Optimal Parameters-based Geographical Detectors (OPGD) Model for Spatial Heterogeneity Analysis and Factor Exploration

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.

Authors’ affiliations

Dr. Yongze Song

Google Scholar, ResearchGate

Research interests: Spatial statistics, sustainable infrastructure

Curtin University, Australia

Email: [email protected]

1. Introduction to GD package

## 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 σ² are the number and population variance of observations within the whole study area, and N_j and σ_j² are the number and population variance of observations within the j th (j=1,…,M) sub-region of an explanatory 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 s² and s_j² are sample variance of observations in the whole study area and in the j th sub-region.

Figure 1. 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.

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.

install.packages("GD")

library("GD")

## This is GD 10.8.
##                         
## 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, 57(5), 593-610. doi: 10.1080/15481603.2020.1760434.
##                         
## If you find that GD runs for a long time without returning results, please try using the gdverse package we developed.
## 

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 methods: equal, natural, quantile (default), geometric, sd and manual
ds1 <- disc(ndvi_40$Tempchange, 4)
ds1
plot(ds1)

3.2 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 2. Process and results of optimal spatial data discretization

 

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.

4.1 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)

Figure 3. Results of factor detector

4.2 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 4. Results of risk detector

4.3 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 5. Results of interaction detector

4.4 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 6. Results of ecological detector

 

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

Figure 7. Spatial scale effects

Figure 8. Overview of global research using geographical detector model (cumulative citations were updated on June 2020). (Song et al. 2020)

Reference

Song, Y., Wang, J.F., Ge, Y., et al. 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, 2020. 57(5): 593-610. doi: 10.1080/15481603.2020.1760434.

Wang, J. F., Li, X. H., Christakos, G., Liao, Y. L., et al. 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, 2010. 24(1), 107-127. doi: 10.1080/13658810802443457.

Wang, J. F., Zhang, T. L., & Fu, B. J. A measure of spatial stratified heterogeneity. Ecological indicators, 2016. 67, 250-256. doi: 10.1016/j.ecolind.2016.02.052.

Luo., P., Song, Y., Zhu, D., Cheng, J., & Meng, L. A generalized heterogeneity model for spatial interpolation. International Journal of Geographical Information Science. 2023, 37(3): 634-659. doi: 10.1080/13658816.2022.2147530.

Guo, J., Wang, J., Xu, C., & Song, Y. Modeling of spatial stratified heterogeneity. GIScience & Remote Sensing, 2020. 59(1), 1660-1677. doi: 10.1080/15481603.2022.2126375.

Song, Y., Wu, P. An interactive detector for spatial associations. International Journal of Geographical Information Science, 2021. doi: 10.1080/13658816.2021.1882680.

Song, Y., Wright, G., Wu, P., Thatcher, D., et al. Segment-Based Spatial Analysis for Assessing Road Infrastructure Performance Using Monitoring Observations and Remote Sensing Data. Remote Sensing, 2018. 10(11): 1696. doi: 10.3390/rs10111696.

Luo, P., Song, Y., Huang, X., Ma, H., et al. Identifying determinants of spatio-temporal disparities in soil moisture of the Northern Hemisphere using a geographically optimal zones-based heterogeneity model. ISPRS Journal of Photogrammetry and Remote Sensing, 2022. 185, 111-128. doi: 10.1016/j.isprsjprs.2022.01.009.

Zhang, Z., Song, Y., & Wu, P. Robust geographical detector. International Journal of Applied Earth Observation and Geoinformation, 2022. 109, 102782. doi: 10.1016/j.jag.2022.102782.

Song, Y., Wu, P., Gilmore, D., et al. A Spatial Heterogeneity-Based Segmentation Model for Analyzing Road Deterioration Network Data in Multi-Scale Infrastructure Systems. IEEE Transactions on Intelligent Transportation Systems, 2020. doi: 10.1109/TITS.2020.3001193.

Luo, P., Song, Y. Wu, P. Spatial disparities in trade-offs: economic and environmental impacts of road infrastructure on continental level. GIScience & Remote Sensing, 2021. doi: 10.1080/15481603.2021.1947624.

Zhang, Z., Song, Y., Archer, N. and Wu, P. Spatial disparity of urban performance from a scaling perspective: a study of industrial features associated with economy, infrastructure, and innovation. GIScience & Remote Sensing. 2023. 60(1), p.2167567. doi: 10.1080/15481603.2023.2167567.