and export of weights

Description

Use vector files for import and export of weights, storing spatial entity coordinates in the arcs, and the entity indices in the data frame.

Usage

nb2lines(nb, wts, coords, proj4string=NULL, as_sf=FALSE)
listw2lines(listw, coords, proj4string=NULL, as_sf=FALSE)
df2sn(df, i="i", i_ID="i_ID", j="j", wt="wt")

Arguments

Details

The neighbour and weights objects may be retrieved by converting the specified columns of the data slot of the SpatialLinesDataFrame object into a spatial.neighbour object, which is then converted into a weights list object.

Value

nb2lines and listw2lines return a SpatialLinesDataFrame object or an sf object; the data frame contains with the from and to indices of the neighbour links and their weights. df2sn converts the data retrieved from reading the data from df back into a spatial.neighbour object.

Note

Original idea due to Gidske Leknes Andersen, Department of Biology, University of Bergen, Norway

Author(s)

Roger Bivand Roger.Bivand@nhh.no

See Also

sn2listw

Examples

columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
col.gal.nb <- read.gal(system.file("weights/columbus.gal", package="spData")[1])
res <- listw2lines(nb2listw(col.gal.nb), st_geometry(columbus))
summary(res)
tf <- paste0(tempfile(), ".gpkg")
st_write(res, dsn=tf, driver="GPKG")
inMap <- st_read(tf)
summary(inMap)
diffnb(sn2listw(df2sn(as.data.frame(inMap)))$neighbours, col.gal.nb)
res1 <- listw2lines(nb2listw(col.gal.nb), as(columbus, "Spatial"))
summary(res1)

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. The helper function listw2U() constructs a weights list object corresponding to the sparse matrix \frac{1}{2} ( \mathbf{W} + \mathbf{W}'.

Usage

nb2listw(neighbours, glist=NULL, style="W", zero.policy=NULL)
listw2U(listw)

Arguments

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 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.

Value

A listw object with the following members:

and attributes:

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

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.

See Also

summary.nb, read.gal

Examples

columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
col.gal.nb <- read.gal(system.file("weights/columbus.gal", package="spData")[1])
coords <- st_coordinates(st_centroid(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$weights, sum)), col="blue")
legend(x=c(0, 1), y=c(7, 9), legend=c("W", "B", "C", "U", "S"), bty="n",
col=c("black", "red", "green", "orange", "blue"), pch=rep(1,5), cex=0.8,
y.intersp=2.5)
summary(nb2listw(col.gal.nb, style="minmax"))
dlist <- nbdists(col.gal.nb, coords)
dlist <- lapply(dlist, function(x) 1/x)
col.w.d <- nb2listw(col.gal.nb, glist=dlist)
summary(unlist(col.w$weights))
summary(unlist(col.w.d$weights))
# introducing other conditions into weights - only earlier sales count
# see http://sal.uiuc.edu/pipermail/openspace/2005-October/000610.html
data(baltimore, package="spData")
set.seed(211)
dates <- sample(1:500, nrow(baltimore), replace=TRUE)
nb_15nn <- knn2nb(knearneigh(cbind(baltimore$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]]]

Distance-based spatial weights for neighbours lists

Description

The nb2listwdist function supplements a neighbours list with spatial weights for the chosen types of distance modelling and coding scheme. While the offered coding schemes parallel those of the nb2listw function, three distance-based types of weights are available: inverse distance weighting (IDW), double-power distance weights, and exponential distance decay. 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

nb2listwdist(neighbours, x, type="idw", style="raw", 
  alpha = 1, dmax = NULL, longlat = NULL, zero.policy=NULL)

Arguments

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 distance-based weights list. Three types of distance weight calculations based on pairwise distances d_{ij} are possible, all of which are controlled by parameter “alpha” (\alpha below):

\textrm{idw: } w_{ij} = d_{ij}^{-\alpha},

\textrm{exp: } w_{ij} = \exp(-\alpha \cdot d_{ij}),

\textrm{dpd: } w_{ij} = \left[1 - \left(d_{ij}/d_{\textrm{max}}\right)^{\alpha}\right]^{\alpha},

the latter of which leads to w_{ij} = 0 for all d_{ij} > d_{\textrm{max}}. Note that IDW weights show extreme behaviour close to 0 and can take on the value infinity. In such cases, the infinite values are replaced by the largest finite weight present in the weights list.

The default coding scheme is “raw”, which outputs the raw distance-based weights without applying any kind of normalisation. In addition, the same coding scheme styles that are also available in the nb2listw function can be 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-stabilising coding scheme proposed by Tiefelsdorf et al. 1999, p. 167-168 (sums over all links to n). 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.

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.

Value

A listw object with the following members:

Author(s)

Rene Westerholt rene.westerholt@tu-dortmund.de

References

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.

See Also

nb2listw, summary.nb

Examples

# World examples
data(world, package="spData")
# neighbours on distance interval [0, 1000] kilometres
# suppressWarnings(st_crs(world) <- "+proj=longlat") # for older PROJ
pts <- st_centroid(st_transform(world, 3857))
nb_world <- dnearneigh(pts, 0, 1000000)
# Moran's I (life expectancy) with IDW with alpha = 2, no coding scheme
world_weights <- nb2listwdist(nb_world, as(pts, "Spatial"), type = "idw",
  alpha = 2, zero.policy = TRUE)
moran.test(world$lifeExp, world_weights, zero.policy = TRUE, na.action = na.pass)
## Not run: 
# Moran's I (life expectancy) with IDW with alpha = 2, no coding scheme
world_weights <- nb2listwdist(nb_world, pts, type = "idw",
  alpha = 2, zero.policy = TRUE)
moran.test(world$lifeExp, world_weights, zero.policy = TRUE, na.action = na.pass)
# Moran's I (life expectancy), DPD, alpha = 2, dmax = 1000 km, no coding scheme
world_weights <- nb2listwdist(nb_world, pts, type = "dpd",
  dmax = 1000000, alpha = 2, zero.policy = TRUE)
moran.test(world$lifeExp, world_weights, zero.policy = TRUE, na.action = na.pass)
# Boston examples
data(boston, package="spData")
boston_coords <- data.frame(x = boston.utm[,1], y = boston.utm[,2])
boston.geoms <- st_as_sf(boston_coords, coords = c("x", "y"), remove = FALSE)
nb_boston <- dnearneigh(boston.geoms, 0, 3)
# Moran's I (crime) with exp weights with alpha = 2, no coding scheme
boston_weights <- nb2listwdist(nb_boston, boston.geoms, type = "exp", alpha = 2,
  style="raw", zero.policy = TRUE)
moran.test(boston.c$CRIM, boston_weights, zero.policy = TRUE, na.action = na.pass)
# Moran's I (crime) with idw weights with alpha = 2, coding scheme = W
boston_weights <- nb2listwdist(nb_boston, boston.geoms, type = "idw", alpha = 2,
  style="W", zero.policy = TRUE)
moran.test(boston.c$CRIM, boston_weights, zero.policy = TRUE, na.action = na.pass)

## End(Not run)

Spatial weights matrices for neighbours lists

Description

The function generates a weights matrix for a neighbours list with spatial weights for the chosen coding scheme.

Usage

nb2mat(neighbours, glist=NULL, style="W", zero.policy=NULL)
listw2mat(listw)

Arguments

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 creates an n by n weights matrix with values given by the coding scheme style chosen. B is the basic binary coding, W is row standardised, C is globally standardised, while S is the variance-stabilizing coding scheme proposed by Tiefelsdorf et al. 1999, p. 167-168.

The function leaves matrix rows as zero for any regions with zero neighbours fore zero.policy TRUE. 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.

Value

An n by n matrix, where n=length(neighbours)

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

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.

See Also

nb2listw

Examples

columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
col005 <- dnearneigh(st_coordinates(st_centroid(st_geometry(columbus),
 of_largest_polygon=TRUE)), 0, 0.5, as.character(columbus$NEIGNO))
summary(col005)
col005.w.mat <- nb2mat(col005, style="B", zero.policy=TRUE)
table(round(rowSums(col005.w.mat)))

Output spatial weights for WinBUGS

Description

Output spatial weights for WinBUGS

Usage

nb2WB(nb)
listw2WB(listw) 

Arguments

Value

A list suitable for convering using dput for WinBUGS

Author(s)

Virgilio Gomez-Rubio

References

http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/geobugs12manual.pdf

See Also

dput

Examples

col.gal.nb <- read.gal(system.file("weights/columbus.gal", package="spData")[1])
x <- nb2WB(col.gal.nb)
dput(x, control=NULL)
x <- listw2WB(nb2listw(col.gal.nb))
dput(x, control=NULL)

Compute cost of edges

Description

The cost of each edge is the distance between it nodes. This function compute this distance using a data.frame with observations vector in each node.

Usage

nbcost(data, id, id.neigh,  method = c("euclidean", "maximum", 
    "manhattan", "canberra", "binary", "minkowski", "mahalanobis"),
    p = 2, cov, inverted = FALSE)
nbcosts(nb, data,  method = c("euclidean", "maximum", 
    "manhattan", "canberra", "binary", "minkowski", "mahalanobis"),
    p = 2, cov, inverted = FALSE)

Arguments

Value

A object of nbdist class. See nbdists for details.

Note

The neighbours must be a connected graph.

Author(s)

Elias T. Krainski and Renato M. Assuncao

See Also

See Also as nbdists, nb2listw

Spatial link distance measures

Description

Given a list of spatial neighbour links (a neighbours list of object type nb), the function returns the Euclidean distances along the links in a list of the same form as the neighbours list. If longlat = TRUE, Great Circle distances are used.

Usage

nbdists(nb, coords, longlat = NULL)

Arguments

Value

A list with class nbdist

Author(s)

Roger Bivand Roger.Bivand@nhh.no

See Also

summary.nb, nb2listw

Examples

columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
col.gal.nb <- read.gal(system.file("weights/columbus.gal", package="spData")[1])
coords <- st_coordinates(st_centroid(columbus))
dlist <- nbdists(col.gal.nb, coords)
dlist <- lapply(dlist, function(x) 1/x)
stem(unlist(dlist))

Higher order neighbours lists

Description

The function creates higher order neighbour lists, where higher order neighbours are only lags links from each other on the graph described by the input neighbours list. It will refuse to lag neighbours lists with the attribute self.included set to TRUE. nblag_cumul cumulates neighbour lists to a single neighbour list (“nb” object).

Usage

nblag(neighbours, maxlag)
nblag_cumul(nblags)

Arguments

Value

returns a list of lagged neighbours lists each with class nb

Author(s)

Roger Bivand Roger.Bivand@nhh.no and Giovanni Millo

See Also

summary.nb

Examples

columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
col.gal.nb <- read.gal(system.file("weights/columbus.gal", package="spData")[1])
coords <- st_coordinates(st_centroid(columbus))
summary(col.gal.nb, coords)
col.lags <- nblag(col.gal.nb, 2)
print(col.lags)
summary(col.lags[[2]], coords)
plot(st_geometry(columbus), border="grey")
plot(col.gal.nb, coords, add=TRUE)
title(main="GAL order 1 (black) and 2 (red) links")
plot(col.lags[[2]], coords, add=TRUE, col="red", lty=2)
cuml <- nblag_cumul(col.lags)
cuml
run <- FALSE
if (require(igraph, quietly=TRUE) && require(spatialreg, quietly=TRUE)) run <- TRUE
if (run) {
W <- as(nb2listw(col.gal.nb), "CsparseMatrix")
G <- graph_from_adjacency_matrix(W, mode="directed", weight="W")
D <- diameter(G)
nbs <- nblag(col.gal.nb, maxlag=D)
n <- length(col.gal.nb)
lmat <- lapply(nbs, nb2mat, style="B", zero.policy=TRUE)
mat <- matrix(0, n, n)
for (i in seq(along=lmat)) mat = mat + i*lmat[[i]]
G2 <- distances(G)
print(all.equal(G2, mat, check.attributes=FALSE))
}

Columbus OH spatial analysis data set - old numbering

Description

The COL.OLD data frame has 49 rows and 22 columns. The observations are ordered and numbered as in the original analyses of the data set in the SpaceStat documentation and in Anselin, L. 1988 Spatial econometrics: methods and models, Dordrecht: Kluwer. Unit of analysis: 49 neighbourhoods in Columbus, OH, 1980 data. In addition the data set includes COL.nb, the neighbours list as used in Anselin (1988).

Usage

data(oldcol)

Format

This data frame contains the following columns:

AREA_PL

computed by ArcView (agrees with areas of polygons in the “columbus” data set

PERIMETER

computed by ArcView

COLUMBUS.

internal polygon ID (ignore)

COLUMBUS.I

another internal polygon ID (ignore)

POLYID

yet another polygon ID

NEIG

neighborhood id value (1-49); conforms to id value used in Spatial Econometrics book.

HOVAL

housing value (in $1,000)

INC

household income (in $1,000)

CRIME

residential burglaries and vehicle thefts per thousand households in the neighborhood

OPEN

open space in neighborhood

PLUMB

percentage housing units without plumbin

DISCBD

distance to CBD

X

x coordinate (in arbitrary digitizing units, not polygon coordinates)

Y

y coordinate (in arbitrary digitizing units, not polygon coordinates)

AREA_SS

neighborhood area (computed by SpaceStat)

NSA

north-south dummy (North=1)

NSB

north-south dummy (North=1)

EW

east-west dummy (East=1)

CP

core-periphery dummy (Core=1)

THOUS

constant=1,000

NEIGNO

NEIG+1,000, alternative neighborhood id value

PERIM

polygon perimeter (computed by SpaceStat)

Details

The row names of COL.OLD and the region.id attribute of COL.nb are set to columbus$NEIGNO.

Note

All source data files prepared by Luc Anselin, Spatial Analysis Laboratory, Department of Agricultural and Consumer Economics, University of Illinois, Urbana-Champaign.

Source

Anselin, Luc. 1988. Spatial econometrics: methods and models. Dordrecht: Kluwer Academic, Table 12.1 p. 189.

Adjust local association measures' p-values

Description

Make an adjustment to local association measures' p-values based on the number of neighbours (+1) of each region, rather than the total number of regions.

Usage

p.adjustSP(p, nb, method = "none")

Arguments

Value

A vector of corrected p-values using only the number of neighbours + 1.

Author(s)

Danlin Yu and Roger Bivand Roger.Bivand@nhh.no

See Also

p.adjust, localG, localmoran

Examples

data(afcon, package="spData")
oid <- order(afcon$id)
resG <- as.vector(localG(afcon$totcon, nb2listw(include.self(paper.nb))))
non <- format.pval(pnorm(2*(abs(resG)), lower.tail=FALSE), 2)
bon <- format.pval(p.adjustSP(pnorm(2*(abs(resG)), lower.tail=FALSE),
 paper.nb, "bonferroni"), 2)
tot <- format.pval(p.adjust(pnorm(2*(abs(resG)), lower.tail=FALSE),
 "bonferroni", n=length(resG)), 2)
data.frame(resG, non, bon, tot, row.names=afcon$name)[oid,]

Plot the Minimum Spanning Tree

Description

This function plots a MST, the nodes are circles and the edges are segments.

Usage

## S3 method for class 'mst'
plot(x, coords, label.areas = NULL, 
   cex.circles = 1, cex.labels = 1, add=FALSE, ...)

Arguments

Author(s)

Elias T. Krainski and Renato M. Assuncao

See Also

See Also as skater and mstree

Examples

### see example in mstree function documentation

Plot a neighbours list

Description

A function to plot a neighbours list given point coordinates to represent the region in two dimensions; plot.listw is a wrapper that passes its neighbours component to plot.nb.

Usage

## S3 method for class 'nb'
plot(x, coords, col="black", points=TRUE, add=FALSE, arrows=FALSE,
 length=0.1, xlim=NULL, ylim=NULL, ...)
## S3 method for class 'listw'
plot(x, coords, col="black", points=TRUE, add=FALSE, arrows=FALSE,
 length=0.1, xlim=NULL, ylim=NULL, ...)

Arguments

Author(s)

Roger Bivand Roger.Bivand@nhh.no

See Also

summary.nb

Examples

columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
col.gal.nb <- read.gal(system.file("weights/columbus.gal", package="spData")[1])
plot(col.gal.nb, st_geometry(columbus))
title(main="GAL order 1 links with first nearest neighbours in red", cex.main=0.6)
plot(col.gal.nb, as(columbus, "Spatial"))
title(main="GAL order 1 links with first nearest neighbours in red", cex.main=0.6)
coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE)
col.knn <- knearneigh(coords, k=1)
plot(knn2nb(col.knn), coords, add=TRUE, col="red", length=0.08)

Plot the object of skater class

Description

This function displays the results of the skater function. The subgraphs are plotted with different colours.

Usage

## S3 method for class 'skater'
plot(x, coords, label.areas = NULL, 
   groups.colors, cex.circles = 1, cex.labels = 1, ...)

Arguments

Author(s)

Elias T. Krainski and Renato M. Assuncao

See Also

See Also as skater and mstree

Examples

### see example in the skater function documentation

Construct neighbours list from polygon list

Description

The function builds a neighbours list based on regions with contiguous boundaries, that is sharing one or more boundary point. The current function is in part interpreted and may run slowly for many regions or detailed boundaries, but from 0.2-16 should not fail because of lack of memory when single polygons are built of very many border coordinates.

Usage

poly2nb(pl, row.names = NULL, snap=NULL, queen=TRUE, useC=TRUE, foundInBox=NULL)

Arguments

Value

A neighbours list with class nb. See card for details of “nb” objects.

Note

From 0.5-8, the function includes faster bounding box indexing and other improvements contributed by Micah Altman. If a cluster is provided using set.ClusterOption, it will be used for finding candidate bounding box overlaps for exact testing for contiguity.

Until 1.1-7, sf polygons included both start and end points, so could erroneously report queen neighbourhood where only rook was present, see https://github.com/r-spatial/spdep/issues/50.

From 1.1-9 with sf 1.0-0, s2 is used in bounding box indexing internally when pl is in geographical coordinates. Because the topology engine of s2 differs from the use of GEOS for planar coordinates by sf, some output differences may be expected. Since treating spherical geometries as planar is also questionable, it is not clear whether spherical contiguous polygon neighbours should simply follow neighbours found by treating the geometries as planar https://github.com/r-spatial/s2/issues/125#issuecomment-864403372. However, current advice is not necessarily to use s2 for finding contiguity neighbours, or at least to check output.

Author(s)

Roger Bivand Roger.Bivand@nhh.no with contributions from Micah Altman

See Also

summary.nb, card

Examples

columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
col.gal.nb <- read.gal(system.file("weights/columbus.gal", package="spData")[1])
coords <- st_coordinates(st_centroid(st_geometry(columbus)))
xx <- poly2nb(as(columbus, "Spatial"))
dxx <- diffnb(xx, col.gal.nb)
plot(st_geometry(columbus), border="grey")
plot(col.gal.nb, coords, add=TRUE)
plot(dxx, coords, add=TRUE, col="red")
title(main=paste("Differences (red) in Columbus GAL weights (black)",
 "and polygon generated queen weights", sep="\n"), cex.main=0.6)
# poly2nb with sf sfc_MULTIPOLYGON objects
sf_xx <- poly2nb(columbus)
diffnb(sf_xx, xx)
sfc_xx <- poly2nb(st_geometry(columbus))
diffnb(sfc_xx, xx)
xxx <- poly2nb(as(columbus, "Spatial"), queen=FALSE)
dxxx <- diffnb(xxx, col.gal.nb)
plot(st_geometry(columbus), border = "grey")
plot(col.gal.nb, coords, add = TRUE)
plot(dxxx, coords, add = TRUE, col = "red")
title(main=paste("Differences (red) in Columbus GAL weights (black)",
 "and polygon generated rook weights", sep="\n"), cex.main=0.6)
cards <- card(xx)
maxconts <- which(cards == max(cards))
if(length(maxconts) > 1) maxconts <- maxconts[1]
fg <- rep("grey", length(cards))
fg[maxconts] <- "red"
fg[xx[[maxconts]]] <- "green"
plot(st_geometry(columbus), col=fg)
title(main="Region with largest number of contiguities", cex.main=0.6)
nc.sids <- st_read(system.file("shapes/sids.gpkg", package="spData")[1], quiet=TRUE)
system.time(xxnb <- poly2nb(nc.sids))
system.time(xxnb <- poly2nb(as(nc.sids, "Spatial")))
plot(st_geometry(nc.sids))
plot(xxnb, st_coordinates(st_centroid(nc.sids)), add=TRUE, col="blue")
sq <- st_polygon(list(rbind(c(0,0), c(1,0), c(1,1), c(0,1), c(0,0))))
sq2 <- sq + c(0,1)
sq3 <- sq + c(1,0)
sq4 <- sq + c(1,1)
gm <- st_sfc(list(sq, sq2, sq3, sq4))
df <- st_as_sf(data.frame(gm, id=1:4))
plot(st_geometry(df))
text(st_coordinates(st_centroid(gm)), as.character(df$id))
unclass(poly2nb(df, queen = FALSE))
col_geoms <- st_geometry(columbus)
col_geoms[1] <- st_buffer(col_geoms[1], dist=-0.05)
st_geometry(columbus) <- col_geoms
poly2nb(columbus)

Probability mapping for rates

Description

The function returns a data frame of rates for counts in populations at risk with crude rates, expected counts of cases, relative risks, and Poisson probabilities.

Usage

probmap(n, x, row.names=NULL, alternative="less")

Arguments

Details

The function returns a data frame, from which rates may be mapped after class intervals have been chosen. The class intervals used in the examples are mostly taken from the referenced source.

Value

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

Bailey T, Gatrell A (1995) Interactive Spatial Data Analysis, Harlow: Longman, pp. 300–303.

See Also

EBest, EBlocal, ppois

Examples

auckland <- st_read(system.file("shapes/auckland.gpkg", package="spData")[1], quiet=TRUE)
res <- probmap(auckland$M77_85, 9*auckland$Und5_81)
rt <- sum(auckland$M77_85)/sum(9*auckland$Und5_81)
ppois_pmap <- numeric(length(auckland$Und5_81))
for (i in seq(along=ppois_pmap)) {
ppois_pmap[i] <- poisson.test(auckland$M77_85[i], r=rt,
  T=(9*auckland$Und5_81[i]), alternative="less")$p.value
all.equal(ppois_pmap, res$pmap)
}
res$id <- 1:nrow(res)
auckland$id <- res$id <- 1:nrow(res)
auckland_res <- merge(auckland, res, by="id")
plot(auckland_res[, "raw"], main="Crude (raw) estimates")
plot(auckland_res[, "relRisk"], main="Standardised mortality ratios")
plot(auckland_res[, "pmap"], main="Poisson probabilities",
 breaks=c(0, 0.05, 0.1, 0.5, 0.9, 0.95, 1))

Compute cost of prune each edge

Description

If any edge are dropped, the MST are pruned. This generate a two subgraphs. So, it makes a tree graphs and tree dissimilarity values are computed, one for each graph. The dissimilarity is the sum over sqared differences between the observactions in the nodes and mean vector of observations in the graph. The dissimilarity of original graph and the sum of dissimilarity of subgraphs are returned.

Usage

prunecost(edges, data, method = c("euclidean", "maximum", "manhattan", 
    "canberra", "binary", "minkowski", "mahalanobis"), 
    p = 2, cov, inverted = FALSE)

Arguments

Value

A vector with the differences between the dissimilarity of all nodes and the dissimilarity sum of all subgraphs obtained by pruning one edge each time.

Author(s)

Elias T. Krainski and Renato M. Assuncao

See Also

See Also as prunemst

Examples

d <- data.frame(a=-2:2, b=runif(5))
e <- matrix(c(1,2, 2,3, 3,4, 4,5), ncol=2, byrow=TRUE)

sum(sweep(d, 2, colMeans(d))^2)

prunecost(e, d)

Prune a Minimun Spanning Tree

Description

This function deletes a first edge and makes two subsets of edges. Each subset is a Minimun Spanning Treee.

Usage

prunemst(edges, only.nodes = TRUE)

Arguments

Value

A list of length two. If only.nodes=TRUE each element is a vector of nodes. If only.nodes=FALSE each element is a list with nodes and edges.

Author(s)

Elias T. Krainski and Renato M. Assuncao

See Also

See Also as mstree

Examples

e <- matrix(c(2,3, 1,2, 3,4, 4,5), ncol=2, byrow=TRUE)
e
prunemst(e)
prunemst(e, only.nodes=FALSE)

Read a GAL lattice file into a neighbours list

Description

The function read.gal() reads a GAL lattice file into a neighbours list for spatial analysis. It will read old and new style (GeoDa) GAL files. The function read.geoda is a helper file for reading comma separated value data files, calling read.csv().

Usage

read.gal(file, region.id=NULL, override.id=FALSE)
read.geoda(file, row.names=NULL, skip=0)

Arguments

Details

Luc Anselin (2003): Spatial Analysis Laboratory, Department of Agricultural and Consumer Economics, University of Illinois, Urbana-Champaign, now dead link: http://www.csiss.org/gispopsci/workshops/2011/PSU/readings/W15_Anselin2007.pdf; Luc Anselin (2003) GeoDa 0.9 User's Guide, pp. 80–81, Spatial Analysis Laboratory, Department of Agricultural and Consumer Economics, University of Illinois, Urbana-Champaign, http://geodacenter.github.io/docs/geoda093.pdf; GAL - Geographical Algorithms Library, University of Newcastle

Value

The function read.gal() returns an object of class nb with a list of integer vectors containing neighbour region number ids. The function read.geoda returns a data frame, and issues a warning if the returned object has only one column.

Note

Example data originally downloaded from now dead link: http://sal.agecon.uiuc.edu/weights/zips/us48.zip

Author(s)

Roger Bivand Roger.Bivand@nhh.no

See Also

summary.nb

Examples

us48.fipsno <- read.geoda(system.file("etc/weights/us48.txt",
 package="spdep")[1])
us48.q <- read.gal(system.file("etc/weights/us48_q.GAL", package="spdep")[1],
 us48.fipsno$Fipsno)
us48.r <- read.gal(system.file("etc/weights/us48_rk.GAL", package="spdep")[1],
 us48.fipsno$Fipsno)
data(state)
if (as.numeric(paste(version$major, version$minor, sep="")) < 19) {
 m50.48 <- match(us48.fipsno$"State.name", state.name)
} else {
 m50.48 <- match(us48.fipsno$"State_name", state.name)
}
plot(us48.q, as.matrix(as.data.frame(state.center))[m50.48,])
plot(diffnb(us48.r, us48.q),
 as.matrix(as.data.frame(state.center))[m50.48,], add=TRUE, col="red")
title(main="Differences between rook and queen criteria imported neighbours lists")

Read and write spatial neighbour files

Description

The "gwt" functions read and write GeoDa GWT files (the example file baltk4.GWT was downloaded from the site given in the reference), and the "dat" functions read and write Matlab sparse matrix files as used by James LeSage's Spatial Econometrics Toolbox (the example file wmat.dat was downloaded from the site given in the reference). The body of the files after any headers should have three columns separated by white space, and the third column must be numeric in the locale of the reading platform (correct decimal separator).

Usage

read.gwt2nb(file, region.id=NULL)
write.sn2gwt(sn, file, shpfile=NULL, ind=NULL, useInd=FALSE, legacy=FALSE)
read.dat2listw(file)
write.sn2dat(sn, file)
read.swmdbf2listw(fn, region.id=NULL, style=NULL, zero.policy=NULL)
read_swm_dbf(fn)
write.swmdbf(listw, file, ind, region.id = attr(listw, "region.id"))
write_swm_dbf(listw, file, ind, region.id = attr(listw, "region.id"))
write.sn2DBF(sn, file)

Arguments

Details

Attempts to honour the region.id argument given when reading GWT and SWM/DBF files. If the region IDs given in region.id= do not match the origins or destinations in the GWT file, an error or warning will be thrown, which should be considered carefully. read_swm_dbf is a simplified interface to read.swmdbf2listw When no-neighbour observations are present, it is advised that region.id= be given in read.swmdbf2listw; while the function should read correctly if the minimum and maximum IDs are present as observations with neighbours without region.id= set, reading using read.swmdbf2listw will fail when the minimum or maximum ID observations have no neighbours and region.id= is not given.

Value

read.gwt2nb returns a neighbour "nb" object with the generalised weights stored as a list element called "dlist" of the "GeoDa" attribute; read.swmdbf2listw returns a "listw" object read from a DBF file exported from an ArcGIS SWM object.

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

Luc Anselin (2003) GeoDa 0.9 User's Guide, pp. 80–81, Spatial Analysis Laboratory, Department of Agricultural and Consumer Economics, University of Illinois, Urbana-Champaign, http://geodacenter.github.io/docs/geoda093.pdf; also material formerly at spatial-econometrics.com/data/contents.html

See Also

read.gal

Examples

data(baltimore, package="spData")
STATION <- baltimore$STATION
gwt1 <- read.gwt2nb(system.file("weights/baltk4.GWT", package="spData")[1],
 STATION)
cat(paste("Neighbours list symmetry;", is.symmetric.nb(gwt1, FALSE, TRUE),
 "\n"))
listw1 <- nb2listw(gwt1, style="B", glist=attr(gwt1, "GeoDa")$dist)
tmpGWT <- tempfile()
write.sn2gwt(listw2sn(listw1), tmpGWT)
gwt2 <- read.gwt2nb(tmpGWT, STATION)
cat(paste("Neighbours list symmetry;", is.symmetric.nb(gwt2, FALSE, TRUE),
 "\n"))
diffnb(gwt1, gwt2)
data(oldcol)
tmpMAT <- tempfile()
COL.W <- nb2listw(COL.nb)
write.sn2dat(listw2sn(COL.W), tmpMAT)
listwmat1 <- read.dat2listw(tmpMAT)
diffnb(listwmat1$neighbours, COL.nb, verbose=TRUE)
listwmat2 <- read.dat2listw(system.file("etc/weights/wmat.dat", 
 package="spdep")[1])
diffnb(listwmat1$neighbours, listwmat2$neighbours, verbose=TRUE)
run <- FALSE
if (require("foreign", quietly=TRUE)) run <- TRUE
if (run) {
nc_sf <- sf::st_read(system.file("gpkg/nc.gpkg", package="sf")[1])
nc_sf$UniqueID <- 1:nrow(nc_sf)
fn <- system.file("etc/misc/nc_contiguity_unique_id.dbf", package="spdep")[1]
nc1 <- read.swmdbf2listw(fn, style="B")
nc1
}
if (run) {
nc1a <- read.swmdbf2listw(fn, region.id=as.character(nc_sf$UniqueID),
 style="B")
all.equal(nc1, nc1a)
}
if (run) {
fn <- system.file("etc/misc/nc_contiguity_unique_id_islands.dbf",
 package="spdep")[1]
try(nc1i <- read.swmdbf2listw(fn, style="B"))
nc1i <- read.swmdbf2listw(fn, style="B", zero.policy=TRUE)
nc1ia <- read.swmdbf2listw(fn, region.id=as.character(nc_sf$UniqueID),
 style="B", zero.policy=TRUE)
nc1ia
}
if (run) {
all.equal(nc1i, nc1ia)
}
if (run) {
(GDAL37 <- as.numeric_version(unname(sf_extSoftVersion()["GDAL"])) >= "3.7.0")
file <- "etc/shapes/california.gpkg.zip"
zipfile <- system.file(file, package="spdep")
if (GDAL37) {
    cal <- st_read(zipfile)
} else {
    td <- tempdir()
    bn <- sub(".zip", "", basename(file), fixed=TRUE)
    target <- unzip(zipfile, files=bn, exdir=td)
    cal <- st_read(target)
}
fn <- system.file("etc/misc/contiguity_myid.dbf", package="spdep")[1]
cal1 <- read.swmdbf2listw(fn, style="B")
cal1a <- read.swmdbf2listw(fn, region.id=as.character(cal$MYID), style="B")
all.equal(cal1, cal1a)
}
if (run) {
fn <- system.file("etc/misc/contiguity_unique_id.dbf", package="spdep")[1]
cal2 <- read.swmdbf2listw(fn, style="B")
cal2a <- read.swmdbf2listw(fn, region.id=as.character(cal$UniqueID), style="B")
all.equal(cal2, cal2a)
}
if (run) {
fn <- system.file("etc/misc/contiguity_unique_id_islands.dbf", package="spdep")[1]
try(cal3i <- read.swmdbf2listw(fn, style="B"))
cal3i <- read.swmdbf2listw(fn, style="B", zero.policy=TRUE)
cal3ia <- read.swmdbf2listw(fn, region.id=as.character(cal$UniqueID), style="B", zero.policy=TRUE)
all.equal(cal3i, cal3ia)
}
if (run) {
cal1a_1n_nb <- cal1a$neighbours
cal1a_1n_nb <- droplinks(cal1a_1n_nb, drop=c("158", "180", "215"), sym=TRUE)
cal1a_1n <- nb2listw(cal1a_1n_nb, style="B", zero.policy=TRUE)
cal1a_1n_sn <- listw2sn(cal1a_1n)
file <- tempfile(fileext=".dbf")
write.sn2DBF(cal1a_1n_sn, file)
cal1a_1n_rt <- read.swmdbf2listw(file, region.id=as.character(cal$MYID),
 style="B", zero.policy=TRUE)
all.equal(cal1a_1n$neighbours, cal1a_1n_rt$neighbours)
}
if (run) {
all.equal(cal1a_1n$weights, cal1a_1n_rt$weights, check.attributes=FALSE)
}
if (run) {
cal1_1n_rt <- read.swmdbf2listw(file, style="B", zero.policy=TRUE)
all(isTRUE(all.equal(cal1a_1n$neighbours, cal1_1n_rt$neighbours)))
}
if (run) {
all(isTRUE(all.equal(cal1a_1n$weights, cal1_1n_rt$weights)))
}

Rotate a set of point by a certain angle

Description

Rotate a set of XY coordinates by an angle (in radians)

Usage

Rotation(xy, angle)

Arguments

Value

A 2-columns matrix of the same size as xy giving the rotated coordinates.

Author(s)

F. Guillaume Blanchet

Examples

set.seed(1)
### Create a set of coordinates
coords <- cbind(runif(20), runif(20))

### Create a series of angles
rad <- seq(0, pi, l=20)

opar <- par(mfrow=c(5,4), mar=c(3,3,1,1))
for(i in rad){
	coords.rot <- Rotation(coords, i)
	plot(coords.rot, xlab="", ylab="")
}
par(opar)

### Rotate the coordinates by an angle of 90 degrees
coords.90 <- Rotation(coords, 90*pi/180)
coords.90

plot(coords, xlim=range(rbind(coords.90,coords)[,1]),
 ylim=range(rbind(coords.90,coords)[,2]), asp=1)
points(coords.90, pch=19)

Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models

Description

Rao's score and adjusted Rao's score tests of linear hypotheses applied to a fitted linear model to examine whether either the spatially lagged dependent variable lag or the spatially lagged independent variable(s) WX should be included in the model, or both (SDM). Adjusted tests are provided for lag and WX adapting to the presence of the other, and a joint test for both. The joint test is equal to the unadjusted of one plus the adjusted of the other. In addition, draft tests are added from Koley (2024, section 6) for spatial Durbin error models to examine whether either the spatially lagged error err or the spatially lagged independent variable(s) WX should be included in the model, or both (SDEM); because of orthogonality, no adjusted tests are required.

Usage

SD.RStests(model, listw, zero.policy = attr(listw, "zero.policy"), test = "SDM",
 Durbin = TRUE)

Arguments

Value

A list of class LMtestlist of htest objects, each with:

Note

The results in the example below agree with those in Table 3, p. 22 in Koley and Bera (2024).

Author(s)

Roger Bivand Roger.Bivand@nhh.no, Malabika Koley and Anil K. Bera

References

Malabika Koley and Anil K. Bera (2024) To use, or not to use the spatial Durbin model? – that is the question, Spatial Economic Analysis, 19:1, 30-56, doi:10.1080/17421772.2023.2256810; Malabika Koley (2024) Specification Testing under General Nesting Spatial Model (Appendix C), https://sites.google.com/view/malabikakoley/research.

See Also

lm, lm.RStests

Examples

columbus <- sf::st_read(system.file("shapes/columbus.gpkg", package="spData")[1])
col.gal.nb <- read.gal(system.file("weights/columbus.gal", package="spData")[1])
col.listw <- nb2listw(col.gal.nb, style="W")
lm_obj <- lm(CRIME ~ INC + HOVAL, data=columbus)
summary(lm.RStests(lm_obj, col.listw, test="all"))
res <- SD.RStests(lm_obj, col.listw, test="SDM")
summary(res)
all.equal(unname(res$SDM_Joint$statistic),
 unname(res$SDM_RSlag$statistic + res$SDM_adjRSWX$statistic))
all.equal(unname(res$SDM_Joint$statistic),
 unname(res$SDM_adjRSlag$statistic + res$SDM_RSWX$statistic))
res <- SD.RStests(lm_obj, col.listw, test="SDEM")
summary(res)
all.equal(unname(res$SDEM_Joint$statistic),
 unname(res$SDEM_RSerr$statistic + res$SDEM_RSWX$statistic))
summary(SD.RStests(lm_obj, nb2listw(col.gal.nb, style="C"), test="all"))
summary(SD.RStests(lm_obj, col.listw, test="all", Durbin= ~ INC))
lm_obj0 <- lm(I(scale(CRIME)) ~ 0 + I(scale(INC)) + I(scale(HOVAL)),
 data=columbus)
summary(SD.RStests(lm_obj0, col.listw, test="all"))
columbusNA <- columbus
columbusNA$HOVAL[15] <- NA
lm_objNA <- lm(CRIME ~ INC + HOVAL, data=columbusNA)
summary(SD.RStests(lm_objNA, col.listw, test="all"))

Options for parallel support

Description

Provides support for the use of parallel computation in the parallel package.

Usage

set.mcOption(value)
get.mcOption()
set.coresOption(value)
get.coresOption()
set.ClusterOption(cl)
get.ClusterOption()

Arguments

Details

Options in the spdep package are held in an environment local to the package namespace and not exported. Option values are set and retrieved with pairs of access functions, get and set. The mc option is set by default to FALSE on Windows systems, as they cannot fork the R session; by default it is TRUE on other systems, but may be set FALSE. If mc is FALSE, the Cluster option is used: if mc is FALSE and the Cluster option is NULL no parallel computing is done, or the Cluster option is passed a “cluster” object created by the parallel or snow package for access without being passed as an argument. The cores option is set to NULL by default, and can be used to store the number of cores to use as an integer. If cores is NULL, facilities from the parallel package will not be used.

Value

The option access functions return their current settings, the assignment functions usually return the previous value of the option.

Note

An extended example is shown in the documentation of aple.mc, including treatment of seeding of RNG for multicore/cluster.

Author(s)

Roger Bivand Roger.Bivand@nhh.no

Examples

ls(envir=spdep:::.spdepOptions)
if (require(parallel, quietly=TRUE)) {
 nc <- max(2L, detectCores(logical=FALSE), na.rm = TRUE)-1L
 nc
# set nc to 1L here
 if (nc > 1L) nc <- 1L
#nc <- ifelse(nc > 2L, 2L, nc)
 coresOpt <- get.coresOption()
 coresOpt
 if (!is.na(nc)) {
  invisible(set.coresOption(nc))
  print(exists("moran.mc"))
  if(.Platform$OS.type == "windows") {
# forking not permitted on Windows - start cluster
   print(get.mcOption())
   cl <- makeCluster(get.coresOption())
   print(clusterEvalQ(cl, exists("moran.mc")))
   set.ClusterOption(cl)
   clusterEvalQ(get.ClusterOption(), library(spdep))
   print(clusterEvalQ(cl, exists("moran.mc")))
   clusterEvalQ(get.ClusterOption(), detach(package:spdep))
   set.ClusterOption(NULL)
   print(clusterEvalQ(cl, exists("moran.mc")))
   stopCluster(cl)
  } else {
   mcOpt <- get.mcOption()
   print(mcOpt)
   print(mclapply(1:get.coresOption(), function(i) exists("moran.mc"),
    mc.cores=get.coresOption()))
   invisible(set.mcOption(FALSE))
   cl <- makeCluster(nc)
   print(clusterEvalQ(cl, exists("moran.mc")))
   set.ClusterOption(cl)
   clusterEvalQ(get.ClusterOption(), library(spdep))
   print(clusterEvalQ(cl, exists("moran.mc")))
   clusterEvalQ(get.ClusterOption(), detach(package:spdep))
   set.ClusterOption(NULL)
   print(clusterEvalQ(cl, exists("moran.mc")))
   stopCluster(cl)
   invisible(set.mcOption(mcOpt))
  }
  invisible(set.coresOption(coresOpt))
 }
}

Control checking of spatial object IDs

Description

Provides support for checking the mutual integrity of spatial neighbour weights and spatial data; similar mechanisms are used for passing global verbose and zero.policy options, and for causing functions creating neighbour objects to warn if there are multiple subgraphs.

Usage

set.spChkOption(check)
get.spChkOption()
chkIDs(x, listw)
spNamedVec(var, data)
set.VerboseOption(check)
get.VerboseOption()
set.ZeroPolicyOption(check)
get.ZeroPolicyOption()
set.SubgraphOption(check)
get.SubgraphOption()
set.SubgraphCeiling(value)
get.SubgraphCeiling()
set.NoNeighbourOption(check)
get.NoNeighbourOption()
set.listw_is_CsparseMatrix_Option(check)
get.listw_is_CsparseMatrix_Option()

Arguments

Details

Analysis functions will have an spChk argument by default set to NULL, and will call get.spChkOption() to get the global spatial option for whether to check or not — this is initialised to FALSE, and consequently should not break anything. It can be changed to TRUE using set.spChkOption(TRUE), or the spChk argument can be assigned in analysis functions. spNamedVec() is provided to ensure that rownames are passed on to single columns taken from two-dimensional arrays and data frames.

Value

set.spChkOption() returns the old logical value, get.spChkOption() returns the current logical value, and chkIDs() returns a logical value for the test lack of difference. spNamedVec() returns the selected column with the names set to the row names of the object from which it has been extracted.

Note

The motivation for this mechanism is provided by the observation that spatial objects on a map and their attribute data values need to be linked uniquely, to avoid spurious results. The reordering between the legacy Columbus data set used the earlier publications and that available for download from the Spacestat website is just one example of a common problem.

Author(s)

Roger Bivand Roger.Bivand@nhh.no

Examples

data(oldcol)
rownames(COL.OLD)
data(columbus, package="spData")
rownames(columbus)
get.spChkOption()
oldChk <- set.spChkOption(TRUE)
get.spChkOption()
chkIDs(COL.OLD, nb2listw(COL.nb))
chkIDs(columbus, nb2listw(col.gal.nb))
chkIDs(columbus, nb2listw(COL.nb))
tmp <- try(moran.test(spNamedVec("CRIME", COL.OLD), nb2listw(COL.nb)))
tmp <- try(moran.test(spNamedVec("CRIME", columbus), nb2listw(col.gal.nb)))
tmp <- try(moran.test(spNamedVec("CRIME", columbus), nb2listw(COL.nb)))
set.spChkOption(FALSE)
get.spChkOption()
moran.test(spNamedVec("CRIME", columbus), nb2listw(COL.nb))
tmp <- try(moran.test(spNamedVec("CRIME", columbus), nb2listw(COL.nb),
 spChk=TRUE), silent=TRUE)
set.spChkOption(oldChk)
get.spChkOption()

Spatial 'K'luster Analysis by Tree Edge Removal

Description

This function implements a SKATER procedure for spatial clustering analysis. This procedure essentialy begins with an edges set, a data set and a number of cuts. The output is an object of 'skater' class and is valid for input again.

Usage

skater(edges, data, ncuts, crit, vec.crit, method = c("euclidean", 
    "maximum", "manhattan", "canberra", "binary", "minkowski", 
    "mahalanobis"), p = 2, cov, inverted = FALSE) 

Arguments

Value

A object of skater class with:

Author(s)

Renato M. Assuncao and Elias T. Krainski

References

Assuncao, R.M., Lage J.P., and Reis, E.A. (2002). Analise de conglomerados espaciais via arvore geradora minima. Revista Brasileira de Estatistica, 62, 1-23.

Assuncao, R. M, Neves, M. C., Camara, G. and Freitas, C. da C. (2006). Efficient regionalization techniques for socio-economic geographical units using minimum spanning trees. International Journal of Geographical Information Science Vol. 20, No. 7, August 2006, 797-811

See Also

See Also as mstree

Examples

### loading data
(GDAL37 <- as.numeric_version(unname(sf_extSoftVersion()["GDAL"])) >= "3.7.0")
file <- "etc/shapes/bhicv.gpkg.zip"
zipfile <- system.file(file, package="spdep")
if (GDAL37) {
    bh <- st_read(zipfile)
} else {
    td <- tempdir()
    bn <- sub(".zip", "", basename(file), fixed=TRUE)
    target <- unzip(zipfile, files=bn, exdir=td)
    bh <- st_read(target)
}
### data standardized 
dim(bh)
dpad <- data.frame(scale(as.data.frame(bh)[,5:8]))

### neighboorhod list
bh.nb <- poly2nb(bh)
bh.nb

### calculating costs
lcosts <- nbcosts(bh.nb, dpad)
head(lcosts)

### making listw
nb.w <- nb2listw(bh.nb, lcosts, style="B")
nb.w

### find a minimum spanning tree
mst.bh <- mstree(nb.w,5)
str(mst.bh)

### the mstree plot
par(mar=c(0,0,0,0))
plot(st_geometry(bh), border=gray(.5))
pts <- st_coordinates(st_centroid(bh))
plot(mst.bh, pts, col=2, 
     cex.lab=.6, cex.circles=0.035, fg="blue", add=TRUE)

### three groups with no restriction
res1 <- spdep::skater(edges=mst.bh[,1:2], data=dpad, ncuts=2)

### groups size
table(res1$groups)

### the skater plot
opar <- par(mar=c(0,0,0,0))
plot(res1, pts, cex.circles=0.035, cex.lab=.7)

### the skater plot, using other colors
plot(res1, pts, cex.circles=0.035, cex.lab=.7,
     groups.colors=heat.colors(length(res1$ed)))

### the Spatial Polygons plot
plot(st_geometry(bh), col=heat.colors(length(res1$edg))[res1$groups])

#par(opar)
### EXPERT OPTIONS

### more one partition
res1b <- spdep::skater(res1, dpad, 1)

### length groups frequency
table(res1$groups)

table(res1b$groups)

### thee groups with minimum population 
res2 <- spdep::skater(mst.bh[,1:2], dpad, 2, 200000, bh$Pop)
table(res2$groups)

### thee groups with minimun number of areas
res3 <- spdep::skater(mst.bh[,1:2], dpad, 2, 3, rep(1,nrow(bh)))
table(res3$groups)

### thee groups with minimun and maximun number of areas
res4 <- spdep::skater(mst.bh[,1:2], dpad, 2, c(20,50), rep(1,nrow(bh)))
table(res4$groups)

### if I want to get groups with 20 to 40 elements
res5 <- spdep::skater(mst.bh[,1:2], dpad, 2,
   c(20,40), rep(1,nrow(bh))) ## DON'T MAKE DIVISIONS 
table(res5$groups)

### In this MST don't have groups with this restrictions
### In this case, first I do one division
### with the minimun criteria
res5a <- spdep::skater(mst.bh[,1:2], dpad, 1, 20, rep(1,nrow(bh))) 
table(res5a$groups)

### and do more one division with the full criteria
res5b <- spdep::skater(res5a, dpad, 1, c(20, 40), rep(1,nrow(bh)))
table(res5b$groups)

### and do more one division with the full criteria
res5c <- spdep::skater(res5b, dpad, 1, c(20, 40), rep(1,nrow(bh)))
table(res5c$groups)

### It don't have another divison with this criteria
res5d <- spdep::skater(res5c, dpad, 1, c(20, 40), rep(1,nrow(bh)))
table(res5d$groups)

## Not run: 
data(boston, package="spData")
bh.nb <- boston.soi
dpad <- data.frame(scale(boston.c[,c(7:10)]))
### calculating costs
system.time(lcosts <- nbcosts(bh.nb, dpad))
### making listw
nb.w <- nb2listw(bh.nb, lcosts, style="B")
### find a minimum spanning tree
mst.bh <- mstree(nb.w,5)
### three groups with no restriction
system.time(res1 <- spdep::skater(mst.bh[,1:2], dpad, 2))
library(parallel)
nc <- max(2L, detectCores(logical=FALSE), na.rm = TRUE)-1L
# set nc to 1L here
if (nc > 1L) nc <- 1L
coresOpt <- get.coresOption()
invisible(set.coresOption(nc))
if(!get.mcOption()) {
# no-op, "snow" parallel calculation not available
  cl <- makeCluster(get.coresOption())
  set.ClusterOption(cl)
}
### calculating costs
system.time(plcosts <- nbcosts(bh.nb, dpad))
all.equal(lcosts, plcosts, check.attributes=FALSE)
### making listw
pnb.w <- nb2listw(bh.nb, plcosts, style="B")
### find a minimum spanning tree
pmst.bh <- mstree(pnb.w,5)
### three groups with no restriction
system.time(pres1 <- spdep::skater(pmst.bh[,1:2], dpad, 2))
if(!get.mcOption()) {
  set.ClusterOption(NULL)
  stopCluster(cl)
}
all.equal(res1, pres1, check.attributes=FALSE)
invisible(set.coresOption(coresOpt))

## End(Not run)

Spatial correlogram

Description

Spatial correlograms for Moran's I and the autocorrelation coefficient, with print and plot helper functions.

Usage

sp.correlogram(neighbours, var, order = 1, method = "corr",
 style = "W", randomisation = TRUE, zero.policy = NULL, spChk=NULL)
## S3 method for class 'spcor'
plot(x, main, ylab, ylim, ...)
## S3 method for class 'spcor'
print(x, p.adj.method="none", ...)

Arguments

Details

The print function also calculates the standard deviates of Moran's I or Geary's C and a two-sided probability value, optionally using p.adjust to correct by the nymber of lags. The plot function plots a bar from the estimated Moran's I, or Geary's C value to +/- twice the square root of its variance (in previous releases only once, not twice). The table includes the count of included observations in brackets after the lag order. Care needs to be shown when interpreting results for few remaining included observations as lag order increases.

Value

returns a list of class spcor:

Author(s)

Roger Bivand, Roger.Bivand@nhh.no

References

Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, pp. 118–122, Martin, R. L., Oeppen, J. E. 1975 The identification of regional forecasting models using space-time correlation functions, Transactions of the Institute of British Geographers, 66, 95–118.

See Also

nblag, moran, p.adjust

Examples

nc.sids <- st_read(system.file("shapes/sids.gpkg", package="spData")[1], quiet=TRUE)
rn <- as.character(nc.sids$FIPS)
ncCC89_nb <- read.gal(system.file("weights/ncCC89.gal", package="spData")[1],
 region.id=rn)
ft.SID74 <- sqrt(1000)*(sqrt(nc.sids$SID74/nc.sids$BIR74) +
  sqrt((nc.sids$SID74+1)/nc.sids$BIR74))
tr.SIDS74 <- ft.SID74*sqrt(nc.sids$BIR74)
cspc <- sp.correlogram(ncCC89_nb, tr.SIDS74, order=8, method="corr",
 zero.policy=TRUE)
print(cspc)
plot(cspc)
Ispc <- sp.correlogram(ncCC89_nb, tr.SIDS74, order=8, method="I",
 zero.policy=TRUE)
print(Ispc)
print(Ispc, "bonferroni")
plot(Ispc)
Cspc <- sp.correlogram(ncCC89_nb, tr.SIDS74, order=8, method="C",
 zero.policy=TRUE)
print(Cspc)
print(Cspc, "bonferroni")
plot(Cspc)
drop.no.neighs <- !(1:length(ncCC89_nb) %in% which(card(ncCC89_nb) == 0))
sub.ncCC89.nb <- subset(ncCC89_nb, drop.no.neighs)
plot(sp.correlogram(sub.ncCC89.nb, subset(tr.SIDS74,  drop.no.neighs),
 order=8, method="corr"))

Mantel-Hubert spatial general cross product statistic

Description

A permutation test for the spatial general cross product statistic with Moran (C_{ij} = z_i z_j), Geary (C_{ij} = (z_i - z_j)^2), and Sokal (C_{ij} = |z_i - z_j|) criteria, for z_i = (x_i - \bar{x}) / \sigma_{x}. plot.mc.sim is a helper function to plot the outcomes of the permutation test.

Usage

sp.mantel.mc(var, listw, nsim, type = "moran", zero.policy = attr(listw, "zero.policy"),
 alternative = "greater", spChk=NULL, return_boot=FALSE)
## S3 method for class 'mc.sim'
plot(x, xlim, xlab, main, sub, ..., ptype="density")

Arguments

Value

A list with class htest and mc.sim containing the following components:

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 22-24, Haining, R. 1990 Spatial data analysis in the social and environmental sciences, Cambridge: Cambridge University Press, p. 230–1. The function has been checked against general matrix code posted to the r-help list by Ben Bolker on 1 May 2001; another mantel() function is in the vegan package.

See Also

moran.mc, joincount.mc, geary.mc

Examples

data(oldcol)
sim1 <- sp.mantel.mc(COL.OLD$CRIME, nb2listw(COL.nb),
 nsim=99, type="geary", alternative="two.sided")
sim1
plot(sim1)
sp.mantel.mc(COL.OLD$CRIME, nb2listw(COL.nb), nsim=99,
 type="sokal", alternative="two.sided")
sp.mantel.mc(COL.OLD$CRIME, nb2listw(COL.nb), nsim=99,
 type="moran")

Return package version number

Description

The function retreives package version and build information

Usage

spdep(build = FALSE)

Arguments

Value

a character vector with one or two elements

Author(s)

Roger Bivand Roger.Bivand@nhh.no

Defunct Functions in Package spdep