This vignette tracks the legacy nb vignette, which was based on part of the first (2008) edition of ASDAR. It adds hints to the code in the nb vignette to use the sf vector representation instead of the sp vector representation to create neighbour objects. .

This is a summary of the results below:

In general, if you need to reproduce results from using

`"Spatial"`

objects in**spdep**, coerce sf objects to sp objects before constructing neighbour objects (particularly if polygon centroids are used for point representation).However, for new work, you should use

`"sf"`

objects read in using**sf**.From

**spdep**1.1-7, a number of steps have been taken to choose more efficient approaches especially for larger data sets, using functions in**sf**and the approximate nearest neighbour (ANN) implementation in**dbscan**rather than**RANN**.

We’ll use the whole NY 8 county set of boundaries, as they challenge the implementations more than just the Syracuse subset. The description of the input geometries from ADSAR is: New York leukemia: used and documented extensively in Waller and Gotway (2004) and with data formerly made available in Chap. 9 of `http://web1.sph.emory.edu/users/lwaller/ch9index.htm`

; the data import process is described in the help file of NY_data in **spData**; geometries downloaded from the CIESIN server at https://sedac.ciesin.columbia.edu/data/set/acrp-boundary-1992/data-download, file /pub/census/usa/tiger/ny/bna_st/t8_36.zip, and extensively edited; a zip archive NY_data.zip of shapefiles and a GAL format neighbours list is on the book website. Further, the zipfile is now at a new location requiring login. The object listw_NY is directly imported from nyadjwts.dbf on the Waller & Gotway (2004) chapter 9 website.

The version of the New York 8 counties geometries used in ASDAR and included as a shapefile in spdep was converted from the original BNA file using an external utility program to convert to MapInfo format and converted on from there using GDAL 1.4.1 (the OGR BNA driver was not then available; it entered OGR at 1.5.0, release at the end of 2007), and contains invalid geometries. What was found in mid-2007 was that included villages were in/excluded by in-out umbilical cords to the boundary of the enclosing tract, when the underlying BNA file was first converted to MapInfo (holes could not exist then).

Here we will use a GPKG file created as follows (rgdal could also be used with the same output; GDAL here is built with GEOS, so the BNA vector driver will use geometry tests: The BNA driver supports reading of polygons with holes or lakes. It determines what is a hole or a lake only from geometrical analysis (inclusion, non-intersection tests) and ignores completely the notion of polygon winding (whether the polygon edges are described clockwise or counter-clockwise). GDAL must be built with GEOS enabled to make geometry test work.):

```
library(sf)
sf_bna <- st_read("t8_36.bna", stringsAsFactors=FALSE)
table(st_is_valid(sf_bna))
sf_bna$AREAKEY <- gsub("\\.", "", sf_bna$Primary.ID)
data(NY_data, package="spData")
key <- as.character(nydata$AREAKEY)
sf_bna1 <- sf_bna[match(key, sf_bna$AREAKEY), c("AREAKEY")]
sf_bna2 <- merge(sf_bna1, nydata, by="AREAKEY")
sf_bna2_utm18 <- st_transform(sf_bna2, "+proj=utm +zone=18 +datum=NAD27")
st_write(sf_bna2_utm18, "NY8_bna_utm18.gpkg")
```

Since the **spdep** package was created, *spatial weights* objects have been constructed as lists with three components and a few attributes, in old-style class `listw`

objects. The first component of a `listw`

object is an `nb`

object, a list of `n`

integer vectors, with at least a character vector `region.id`

attribute with `n`

unique values (like the `row.names`

of a `data.frame`

object); `n`

is the number of spatial entities. Component `i`

of this list contains the integer identifiers of the neighbours of `i`

as a sorted vector with no duplication and values in `1:n`

; if `i`

has no neighbours, the component is a vector of length `1`

with value `0L`

. The `nb`

object may contain an attribute indicating whether it is symmetric or not, that is whether `i`

is a neighbour of `j`

implies that `j`

is a neighbour of `i`

. Some neighbour definitions are symmetric by construction, such as contiguities or distance thresholds, others are asymmetric, such as `k`

-nearest neighbours. The `nb`

object redundantly stores both `i`

-`j`

and `j`

-`i`

links.

The second component of a `listw`

object is a list of `n`

numeric vectors, each of the same length as the corresponding non-zero vectors in the `nb`

object. These give the values of the spatial weights for each `i`

-`j`

neighbour pair. It is often the case that while the neighbours are symmetric by construction, the weights are not, as for example when weights are *row-standardised* by dividing each row of input weights by the count of neighbours or cardinality of the neighbour set of `i`

. In the `nb2listw`

function, it is also possible to pass through general weights, such as inverse distances, shares of boundary lengths and so on.

The third component of a `listw`

object records the `style`

of the weights as a character code, with `"B"`

for binary weights taking values zero or one (only one is recorded), `"W"`

for row-standardised weights, and so on. In order to subset `listw`

objects, knowledge of the `style`

may be necessary.

First some housekeeping and setup to permit this vignette to be built when packages are missing or out-of-date:

```
if (!suppressPackageStartupMessages(require(sf, quietly=TRUE))) {
message("install the sf package")
dothis <- FALSE
}
if (dothis) sf_extSoftVersion()
```

```
## GEOS GDAL proj.4 GDAL_with_GEOS USE_PROJ_H PROJ
## "3.10.0dev" "3.3.2" "8.1.1" "true" "true" "8.1.1"
```

Let us read the GPKG file with valid geometries in to ‘sf’ and ‘sp’ objects:

```
NY8_sf <- st_read(system.file("shapes/NY8_bna_utm18.gpkg", package="spData"), quiet=TRUE)
table(st_is_valid(NY8_sf))
```

```
##
## TRUE
## 281
```

Here we first generate a queen contiguity nb object using the legacy spdep approach. This first either uses a pre-computed list of vectors of probable neighbours or finds intersecting bounding boxes internally. Then the points on the boundaries of each set of polygons making up an observation are checked for a distance less than snap to any of the points of the set of polygons making up an observation included in the set of candidate neighbours. Because contiguity is symmetric, only i to j contiguities are tested. A queen contiguity is found as soon as one point matches, a rook contiguity as soon as two points match:

```
suppressPackageStartupMessages(library(spdep))
reps <- 10
eps <- sqrt(.Machine$double.eps)
system.time(for(i in 1:reps) NY8_sf_1_nb <- poly2nb(NY8_sf, queen=TRUE, snap=eps))/reps
```

```
## user system elapsed
## 0.0988 0.0004 0.0994
```

Using spatial indices to check intersection of polygons is much faster than the legacy method in poly2nb. From **spdep** 1.1-7, use is made of GEOS through **sf** to find candidate neighbours when `foundInBox=NULL`

, the default value. Because contiguity is symmetric by definition, `foundInBox=`

only requires intersections for higher indices, leading to a slight overhead to remove duplicates, as `st_intersects()`

reports both `i j`

ans `j i`

relationships. As `st_intersects()`

does not report whether neighbours are `queen`

or `rook`

, a further step is needed to distinguish the two cases.

`NY8_sf_1_nb`

```
## Neighbour list object:
## Number of regions: 281
## Number of nonzero links: 1632
## Percentage nonzero weights: 2.066843
## Average number of links: 5.807829
```

spdep::poly2nb uses two heuristics, first to find candidate neighbours from intersecting polygons (`st_intersects()`

), and second to use the symmetry of the relationship to halve the number of remaining tests. This means that performance is linear in n, but with overhead for identifying candidates, and back-filling symmetric neighbours. Further, `spdep::poly2nb()`

stops searching for queen contiguity as soon as the first neighbour point is found within snap distance (if not identical, which is tested first); a second neighbour point indicates rook contiguities. For details of alternatives for spherical geometries, see section @ref(spher-poly2nb) below.

Next, we explore a further possible source of differences in neighbour object reproduction, using the original version of the tract boundaries used in ASDAR, but with some invalid geometries as mentioned earlier:

```
NY8_sf_old <- st_read(system.file("shapes/NY8_utm18.shp", package="spData"), quiet=TRUE)
table(st_is_valid(NY8_sf_old))
```

```
##
## FALSE TRUE
## 5 276
```

We can see that there are a number of differences between the neighbour sets derived from the fully valid geometries and the older partly invalid set:

```
try(NY8_sf_old_1_nb <- poly2nb(NY8_sf_old), silent = TRUE)
all.equal(NY8_sf_old_1_nb, NY8_sf_1_nb, check.attributes=FALSE)
```

```
## [1] "Component 57: Numeric: lengths (4, 5) differ"
## [2] "Component 58: Numeric: lengths (5, 6) differ"
## [3] "Component 66: Numeric: lengths (7, 11) differ"
## [4] "Component 73: Numeric: lengths (4, 5) differ"
## [5] "Component 260: Numeric: lengths (8, 9) differ"
```

Using `st_make_valid()`

to make the geometries valid:

```
NY8_sf_old_val <- st_make_valid(NY8_sf_old, dist=0)
table(st_is_valid(NY8_sf_old_val))
```

```
##
## TRUE
## 281
```

we also see that the geometry type of the geometry column changes:

`class(st_geometry(NY8_sf_old))`

`## [1] "sfc_POLYGON" "sfc"`

`class(st_geometry(NY8_sf_old_val))`

`## [1] "sfc_GEOMETRY" "sfc"`

and checking the `"sfg"`

objects, two now have objects of different topological dimensions.

`table(sapply(st_geometry(NY8_sf_old_val), function(x) class(x)[[2]]))`

```
##
## GEOMETRYCOLLECTION MULTIPOLYGON POLYGON
## 2 2 277
```

This can be remedied using `st_collection_extract()`

to get the polygon objects:

```
NY8_sf_old_val <- st_collection_extract(NY8_sf_old_val, "POLYGON")
table(sapply(st_geometry(NY8_sf_old_val), function(x) class(x)[[2]]))
```

```
##
## MULTIPOLYGON
## 281
```

However, in making the geometries valid, we change the geometries, so the new sets of neighbours still differ from those made with the valid geometries in the same ways as before imposing validity:

```
try(NY8_sf_old_1_nb_val <- poly2nb(NY8_sf_old_val), silent = TRUE)
all.equal(NY8_sf_old_1_nb_val, NY8_sf_1_nb, check.attributes=FALSE)
```

```
## [1] "Component 57: Numeric: lengths (4, 5) differ"
## [2] "Component 58: Numeric: lengths (5, 6) differ"
## [3] "Component 66: Numeric: lengths (7, 11) differ"
## [4] "Component 73: Numeric: lengths (4, 5) differ"
## [5] "Component 260: Numeric: lengths (8, 9) differ"
```

The neighbour sets are the same for the old boundaries with or without imposing validity:

`all.equal(NY8_sf_old_1_nb_val, NY8_sf_old_1_nb, check.attributes=FALSE)`

`## [1] TRUE`

`knearneigh()`

and `dnearneigh()`

require point support, so decisions must be taken about how to place the point in the areal object. We can use `st_centroid()`

to get the centroids, using the `of_largest_polygon=TRUE`

argument to make sure that the centroid is that of the largest polygon id the observation is made up of more than one external ring:

`NY8_ct_sf <- st_centroid(st_geometry(NY8_sf), of_largest_polygon=TRUE)`

or `st_point_on_surface()`

which guarantees that the point will fall on the surface of a member polygon:

`NY8_pos_sf <- st_point_on_surface(st_geometry(NY8_sf))`

or indeed taking the centre of the largest inscribed circle (the function returns a radius line segment, so we choose the central point, not the point on the circle):

```
if (unname(sf_extSoftVersion()["GEOS"] >= "3.9.0"))
NY8_cic_sf <- st_cast(st_inscribed_circle(st_geometry(NY8_sf), nQuadSegs=0), "POINT")[(1:(2*nrow(NY8_sf)) %% 2) != 0]
```

We need to check whether coordinates are planar or not:

`st_is_longlat(NY8_ct_sf)`

`## [1] FALSE`

From this, we can check the graph-based neighbours (planar coordinates only):

```
suppressPackageStartupMessages(require(deldir))
NY84_nb <- tri2nb(NY8_ct_sf)
if (require(dbscan, quietly=TRUE)) {
NY85_nb <- graph2nb(soi.graph(NY84_nb, NY8_ct_sf))
} else NY85_nb <- NULL
NY86_nb <- graph2nb(gabrielneigh(NY8_ct_sf))
NY87_nb <- graph2nb(relativeneigh(NY8_ct_sf))
```

K-nearest neighbours use the coordinate matrices, and can handle Great Circle distances, but this is not demonstrated here, as the data set used is planar, in which case `dbscan::kNN()`

in 2D or 3D building a kd-tree is used:

`system.time(for (i in 1:reps) NY88_nb_sf <- knn2nb(knearneigh(NY8_ct_sf, k=1)))/reps`

```
## user system elapsed
## 0.0490 0.0006 0.0498
```

Legacy code may be used omitting the kd-tree:

`system.time(for (i in 1:reps) NY89_nb_sf <- knn2nb(knearneigh(NY8_ct_sf, k=1, use_kd_tree=FALSE)))/reps`

```
## user system elapsed
## 0.0495 0.0007 0.0503
```

Distance neighbours need a threshold - `nbdists`

shows the maximum distance to first nearest neighbour:

```
dsts <- unlist(nbdists(NY88_nb_sf, NY8_ct_sf))
summary(dsts)
```

```
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 82.85 912.85 1801.11 3441.04 4461.26 17033.11
```

`max_1nn <- max(dsts)`

`dnearneigh`

can also handle Great Circle distances, but this is not demonstrated here, as the data set used is planar:

`system.time(for (i in 1:reps) NY810_nb <- dnearneigh(NY8_ct_sf, d1=0, d2=0.75*max_1nn))/reps`

```
## user system elapsed
## 0.0639 0.0003 0.0644
```

By default, the function uses `dbscan::frNN()`

to build a kd-tree in 2D or 3D which is then used to find distance neighbours. For small n, the argument `use_kd_tree=FALSE`

may speed up computation a little by reverting to legacy code not building a kd-tree first, but in general the differences are so small that the user will not notice:

`system.time(for (i in 1:reps) NY811_nb <- dnearneigh(NY8_ct_sf, d1=0, d2=0.75*max_1nn, use_kd_tree=FALSE))/reps`

```
## user system elapsed
## 0.0493 0.0005 0.0499
```

Spherical point-based neighbours may be found using Great Circle distances. These have been used for many years, but the switch of **sf** 1.0-0 to use **s2** by default has opened up new opportunities where spatial indexing on the sphere may help.

```
pts_ll <- st_transform(NY8_ct_sf, "OGC:CRS84")
st_is_longlat(pts_ll)
```

`## [1] TRUE`

If the input geometries are in geographical coordinates, and `sf_use_s2()`

is `TRUE`

, `knearneigh()`

will use spatially indexed points and `s2::s2_closest_edges()`

(see https://github.com/r-spatial/s2/issues/125#issuecomment-860107442)

`(old_use_s2 <- sf_use_s2())`

`## [1] TRUE`

and performs well with also with larger data sets:

```
sf_use_s2(TRUE)
system.time(for (i in 1:reps) pts_ll1_nb <- knn2nb(knearneigh(pts_ll, k=6)))/reps
```

```
## user system elapsed
## 0.0223 0.0001 0.0224
```

For this smaller data set, the legacy approach without spatial indexing is adequate, but slows down as the number of observations increases:

`sf_use_s2(FALSE)`

`## Spherical geometry (s2) switched off`

`system.time(for (i in 1:reps) pts_ll2_nb <- knn2nb(knearneigh(pts_ll, k=6)))/reps`

```
## user system elapsed
## 0.0190 0.0001 0.0191
```

The WGS84 ellipsoid Great Circle distances differ a very little from the **s2** spherical distances, yielding output that here diverges for two tract centroids:

`all.equal(pts_ll1_nb, pts_ll2_nb, check.attributes=FALSE)`

```
## [1] "Component 52: Mean relative difference: 1.466667"
## [2] "Component 124: Mean relative difference: 0.0251046"
```

`pts_ll1_nb[[52]]`

`## [1] 15 38 48 49 50 53`

`pts_ll2_nb[[52]]`

`## [1] 37 38 48 49 50 53`

`pts_ll1_nb[[124]]`

`## [1] 117 122 123 125 133 134`

`pts_ll2_nb[[124]]`

`## [1] 116 117 123 125 133 134`

`sf_use_s2(old_use_s2)`

`## Spherical geometry (s2) switched on`

Distance neighbours are more problematic. While `nbdists()`

works well with **s2** spherical coordinates, none of the tried adaptations for `dnearneigh()`

work adequately yet. An argument `avoid_s2=`

is TRUE by default, using the legacy brute-force approach, but only calculating distances from `i`

to `j`

and copying those to `j`

to `i`

through symmetry. Further, the legacy approach only calculates distances once, and selects the observations between `d1`

and `d2`

as neighbours. The distance metric is alway `"km"`

.

If we permit **s2** methods to run, without other arguments set, buffers are constructed around the points to `d2`

, then these buffers are intersected with the points:

`system.time(pts_ll3_nb <- dnearneigh(pts_ll, d1=0, d2=0.75*max_1nn, use_s2=TRUE))`

```
## user system elapsed
## 0.843 0.000 0.845
```

Time can be saved by reducing the cell count used to approximate the buffer:

`system.time(pts_ll4_nb <- dnearneigh(pts_ll, d1=0, d2=0.75*max_1nn, use_s2=TRUE, max_cells=500))`

```
## user system elapsed
## 1.798 0.000 1.801
```

Alternatively, brute-force spherical distances can be used, not (yet) using spatial indexing; performance also deteriorates with increasing numbers of observations:

`system.time(for (i in 1:(reps/5)) pts_ll5_nb <- dnearneigh(pts_ll, d1=0, d2=0.75*max_1nn, use_s2=TRUE, dwithin=TRUE))/(reps/5)`

```
## user system elapsed
## 0.0545 0.0000 0.0550
```

For the moment, `avoid_s2=`

is `TRUE`

by default as more remains to be examined to find out how to benefit from spherical spatial indexing, also because all the **s2** approaches need two runs to handle the `d1`

-`d2`

interval, and none of them benefit from symmetry:

`system.time(for (i in 1:reps) pts_ll6_nb <- dnearneigh(pts_ll, d1=0, d2=0.75*max_1nn))/reps`

```
## user system elapsed
## 0.0105 0.0000 0.0105
```

It also turns out that when **sf** functions are used to find contiguity neighbours, **s2** spatial indexing functionality is accessed in finding candidate neighbours in intersecting geometries.

```
NY8_sf_ll <- st_transform(NY8_sf, "OGC:CRS84")
st_is_longlat(NY8_sf_ll)
```

`## [1] TRUE`

The timings are a little slower when `st_intersects()`

hands off geometry predicates to `s2_intersects_matrix()`

, but the results are the same, and because spatial indexing is used, this scles well for larger data sets:

`system.time(for (i in 1:reps) NY8_sf_1_nb_ll <- poly2nb(NY8_sf_ll, queen=TRUE, snap=eps))/reps`

```
## user system elapsed
## 0.1446 0.0003 0.1451
```

`all.equal(NY8_sf_1_nb, NY8_sf_1_nb_ll, check.attributes=FALSE)`

`## [1] TRUE`