Spatial stratified heterogeneity can be measured using geographical detectors (Wang et al. 2010, Wang et al. 2016).
GD package consists of four parts:
the optimal discretization of continuous data;
four primary functions of geographical detectors, including factor detector, risk detector, interaction detector and ecological detector;
comparison of size effects of spatial unit;
visualizations of results.
GD package includes three datasets:
NDVI (ndvi_5, ndvi_10, ndvi_20, ndvi_30, ndvi_40 and ndvi_50): spatial data of vegetation changes NDVI with six sizes of grids, 5 km, 10 km, 20 km, 30 km, 40 km and 50 km;
H1N1 (h1n1_50, h1n1_100 and h1n1_150): spatial data of influenza A virus subtype H1N1 incidences with the spatial grid sizes of 50 km, 100 km and 150 km;
road_GD: line segment based spatial data of road conditions (Song et al. 2018).
Further information can be found on the manual of GD package.
More applications of geographical detectors are listed on Geodetector website.
Categorical variables are required for geographical detectors, so continuous variables should be discretized before modelling. GD package provides two options: discretization with given parameters, including discretization methods and numbers of intervals, and optimal discretization with a series of optional parameter combinations. Dataset ndvi_40 is used as an example for explanation.
library("GD")
data("ndvi_40")
head(ndvi_40)[1:3,]
#> NDVIchange Climatezone Mining Tempchange Precipitation GDP Popdensity
#> 1 0.11599 Bwk low 0.25598 236.54 12.55 1.44957
#> 2 0.01783 Bwk low 0.27341 213.55 2.69 0.80124
#> 3 0.13817 Bsk low 0.30247 448.88 20.06 11.49432disc## discretization methods: equal, natural, quantile (default), geometric, sd and manual
ds1 <- disc(ndvi_40$Tempchange, 4)
ds1
plot(ds1)Further information can be found on the manual of GD package.
optidisc## set optional discretization methods and numbers of intervals
discmethod <- c("equal","natural","quantile","geometric","sd")
discitv <- c(3:7)
## optimal discretization
odc1 <- optidisc(continuous_variable = ndvi_40$Tempchange,
response_variable = ndvi_40$NDVIchange,
discmethod, discitv)
odc1
plot(odc1)GD package provides two options for geographical detectors modelling: * four functions are performed step by step: gd for factor detector, riskmean and gdrisk for risk detector, gdinteract for interaction detector and gdeco for ecological detector; * optimal discretization and geographical detectors are performed using a one-step function gdm.
gdm## NDVI: ndvi_40
## define elements orders of categorical variables
cz <- c("Bwk","Bsk","Dwa","Dwb","Dwc") ## climate zone
mp <- c("very low","low","medium","high","very high") ## mining production
ndvi_40$Climatezone <- as.numeric(1:5)[match(ndvi_40$Climatezone, cz)]
ndvi_40$Mining <- as.numeric(1:5)[match(ndvi_40$Mining, mp)]
## set optional parameters of optimal discretization
## optional methods: equal, natural, quantile, geometric, sd and manual
discmethod <- c("equal","natural","quantile")
discitv <- c(4:6)
## "gdm" function
ndvigdm <- gdm(NDVIchange ~ Climatezone + Mining + Tempchange + GDP,
continuous_variable = c("Tempchange", "GDP"),
data = ndvi_40,
discmethod = discmethod, discitv = discitv)
ndvigdm
plot(ndvigdm)
## H1N1: h1n1_100
## set optional parameters of optimal discretization
discmethod <- c("equal","natural","quantile","geometric","sd")
discitv <- c(3:7)
continuous_variable <- colnames(h1n1_100)[-c(1,11)]
## "gdm" function
h1n1gdm <- gdm(H1N1 ~ .,
continuous_variable = continuous_variable,
data = h1n1_100,
discmethod = discmethod, discitv = discitv)
h1n1gdm
plot(h1n1gdm)gd## a categorical explanatory variable
g1 <- gd(NDVIchange ~ Climatezone, data = ndvi_40)
g1
## multiple categorical explanatory variables
g2 <- gd(NDVIchange ~ ., data = ndvi_40[,1:3])
g2
plot(g2)
## multiple variables inclusing continuous variables
discmethod <- c("equal","natural","quantile","geometric","sd")
discitv <- c(3:7)
data_ndvi <- ndvi_40
odc1 <- optidisc(continuous_variable = data_ndvi[,4:7],
response_variable = data_ndvi$NDVIchange,
discmethod, discitv)
for (i in 4:7){
data_ndvi[,i] <- stra(data_ndvi[,i], odc1[[i-3]]$itv)
}
g3 <- gd(NDVIchange ~ ., data = data_ndvi)
g3
plot(g3)riskmean and gdriskRisk mean values by variables:
## categorical explanatory variables
rm1 <- riskmean(NDVIchange ~ Climatezone + Mining, data = ndvi_40)
rm1
plot(rm1)
## multiple variables inclusing continuous variables
rm3 <- riskmean(NDVIchange ~ ., data = data_ndvi)
rm3
plot(rm3)Risk matrix:
## categorical explanatory variables
gr1 <- gdrisk(NDVIchange ~ Climatezone + Mining, data = ndvi_40)
gr1
plot(gr1)
## multiple variables inclusing continuous variables
gd3 <- gdrisk(NDVIchange ~ ., data = data_ndvi)
gd3
plot(gd3)gdinteract## categorical explanatory variables
gi1 <- gdinteract(NDVIchange ~ Climatezone + Mining, data = ndvi_40)
gi1
## multiple variables inclusing continuous variables
gi3 <- gdinteract(NDVIchange ~ ., data = data_ndvi)
gi3
plot(gi3)gdeco## categorical explanatory variables
ge1 <- gdeco(NDVIchange ~ Climatezone + Mining, data = ndvi_40)
ge1
## multiple variables inclusing continuous variables
gd3 <- gdeco(NDVIchange ~ ., data = data_ndvi)
gd3
plot(gd3)ndvilist <- list(ndvi_10, ndvi_20, ndvi_30, ndvi_40, ndvi_50)
su <- c(10,20,30,40,50) ## sizes of spatial units
gdlist <- list() ## list of all geographical detectors results
## set optional parameters of optimal discretization
discmethod <- c("equal","natural","quantile","geometric","sd")
discitv <- c(3:7)
## "gdm" function (~ 40s)
for (i in 1:length(su)){
ndvidata <- ndvilist[[i]]
gdlist[[i]] <- gdm(NDVIchange ~ .,
continuous_variable = c("Tempchange", "Precipitation", "GDP", "Popdensity"),
data = ndvidata,
discmethod = discmethod, discitv = discitv)
}
## size effects of spatial units
sesu(gdlist, su) Song Y (2018). GD: Geographical Detectors. R package, https://CRAN.R-project.org/package=GD.
Wang J, Li X, Christakos G, Liao Y, Zhang T, Gu X and Zheng X (2010). “Geographical Detectors-Based Health Risk Assessment and its Application in the Neural Tube Defects Study of the Heshun Region, China.” International Journal of Geographical Information Science, 24(1), pp. 107-127. doi: 10.1080/13658810802443457.
Wang J, Zhang T and Fu B (2016). “A measure of spatial stratified heterogeneity.” Ecological Indicators, 67, pp. 250-256. doi: 10.1016/j.ecolind.2016.02.052.
Song Y, Wang X, Wright G, Thatcher D, Wu P and Felix P (2018). “Traffic Volume Prediction With Segment-Based Regression Kriging and its Implementation in Assessing the Impact of Heavy Vehicles.” IEEE Transactions on Intelligent Transportation Systems, pp. 1-12. doi: 10.1109/TITS.2018.2805817.
Xu C and Wang J (2018). Geodetector Website. http://www.geodetector.org/.