Optimal Parameters-based Geographical Detectors (OPGD) Model for Spatial Heterogeneity Analysis and Factor Exploration
Yongze Song
2021-04-27
Current version: GD v1.10
Recommendation: Understanding Spatial Stratified Heterogeneity Using R
Citation for package GD
To cite GD R package in publications, please use:
Song, Y., Wang, J., Ge, Y. & Xu, C. (2020) “An optimal parameters-based geographical detector model enhances geographic characteristics of explanatory variables for spatial heterogeneity analysis: Cases with different types of spatial data”, GIScience & Remote Sensing. 57(5), 593-610. doi: 10.1080/15481603.2020.1760434.
1. Introduction to GD package
The model can be used to address following issues:
Explore potential factors or explanatory variables from a spatial perspective.
Explore potential interactive impacts of geogrpahical variables.
Identify high-risk or low-risk regions from potential explanatory variables.
The GD package makes following steps fast and easy:
It contains both supervised and unsupervised spatial data discretization methods, and the optimal spatial discretization method for continuous variables;
It contains four primary functions of geographical detectors, including factor detector, risk detector, interaction detector and ecological detector;
It can be used to compare size effects of spatial unit;
It provides diverse visualizations of spatial analysis results;
It contains detailed significance tests for spatial analysis in each step of geographical detectors.
Start from the one-step function: gdm (Highly Recommended)
The pacakge provides a one-step function for performing optimal discretization and geographical detectors at the same time.
The output contains all data and visualization results.
## install and library the pacakge
install.packages("GD")
library("GD")
## Example 1
## NDVI: ndvi_40
## 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
## In this case, Climatezone and Mining are categorical variables,
## and Tempchange and GDP are continuous variables.
ndvigdm <- gdm(NDVIchange ~ Climatezone + Mining + Tempchange + GDP,
continuous_variable = c("Tempchange", "GDP"),
data = ndvi_40,
discmethod = discmethod, discitv = discitv) # ~3s
ndvigdm
plot(ndvigdm)
## Example 2
## 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)
2. Geographical detector model
Spatial stratified heterogeneity can be measured using geographical detectors (Wang et al. 2010, Wang et al. 2016).
Power of determinants is computed using a \(Q\)-statistic:
\[Q=1-\displaystyle \frac{\sum_{j=1}^{M} N_{j} \sigma_{j}^2}{N \sigma^2} \]
where \(N\) and \(\sigma^2\) are the number and population variance of observations within the whole study area, and \(N_{j}\) and \(\sigma_{j}^2\) are the number and population variance of observations within the \(j\) th (\(j\)=1,…,\(M\)) sub-region of an explantory variable.
Please note that in R environment, sd and var functions are used for computing sample standard deviation and sample variance. If sample variance is used in the computation, the equation of \(Q\)-statistic can be converted to:
\[Q=1-\displaystyle \frac{\sum_{j=1}^{M} (N_{j}-1) s_{j}^2}{(N-1) s^2} \]
where \(s^2\) and \(s_{j}^2\) are sample variance of observations in the whole study area and in the \(j\) th sub-region.
Further information can be found on the manual of GD package.
More applications of geographical detectors are listed on Geodetector website.
3. Spatial data discretization
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.
## This is GD 1.10.
##
## To cite GD in publications, please use:
##
## Song, Y., Wang, J., Ge, Y. & Xu, C. (2020) An optimal parameters-based geographical detector model enhances geographic characteristics of explanatory variables for spatial heterogeneity analysis: Cases with different types of spatial data, GIScience & Remote Sensing, 57(5), 593-610. doi: 10.1080/15481603.2020.1760434.
##
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 11.49432
Discretization with given parameters: disc
## discretization methods: equal, natural, quantile (default), geometric, sd and manual
ds1 <- disc(ndvi_40$Tempchange, 4)
ds1
plot(ds1)
Further information can be found on the manual of GD package.
Optimal discretization: optidisc
## set optional discretization methods and numbers of intervals
discmethod <- c("equal","natural","quantile","geometric","sd")
discitv <- c(4:7)
## optimal discretization
odc1 <- optidisc(NDVIchange ~ Tempchange, data = ndvi_40,
discmethod, discitv)
odc1
plot(odc1)
4. Geographical detectors
GD package provides two options for geographical detectors modelling:
four functions are performed step by step: gd for factor detector, riskmean and gdrisk for risk detector, gdinteract for interaction detector and gdeco for ecological detector;
optimal discretization and geographical detectors are performed using a one-step function gdm.
Factor detector: gd
## a categorical explanatory variable
g1 <- gd(NDVIchange ~ Climatezone, data = ndvi_40)
g1
## multiple categorical explanatory variables
g2 <- gd(NDVIchange ~ ., data = ndvi_40[,1:3])
g2
plot(g2)
## multiple variables including continuous variables
discmethod <- c("equal","natural","quantile","geometric","sd")
discitv <- c(3:7)
data.ndvi <- ndvi_40
data.continuous <- data.ndvi[, c(1, 4:7)]
odc1 <- optidisc(NDVIchange ~ ., data = data.continuous, discmethod, discitv) # ~14s
data.continuous <- do.call(cbind, lapply(1:4, function(x)
data.frame(cut(data.continuous[, -1][, x], unique(odc1[[x]]$itv), include.lowest = TRUE))))
# add stratified data to explanatory variables
data.ndvi[, 4:7] <- data.continuous
g3 <- gd(NDVIchange ~ ., data = data.ndvi)
g3
plot(g3)
Risk detector: riskmean and gdrisk
Risk mean values by variables:
## categorical explanatory variables
rm1 <- riskmean(NDVIchange ~ Climatezone + Mining, data = ndvi_40)
rm1
plot(rm1)
## multiple variables inclusing continuous variables
rm2 <- riskmean(NDVIchange ~ ., data = data.ndvi)
rm2
plot(rm2)
Risk matrix:
## categorical explanatory variables
gr1 <- gdrisk(NDVIchange ~ Climatezone + Mining, data = ndvi_40)
gr1
plot(gr1)
## multiple variables inclusing continuous variables
gr2 <- gdrisk(NDVIchange ~ ., data = data.ndvi)
gr2
plot(gr2)
Interaction detector: gdinteract
## categorical explanatory variables
gi1 <- gdinteract(NDVIchange ~ Climatezone + Mining, data = ndvi_40)
gi1
## multiple variables inclusing continuous variables
gi2 <- gdinteract(NDVIchange ~ ., data = data.ndvi)
gi2
plot(gi2)
Ecological detector: 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)
5. Comparison of size effects of spatial unit
ndvilist <- list(ndvi_20, ndvi_30, ndvi_40, ndvi_50)
su <- c(20,30,40,50) ## sizes of spatial units
## "gdm" function
gdlist <- lapply(ndvilist, function(x){
gdm(NDVIchange ~ Climatezone + Mining + Tempchange + GDP,
continuous_variable = c("Tempchange", "GDP"),
data = x, discmethod = "quantile", discitv = 6)
})
sesu(gdlist, su) ## size effects of spatial units
Reference
Song Y, Wang J, Ge Y and Xu C (2020) “An optimal parameters-based geographical detector model enhances geographic characteristics of explanatory variables for spatial heterogeneity analysis: Cases with different types of spatial data.” GIScience & Remote Sensing, 57(5), pp. 593-610. doi: 10.1080/15481603.2020.1760434.
Song Y, Wright G, Wu P, Thatcher D, McHugh T, Li Q, Li SJ and Wang X (2018). “Segment-Based Spatial Analysis for Assessing Road Infrastructure Performance Using Monitoring Observations and Remote Sensing Data”. Remote Sensing, 10(11), pp. 1696. doi: 10.3390/rs10111696.
Song Y, Wu P, Gilmore D and Li Q (2020). “A Spatial Heterogeneity-Based Segmentation Model for Analyzing Road Deterioration Network Data in Multi-Scale Infrastructure Systems.” IEEE Transactions on Intelligent Transportation Systems. doi: 10.1109/TITS.2020.3001193.
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.
