Optimal Parameters-based Geographical Detectors
Yongze Song
2020-05-28
Latest version
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. 
Authors’ affiliations
Dr. Yongze Song
Research interests: Spatial statistics, sustainable infrastructure
Curtin University, Australia
Email yongze.song@curtin.edu.au
Award:
Global Peer Review Awards 2019: Top reviewers in Geosciences (top 1%) and in Cross-field (top 1%).
R Packages:
GD
SK
EDA
HS
Introduction to GD package
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.
Figure 1. Overview of global research using geographical detector model (cumulative citations were updated on June 2020). (Song et al. 2020)
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.
Figure 2. General calculation process and relationships of functions in GD package (Song et al. 2020)
Further information can be found on the manual of GD package.
More applications of geographical detectors are listed on Geodetector website.
Discretization and optimal 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.
install.packages("GD")library("GD")
#> This is GD 1.8.
#>
#> 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, 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 11.49432Discretization 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)
Figure 3. Process and results of optimal spatial data discretization
(Optimal Parameters-based) Geographical Detectors
GD package provides two options for geographical detectors modelling:
four functions are performed step by step:
gdfor factor detector,riskmeanandgdriskfor risk detector,gdinteractfor interaction detector andgdecofor ecological detector;optimal discretization and geographical detectors are performed using a one-step function
gdm.
A one-step function: gdm (Highly Recommended)
## 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
ndvigdm <- gdm(NDVIchange ~ Climatezone + Mining + Tempchange + GDP,
continuous_variable = c("Tempchange", "GDP"),
data = ndvi_20,
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)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 inclusing 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)
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)
Figure 4. Results of factor detector
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)
Figure 5. Results of risk detector
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)
Figure 6. Results of interaction detector
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)
Figure 7. Results of ecological detector
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
Figure 8. Spatial scale effects
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, doi: 10.1080/15481603.2020.1760434.
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.
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.
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, Wang X, Wright G, Thatcher D, Wu P and Felix P (2019). “Traffic Volume Prediction With Segment-Based Regression Kriging and its Implementation in Assessing the Impact of Heavy Vehicles.” IEEE Transactions on Intelligent Transportation Systems, 20(1), pp. 232 - 243. doi: 10.1109/TITS.2018.2805817.
Xu C and Wang J (2018). Geodetector Website. http://www.geodetector.cn.