28 区域数据分析

28.1 苏格兰唇癌数据分析

Everything is related to everything else, but near things are more related than distant things.

— Waldo Tobler (Tobler 1970)

空间区域数据分析

空间区域数据的贝叶斯建模

Bayesian spatial and spatio-temporal GLMMs with possible extremes glmmfields
Bayesian spatial analysis geostan
Spatial Models in Stan: Intrinsic Auto-Regressive Models for Areal Data
Exact sparse CAR models in Stan 网页文档
Spatial Models in Stan: Intrinsic Auto-Regressive Models for Areal Data 网页文档原始数据和代码，接上面苏格兰唇癌数据分析，用 CmdStanR 更新后的代码
Spatial modeling of areal data. Lip cancer in Scotland INLA 建模
CAR models Scotland Lip cancer dataset Stan 建模
空间计量区域数据分析 on-the-use-of-r-for-spatial-econometrics

响应变量服从泊松分布

BYM-INLA (Blangiardo 等 2013; Moraga 2020)
BYM-Stan (Morris 等 2019; Donegan 2022; Cabral, Bolin, 和 Rue 2022)

记录 1975-1986 年苏格兰 56 个地区的唇癌病例数，这是一个按地区汇总的数据。

library(sf)

Linking to GEOS 3.11.1, GDAL 3.6.4, PROJ 9.1.1; sf_use_s2() is TRUE

scotlips <- st_read('data/scotland/scotland.shp', crs = st_crs("EPSG:27700"))

Reading layer `scotland' from data source 
  `/__w/data-analysis-in-action/data-analysis-in-action/data/scotland/scotland.shp' 
  using driver `ESRI Shapefile'
Simple feature collection with 56 features and 9 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 7150.759 ymin: 529557.2 xmax: 468393.4 ymax: 1218479
Projected CRS: OSGB36 / British National Grid

str(scotlips)

Classes 'sf' and 'data.frame':  56 obs. of  10 variables:
 $ SP_ID    : chr  "12" "13" "19" "02" ...
 $ NAME     : chr  "Sutherland" "Nairn" "Inverness" "Banff-Buchan" ...
 $ ID       : num  12 13 19 2 17 16 21 50 15 25 ...
 $ District : int  12 13 19 2 17 16 21 50 15 25 ...
 $ Observed : int  5 3 9 39 2 9 16 6 17 19 ...
 $ Expected : num  1.8 1.1 5.5 8.7 1.1 4.6 10.5 19.6 7.8 15.5 ...
 $ pcaff    : int  16 10 7 16 10 16 7 1 7 1 ...
 $ Latitude : num  58.1 57.5 57.2 57.6 57.1 ...
 $ Longitude: num  4.64 3.98 4.73 2.36 4.09 3 2.98 3.2 3.1 3.3 ...
 $ geometry :sfc_MULTIPOLYGON of length 56; first list element: List of 1
  ..$ :List of 1
  .. ..$ : num [1:73, 1:2] 254302 254442 253074 245057 259217 ...
  ..- attr(*, "class")= chr [1:3] "XY" "MULTIPOLYGON" "sfg"
 - attr(*, "sf_column")= chr "geometry"
 - attr(*, "agr")= Factor w/ 3 levels "constant","aggregate",..: NA NA NA NA NA NA NA NA NA
  ..- attr(*, "names")= chr [1:9] "SP_ID" "NAME" "ID" "District" ...

library(ggplot2)
ggplot() +
  geom_sf(data = scotlips, aes(fill = Observed)) +
  scale_fill_viridis_c() +
  theme_minimal()

28.2 美国各州犯罪率分析

响应变量服从高斯分布的调查数据 (Bivand 2001)

数据集 USArrests 记录 1973 年美国各州每 10 万居民中因谋杀 Murder、袭击 Assault 和强奸 Rape 被警察逮捕的人数以及城市人口所占百分比（可以看作城市化率）。

表格 28.1: 数据集 USArrests（部分）

州名	区域划分	谋杀犯	袭击犯	城市化率	强奸犯
Alabama	South	13.2	236	58	21.2
Alaska	West	10.0	263	48	44.5
Arizona	West	8.1	294	80	31.0
Arkansas	South	8.8	190	50	19.5
California	West	9.0	276	91	40.6
Colorado	West	7.9	204	78	38.7

library(sf)
# 州数据
us_state_sf <- readRDS("data/us-state-map-2010.rds")
# 观测数据
us_state_df <- merge(x = us_state_sf, y = us_arrests,
  by.x = "NAME", by.y = "state_name", all.x = TRUE)

ggplot() +
  geom_sf(
    data = us_state_df, aes(fill = Assault), color = "gray80", lwd = 0.25) +
  scale_fill_viridis_c(option = "plasma", na.value = "white") +
  theme_void()

1973 年美国各州因袭击被逮捕的人数与城市化率的关系：相关分析

代码

library(ggrepel)
ggplot(data = us_arrests, aes(x = UrbanPop, y = Assault)) +
  geom_point(aes(color = state_region)) +
  geom_text_repel(aes(label = state_name), size = 3, seed = 2022) +
  theme_classic() +
  labs(x = "城市化率（%）", y = "因袭击被逮捕人数", color = "区域划分")

阿拉斯加州和夏威夷州与其它州都不相连，属于孤立的情况，下面在空间相关性的分析中排除这两个州。

# 州的中心
centers48 <- subset(
  x = data.frame(x = state.center$x, y = state.center$y),
  subset = !state.name %in% c("Alaska", "Hawaii")
)
# 观测数据
arrests48 <- subset(
  x = USArrests,
  subset = !rownames(USArrests) %in% c("Alaska", "Hawaii")
)

library(spData)
library(spdep)
# KNN
k4.48 <- knn2nb(knearneigh(as.matrix(centers48), k = 4))
# Moran I test
moran.test(x = arrests48$Assault, listw = nb2listw(k4.48))


    Moran I test under randomisation

data:  arrests48$Assault  
weights: nb2listw(k4.48)    

Moran I statistic standard deviate = 3.4216, p-value = 0.0003113
alternative hypothesis: greater
sample estimates:
Moran I statistic       Expectation          Variance 
      0.294385644      -0.021276596       0.008511253

# Permutation test for Moran's I statistic
moran.mc(x = arrests48$Assault, listw = nb2listw(k4.48), nsim = 499)


    Monte-Carlo simulation of Moran I

data:  arrests48$Assault 
weights: nb2listw(k4.48)  
number of simulations + 1: 500 

statistic = 0.29439, observed rank = 500, p-value = 0.002
alternative hypothesis: greater