From 00b6f8b0b0ebaf04cd2c8c72c1df7718191529de Mon Sep 17 00:00:00 2001 From: Derek Sollberger Date: Sat, 9 Sep 2023 06:56:08 -0700 Subject: [PATCH] cohort 1 (#8) * cohort 1 chapter 14 * Add tmap --------- Co-authored-by: Jon Harmon --- 14_proximity-and-areal-data.Rmd | 338 +++++++++++++++++++++++++++++++- DESCRIPTION | 5 + images/Pennsylvania_voronoi.png | Bin 0 -> 39036 bytes images/mappennsylvania-1.png | Bin 0 -> 18904 bytes images/mapsirs-1.png | Bin 0 -> 39402 bytes 5 files changed, 339 insertions(+), 4 deletions(-) create mode 100644 images/Pennsylvania_voronoi.png create mode 100644 images/mappennsylvania-1.png create mode 100644 images/mapsirs-1.png diff --git a/14_proximity-and-areal-data.Rmd b/14_proximity-and-areal-data.Rmd index ac9f67b..a53d59c 100644 --- a/14_proximity-and-areal-data.Rmd +++ b/14_proximity-and-areal-data.Rmd @@ -2,12 +2,342 @@ **Learning objectives:** -- THESE ARE NICE TO HAVE BUT NOT ABSOLUTELY NECESSARY +* consider the definition of areal data +* discuss matters of graph theory +* explore various methods of finding neighbors -## SLIDE 1 {-} +```{r, message = FALSE, warning = FALSE} +library("dbscan") #density-based clustering +library("igraph") #graph networks +library("Matrix") #for sparse representation +library("sf") #simple features +library("spatialreg") #spatial regression analysis +library("spdep") #spatial dependence +library("tmap") #quick, thematic maps + +data(pol_pres15, package = "spDataLarge") #Poland 2015 election data + +sessionInfo() +``` + + +## Areal Data + +*Areal units* of observation are very often used when simultaneous observations are aggregated within non-overlapping boundaries. + +**Example:** Lung cancer SIR (standardized incidence rate) in Pennsylvania + +![image credit: Paula Moraga](images/mapsirs-1.png) + +## Proximity Data + +By *proximity*, we mean closeness in ways that make sense for the data generation processes thought to be involved. In cross-sectional geostatistical analysis with point support, measured distance makes sense for typical data generation processes. + +**Example:** Voronoi diagram of Pennsylvania + +![image credit: John Nerbonne](images/Pennsylvania_voronoi.png) + +## Support + +By *support* of data we mean the physical size (length, area, volume) associated with an individual observational unit + +* It is possible to represent the support of areal data by a point, despite the fact that the data have polygonal support +* When the intrinsic support of the data is represented as points, but the underlying process is **between proximate observations** rather than driven chiefly by distance between observations +* risk of misrepresenting the footprint of the underlying spatial processes + +## Representing Proximity + +Ideas for spatial autocorrelation + +* (graph theory) undirected graph, and its neighbors, or +* (geospatial) variogram + +But what about + +* islands? +* disconnected subgraphs? +* sparse areas (cutoff by distance threshold) + +## spdep package + +`spdep` package: [spatial dependence](https://cran.r-project.org/web/packages/spdep/index.html) + +* `nb` class for neighbor + + - list of length `0L` for no neighbors + +* `listw` object + + 1. `nb` object + 2. list of numerical weights + 3. how the weights were calculated + +* `spatialreg` package now has the functions for constructing and handling neighbour and spatial weights objects, tests for spatial autocorrelation, and model fitting functions that used to be in `spdep` + + +## Example: Poland 2015 Election + +```{r} +pol_pres15 |> + subset(select = c(TERYT, name, types)) |> + head() +``` + +```{r} +# tmap +tm_shape(pol_pres15) + tm_fill("types") +``` + +For safety’s sake, we impose topological validity: + +```{r} +if (!all(st_is_valid(pol_pres15))) + pol_pres15 <- st_make_valid(pol_pres15) +``` + + +## Contiguous Neighbors + +For each observation, the `poly2nb` function checks whether + +* at least one (`queen = TRUE`) +* at least two ("rook", `queen = FALSE`) + +points are within `snap` distance of each other. + +```{r} +pol_pres15 |> poly2nb(queen = TRUE) -> nb_q +``` + +```{r} +print(nb_q) +``` + +* `s2` spherical coordinates are used by default +* symmetric relationships assumed +* `row.names` may be customized + +### Connected + +Are the data connected? (Some model estimation techniques do not support graphs that are not connected.) + +```{r, eval = FALSE} +(nb_q |> n.comp.nb())$nc +# result: 1 for TRUE (more than one for FALSE) +``` + +
+verbose code +```{r} +#library(Matrix, warn.conflicts = FALSE) +#library(spatialreg, warn.conflicts = FALSE) +nb_q |> + nb2listw(style = "B") |> + as("CsparseMatrix") -> smat +#library(igraph, warn.conflicts = FALSE) +smat |> graph.adjacency() -> g1 + +g1 |> count_components() +``` + +
+ + +## Graph-Based Neighbors + +The simplest form is by using triangulation, here using the `deldir` package + +```{r} +# get centroids and save their coordinates +pol_pres15 |> + st_geometry() |> + st_centroid(of_largest_polygon = TRUE) -> coords + +# triangulation +(coords |> tri2nb() -> nb_tri) +``` + +### How Far Away are the Neighbors? + +```{r} +# results in meters +nb_tri |> + nbdists(coords) |> + unlist() |> + summary() +``` + +### Sphere of Influence + +The Sphere of Influence `soi.graph` function takes triangulated neighbours and prunes off neighbour relationships represented by edges that are unusually long for each point. + +```{r} +(nb_tri |> + soi.graph(coords) |> + graph2nb() -> nb_soi) +``` + +```{r} +# Poland +pol_pres15 |> + st_geometry() |> + plot(border = "grey", lwd = 0.5) +``` + +```{r} +# triangulation +plot(nb_tri, + coords = coords, points = FALSE, lwd = 0.5) +``` + +```{r} +# sphere of influence +plot(nb_soi, + coords = coords, points = FALSE, lwd = 0.5) +``` + + +## Distance-Based Neighbors + +* Distance-based neighbours can be constructed using `dnearneigh`, with a distance band with lower `d1=` and upper `d2=` bounds controlled by the `bounds=` argument +* The `knearneigh` function for -nearest neighbours returns a `knn` object, converted to an `nb` object using `knn2nb` +* Computation speed boost through `dbscan` package +* The `nbdists` function returns the length of neighbour relationship edges + +```{r} +coords |> + knearneigh(k = 1) |> + knn2nb() |> + nbdists(coords) |> + unlist() |> + summary() +``` + +Here the largest first nearest neighbour distance is just under 18 km, so using this as the upper threshold gives certainty that all units will have at least one neighbour. + +```{r} +# maybe no neighbors +coords |> dnearneigh(0, 16000) -> nb_d16 + +# at least one neighbor +coords |> dnearneigh(0, 18000) -> nb_d18 +``` + +* Adding 300 m to the threshold gives us a neighbour object with no no-neighbour units, and all units can be reached from all others across the graph. + +```{r} +# connected graph +coords |> dnearneigh(0, 18300) -> nb_d183 +``` + +It is possible to control the numbers of neighbours directly using -nearest neighbours, either accepting asymmetric neighbours + +```{r} +coords |> knearneigh(k = 6) -> knn_k6 + +# asymmetrical +knn_k6 |> knn2nb() -> nb_k6 + +# symmetrical +knn_k6 |> knn2nb(sym = TRUE) -> nb_k6s +``` + +## Weights Specification + +Once neighbour objects are available, further choices need to be made in specifying the weights objects. + +* The `nb2listw` function is used to create a `listw` weights object with an `nb` object, a matching list of weights vectors, and a style specification +* Because handling no-neighbour observations now begins to matter, the `zero.policy=` argument is introduced (default: `FALSE`) +* `n`: number of observations +* $S_{0}$: sum of weights + + +The "B" binary style gives a weight of unity to each neighbour relationship, and typically up-weights units with no boundaries on the edge of the study area, having a higher count of neighbours. + +```{r} +nb_q |> nb2listw(style = "B") -> lw_q_B + +lw_q_B |> + spweights.constants() |> + data.frame() |> + subset(select = c(n, S0)) +``` + +The "W" row-standardised style up-weights units around the edge of the study area that necessarily have fewer neighbours. This style first gives a weight of unity to each neighbour relationship, then it divides these weights by the per unit sums of weights (caution: avoid no-neighbors) + +```{r} +nb_q |> nb2listw(style = "W") -> lw_q_W + +lw_q_W |> + spweights.constants() |> + data.frame() |> + subset(select = c(n, S0)) +``` + +### Inverse Distance Weights + +```{r} +nb_d183 |> + nbdists(coords) |> + lapply(function(x) 1/(x/1000)) -> gwts +``` + +No-neighbour handling is by default to prevent the construction of a weights object, making the analyst take a position on how to proceed. + +```{r} +(nb_d183 |> nb2listw(glist=gwts, style="B") -> lw_d183_idw_B) |> + spweights.constants() |> + data.frame() |> + subset(select=c(n, S0)) +``` + +Use can be made of the `zero.policy=` argument to many functions used with `nb` and `listw` objects. + +```{r} +(nb_d16 |> + nb2listw(style="B", zero.policy=TRUE) |> + spweights.constants(zero.policy=TRUE) |> + data.frame() |> + subset(select=c(n, S0))) +``` + + +## Higher-Order Neighbors + +If we wish to create an object showing to neighbours, where $i$ is a neighbour of $j$, and $j$ in turn is a neighbour of $k$, so taking two steps on the neighbour graph, we can use `nblag` (automatically removes $i$ to $i$ self-neighbours) + +```{r} +nb_q |> nblag(2) -> nb_q2 +``` + +Returning to the graph representation of the same neighbour object, we can ask how many steps might be needed to traverse the graph? + +```{r} +igraph::diameter(g1) #where g1 is a graph object +``` + +We step out from each observation across the graph to establish the number of steps needed to reach each other observation by the shortest path (creating an $n \times n$ matrix `sps`), once again finding the same maximum count. + +```{r} +g1 |> shortest.paths() -> sps +sps |> apply(2, max) -> spmax + +spmax |> max() +``` + +The municipality with the maximum count is called Lutowiska, close to the Ukrainian border in the far south east of the country. + +```{r} +mr <- which.max(spmax) +pol_pres15$name0[mr] +``` + +```{r} +pol_pres15$sps1 <- sps[,mr] +tm_shape(pol_pres15) + + tm_fill("sps1", title = "Shortest path\ncount") +``` -- ADD SLIDES AS SECTIONS (`##`). -- TRY TO KEEP THEM RELATIVELY SLIDE-LIKE; THESE ARE NOTES, NOT THE BOOK ITSELF. ## Meeting Videos {-} diff --git a/DESCRIPTION b/DESCRIPTION index 6eed786..65efddb 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -13,8 +13,10 @@ Imports: class, colorspace, cubelyr, + dbscan, dplyr, ggplot2, + igraph, maps, MASS, randomForest, @@ -23,9 +25,12 @@ Imports: rnaturalearthdata, s2, sf, + spatialreg, spDataLarge, + spdep, stars, tidyr, + tmap, units, xts Remotes: diff --git a/images/Pennsylvania_voronoi.png b/images/Pennsylvania_voronoi.png new file mode 100644 index 0000000000000000000000000000000000000000..ff9614638963ec30b58bbd3cc9f8698036af931c GIT binary patch literal 39036 zcmbqbhd-75`?twFNyw-ZLXspa*?SYR_s-sX&m_Ck$;!$~60)*MLbCTJD=RCT-{txK z2|usrdA)ji>fHDJxj&!ldavt5sVd8m5YiB0U|^8Q$x5nWU|`n3zr+Ms@H@i~jo?4t 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