Post on 19-Feb-2022
181203Geodetector & Its Applications in Natural & Social Sciences
(C) wangjf@Lreis.ac.cn1
2018.12.03
Geodetector & Its Applications in Natural & Social Sciences
Wang JinfengState Key Laboratory of Resources & Environmental Information System
Institute of Geographical Sciences & Nature Resources ResearchChinese Academy of Sciences
Beijing 100101, PRCwangjf@Lreis.ac.cnwww.geodetector.cn
Sharp tools make good work-- The Analects of Confucius
1. Background
2. Spatial Stratified Heterogeneity: Geodetector
3. Properties of Geodetector
4. Software & Examples
5. Q/A
6. Flexible Geodetector
7. Summary
181203Geodetector & Its Applications in Natural & Social Sciences
(C) wangjf@Lreis.ac.cn2
2018.12.03
1. Background
2. Spatial Stratified Heterogeneity: Geodetector
3. Properties of Geodetector
4. Software & Examples
5. Q/A
6. Flexible Geodetector
7. Summary
Geo
Heterogeneity
Graphy
Strata
Spatial Stratified Heterogeneity(SSH)
Wang JF, Zhang TL, Fu BJ. 2016. A measure of spatial stratified heterogeneity. Ecological Indicators 7: 250-256.
181203Geodetector & Its Applications in Natural & Social Sciences
(C) wangjf@Lreis.ac.cn3
2018.12.03
Spatial Stratified Heterogeneity (SSH) is Prevalent in Nature
within strata is more similar than between strata
Ecological Zones
Landuse Types
In east China, 36% land supports 96% human population;
In west China, 64% land supports 4% human population.
Plague ~ Dryness (±b) Xu et al. 2011. PNAS Flood in Canada (fs, fa) Buttle et al. 2016. CWRJ
Wet Dry
China
ChallengeChallenge
North China South China
Wet Dry Wet DryWet Dry
South China
SSH� Spatial�Counfounding
Wang JF, Zhang TL, Fu BJ. 2016. A measure of spatial stratified heterogeneity. Ecological Indicators 7: 250-256.
181203Geodetector & Its Applications in Natural & Social Sciences
(C) wangjf@Lreis.ac.cn4
2018.12.03
Annual Temperature in China in 1900 ?
Climate zones (SSH)
Meteorological Stations in China in 1900
SSH� Bias�of�Sample
Wang JF, Xu CD, Hu MG, Li QX, Yan ZW, Zhao P, Jones P. 2014. A new estimate of the China temperature anomaly series and uncertainty assessment in 1900-2006. Journal of Geophysical Research 119(1): 1-9.
SSH:�A�Spatial�Pattern
World ecological zones China NDVI pattern
US land dissection pattern China population pattern
94%6%
181203Geodetector & Its Applications in Natural & Social Sciences
(C) wangjf@Lreis.ac.cn5
2018.12.03
SSH� Spatial�Attribution
World ecological zones China NDVI pattern
q = 0.53*** 53% of NDVI variation
is attributed to climate zones in China
Humidity province
Latitudinalregions
Altitudinalbelts
q = 0.323***Moran’s I = 0.24
Rodents’Density Interpolation
Spatial autocorrelation (SAC) is too weak for a SAC basedinterpolation: Kriging, IDW, Spline, etc.When population is SSH, Sandwich interpolation works
SSH�based�Spatial�Interpolation
Sem
ivariogram
Distance (m)
181203Geodetector & Its Applications in Natural & Social Sciences
(C) wangjf@Lreis.ac.cn6
2018.12.03
SSH confoundingSSH sample biasSSH patternSSH attributionSSH interpolation
SSH is prevalent
in the nature
Statistics for Spatial Stratified Heterogeneity
Measure & Attribute Inference Decision Making
SSH confoundingSSH sample biasSSH patternSSH attributionSSH interpolation
SSH is prevalent
in the nature
Statistics for Spatial Stratified Heterogeneity
Measure & Attribute Inference Decision Making
181203Geodetector & Its Applications in Natural & Social Sciences
(C) wangjf@Lreis.ac.cn7
2018.12.03
1. Background
2. Spatial Stratified Heterogeneity: Geodetector
3. Properties of Geodetector
4. Software & Examples
5. Q/A
6. Flexible Geodetector
7. Summary
Wang JF, Zhang TL, Fu BJ. 2016. A measure of spatial stratified heterogeneity. Ecological Indicators 7: 250-256.
q = 1∑
YSample
h = 1h = 2
h = 1 h = 3 h = 4SSH(Y)
Spatial Stratified Heterogeneity (SSH): Measure(Pattern: within strata is more similar than between strata)
~ F(L1, NL; )q [0, 1], Y has 100q% degree of SSH= 0, if Y has no SSH= 1, if Y is fully SSH
181203Geodetector & Its Applications in Natural & Social Sciences
(C) wangjf@Lreis.ac.cn8
2018.12.03
Nw = 32NB = 32
5.0y25.02
Goodchild M. 1986. CATMOG, GeoBooks, Norwich
32
0 1
q = 0
Wang JF, Zhang TL, Fu BJ. 2016. A measure of spatial stratified heterogeneity. Ecological Indicators 67: 250-256.
Line 1
q1 = 1***
Line 1
q1 = 0.16*
Line 2
q2 = 0.27** q1&2 = 0.67***
Line 2
q2 = 0
I = -1.000 I = +0.393 I = +0.857
Moran P. 1950. Notes on continuous stochastic phenomena. Biometrika 37:17-23.
Wang JF, Zhang TL, Fu BJ. 2016. A measure of spatial stratified heterogeneity. Ecological Indicators 7: 250-256.
q = 1∑
YSample
h = 1h = 2
h = 1 h = 3 h = 4SSH(X)
Spatial Stratified Heterogeneity (SSH): Attribute(Axiom: If X causes Y, then their maps would be coupled)
q [0, 1], 100q% of Y is explained by X0, if Y is independent to X1, if Y is fully depended upon X
~ F(L1, NL; )
181203Geodetector & Its Applications in Natural & Social Sciences
(C) wangjf@Lreis.ac.cn9
2018.12.03
q(NDVI | climate zones)= 0.53***Climate zones explain 53% of NDVI variation in China
q(Y | #X):If X controls Y, they will be spatially coupled
1. Background
2. Spatial Stratified Heterogeneity: Geodetector
3. Properties of Geodetector
4. Software & Examples
5. Q/A
6. Flexible Geodetector
7. Summary
181203Geodetector & Its Applications in Natural & Social Sciences
(C) wangjf@Lreis.ac.cn10
2018.12.03
(# in 0D)
(Pairs in 0D)
(Order in 1D)
(Coupled in 2D)
(1) Correlation Causation
Wang JF, Zhang TL, Fu BJ. 2016. A measure of spatial stratified heterogeneity. Ecological Indicators 7: 250-256.
y
x
#
Nonlinear
Linear
Histogram Pearson Corr. Pearson Corr. Geodetector q
Linear
y
x y
xy
x
I would rather discover one causal law
than be King of Persia-- Democritus
(460-370 B.C.)
Confounding
Overfitting+
+
SSH
Global modelsY = a + bX
Figure 5: GWR showing the coefficients from the output. Positive values indicate a positive association, while negative values indicate a negative associationhttp://blogs.oregonstate.edu/geog566spatialstatistics/2017/06/11/beetle-outbreaks-wildfire-overlapping-time-space/
Local modelsY = a(s) + b(s)X
(2) Global Local SSH
Wang JF, Zhang TL, Fu BJ. 2016. A measure of spatial stratified heterogeneity. Ecological Indicators 7: 250-256.
Xu et al 2011,PNAS
Interpret in Strata
Geodetector
Modeling in Strata Strata
Strata
181203Geodetector & Its Applications in Natural & Social Sciences
(C) wangjf@Lreis.ac.cn11
2018.12.03
Y
X2
X1
X1 ∩ X2
X13
X11
X12
X22
X21
X23
X11∩X22
X11∩X21
X13∩X21
X13∩X22
X12∩X22
X11∩X23
X13∩X23
(3) Interaction: Y X1 ∩ X2
Name Mechanism; Equation Test Conclusion
CorrelationG883; E107
Linear:
= ∑ ̅
∑ ̅ ∑
F =/
/
~ F(k-1, n-k)
Regression(& MLM)G62 G84G259,893G140,258
Linear: y = a + bx;
b = ∑ ̅
∑ ̅;R2=1 -
= b2∑ ̅=
∑ ̅ ∑ ̅ ∑
F =/
/
~ F(k-1, n-k)
1. X explains linearly 100R2% of Y
2. =
ANOVAG140;C333;C337
Means in strata:Yij = ai + eij
Assume: Eeij = 0,Veij = const.
H0: 1 = … = k
= [0. +)
~ F(k - 1; n - k)
Significance of the difference btw means in strata
Classification Min SSW + Max SSB: Kmeans;
F == [0. +)
~ F(k-1; n-k);Kappa
Classes
Geodetectorq-statistic
Min SSW + Max SSB
q = 1 - = 1 -∑
=
H0: h2 = 2
= [0. 1]
~ F(L-1; N-L; )
1. SSH degree of Y2. X explains 100q% of Y
3. = in strata
Mean & Var
ANOVA F = F = 9894 N/A N/A F = 0
q-statistic q = 1 q = 0.8 q = 0.7 q = 0.6 q = 0
181203Geodetector & Its Applications in Natural & Social Sciences
(C) wangjf@Lreis.ac.cn12
2018.12.03
Properties of Geodetector
(1) Finds coupling between y & x, no assumption of linearity or nonlinearity.
(2) Avoid confounding btw x and by a prior stratification of population by the others, then apply Geodetector (y|x).
(3) Finds general interaction between x1 and x2, no assumption of product as in econometrics.
(4) Explanatory variable x could be categorical, response variable y is numerical; numerical x should be stratified.
(5) When sample is small, Geodetector outperforms regression, because stratification creates homogeneity. so a sample becomes more representative in each stratum.
(6) Immune collinearity between covariates x1 and x2.(7) Stratification is flexible: spatial, time, attribute, spectrum.
1. Background
2. Spatial Stratified Heterogeneity: Geodetector
3. Properties of Geodetector
4. Software & Examples
5. Q/A
6. Flexible Geodetector
7. Summary
181203Geodetector & Its Applications in Natural & Social Sciences
(C) wangjf@Lreis.ac.cn13
2018.12.03
Software: www.geodetector.cn
Prepare data Run software Output
y
X
Pollution: Soil Antibiotic in a Town Medicine: NTD in a County
Nature: Dissection in USA Social: Urbanization in China
181203Geodetector & Its Applications in Natural & Social Sciences
(C) wangjf@Lreis.ac.cn14
2018.12.03
Determinants of Land Dissection Density in US
Luo W, Jasiewicz J, Stepinski T, et al. 2016. Spatial association between dissection density and environmental factors over the entire conterminous United States, Geophys. Res. Lett. 43: 692–700
Y
Y X
lithology Glaciation Elevation
Slope Precipitation Permeability
刘彦随,杨忍. 2012.中国县域城镇化的空间特征与形成机理. 地理学报 67(8): 1011–1020
Area Fixedinvest
Dist fromcenter city
Farmerincome
Indusstruct
Populadensity
Cropper cpt
GDPPer cpt
Transportation
Elevation
Precipitation
106 Highway 0.30 0.34 0.58 0.18 0.10 0.45 0.53 0.13 0.00 0.11
North Border 0.06 0.03 0.13 0.05 0.01 0.23 0.02 0.21 0.22 0.18
Eastern Coast 0.16 0.17 0.26 0.10 0.28 0.09 0.36 0.08 0.05 0.01
Yangzi River 0.27 0.19 0.39 0.33 0.29 0.21 0.53 0.13 0.19 0.07
Belt & Road 0.51 0.28 0.41 0.22 0.04 0.22 0.29 0.03 0.01 0.17
Y X
Driving Forces of Urbanization in China
Y
181203Geodetector & Its Applications in Natural & Social Sciences
(C) wangjf@Lreis.ac.cn15
2018.12.03
Y X
Determinants of Soil Antibiotic in a Town
Li XW, et al. 2013. Influence of planting patterns on Fluoroquinolone residues in the soil of an intensive vegetable cultivation area in north China. Science of the Total Environment 458-460: 63-69.
Vegetable planting models (0.28) > chicken dung quantity (0.20) > elevation (0.18) > planting age (0.09) > chicken dung types (0.06) > area of greenhouse (0.02).
Y
Y X
Determinants of NTD in a County
Lithology Types
Topography
Soil Types
Wang JF, Li XH, Christakos G, et al 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): 107-127.
Primary environment (watershed, lithozone, and soil) strongly controls the NTD. Basic nutrition (food) is more important than artificial environment (fertilizer) in
controlling the spatial pattern of NTDs. Ancient materials released from faults then spreading along slopes dramatically
increase the risk of NTDs.
Y
181203Geodetector & Its Applications in Natural & Social Sciences
(C) wangjf@Lreis.ac.cn16
2018.12.03
1. Background
2. Spatial Stratified Heterogeneity: Geodetector
3. Properties of Geodetector
4. Software & Examples
5. Q/A
6. Flexible Geodetector
7. Summary
How to make stratification (MS)1. If x is categorical, that’s fine;2. If x is numerical:(1) MS according to the existing commons in your discipline;(2) Try different stratifications{h}, use the one with bigger q, good explanation
like regression, (OLS) try different {b}, use one which maximize R2.(3) Equally divided 7 strata, according to the human sense, like ARCGIS.3. Multi {xi} may have different strata {hi}, like {xi}~{bi} in regressionWhen software reports error or abnormal result, please checkNumerical X should be stratified, > 2 sample units are required in each stratum.q value and p valueWhen measuring SSH of a variable y: 100q% SSH degree, at p sig. level.When attributing y to x: x explains 100q% of y, no need to report p value.Should qi = 1 ?No, because of nonlinear coupling between y and x, and interaction between x.Direction of q ?No direction for nonlinear; linear then direction in strata.Big sample, say 1m pixels of a remote sensing imageResampling, 100 sample units in a stratum is fine; R-Geodetector software
181203Geodetector & Its Applications in Natural & Social Sciences
(C) wangjf@Lreis.ac.cn17
2018.12.03
1. Background
2. Spatial Stratified Heterogeneity: Geodetector
3. Properties of Geodetector
4. Software & Examples
5. Q/A
6. Flexible Geodetector
7. Summary
1. Measure SSH: q(y|#), where # stands for strata
2. Find SSH: q(y|#)
3. Ranking factors {xk}:qk(y|#xk), k
4. Compare factors’ ranks{xk} btw regions{z}: qzk(y|#xk)
5. Factors’ rank {xk} evolves in time {t}: qtk(y|#xk)
6. Compare factors’ ranks{xk} btw PCAs {s}: qsk(y|#xk)
7. Product interact q(y|x1x2) General interact q(y|#x1#x2)
8. To get higher q value:
(1) First, linear regress y ~ x + e; then Geodetector (e|x);
(2) Super q algorithm: try different strata, get the one max q.
9. dy/dx: Geodetector to find SSH; then regress y~x in strata.
10. If categorical y & numerical x, use the software in (x|y)
11. Visualize Gedetector (please see the next slides …)
181203Geodetector & Its Applications in Natural & Social Sciences
(C) wangjf@Lreis.ac.cn18
2018.12.03
Fig. 7. Determinant power of factors influencing hazard index for health risk Wang HF, et al 2018. EP
Visualization of Geodetector q values
Figure 5: Power of each determinant in ascending sequence (Zhang KS, et al 2017. JTLU)
Figure 6. The power of determinant for the investment in residential buildings (IRB), immigrant (Yang SF, et al 2017. Sustainability)
Visualization of Geodetector’s interaction btw two variables
Song YZ, et al 2018. RSRen Y, et al 2016. EP
181203Geodetector & Its Applications in Natural & Social Sciences
(C) wangjf@Lreis.ac.cn19
2018.12.03
1. Background
2. Spatial Stratified Heterogeneity: Geodetector
3. Properties of Geodetector
4. Software & Examples
5. Q/A
6. Flexible Geodetector
7. Summary
Sampling
Monitor
Remotesensing Spatial Statistics
Mathematics
Data Modelling Population
Modern�Paradigm�in�Geographic�Studies
Prediction
Patterns
Attribution
181203Geodetector & Its Applications in Natural & Social Sciences
(C) wangjf@Lreis.ac.cn20
2018.12.03
Population
Statistics
Spatial Autocorrelation(1950 ~ 1995)
Spatial Heterogeneity
Local(1992 ~ 2000)
Stratified(2010-)
Measure Moran I; Semivariogram Gi; LISA; SatScan Geodetector q
Attribution Spatial regress; BHM GWR Geodetector q
Prediction Kriging; IDW; Spine N/A Sandwich; MSN, Bshade; SPA
Spatial�Statistics
Wang JF, Zhang TL, Fu BJ. 2016. A measure of spatial stratified heterogeneity. Ecological Indicators 7: 250-256.
q = 1∑
h = 1h = 2
h = 1 h = 3 h = 4
Sample
Geodetector
181203Geodetector & Its Applications in Natural & Social Sciences
(C) wangjf@Lreis.ac.cn21
2018.12.03
Applications of Geodetector q
Spatial stratified heterogeneity (SSH) is prevalent in the nature• Good news: understand the nature; linearization • Bad news: cause sample bias; global model confounded
Properties of Geodetector q• Y is numerical, X is categorical• Y = q(X): general coupling, no assumption of linearity, • Y = q(X1 X2): general interaction, not limitation of product.• The stratification is flexible: in spatial, temporal, attribute, spectrum, etc.
Aim Algorithms Interpretation
#Yq(Y | #); q [0, 1]
q = 0, no SSH; q = 1, perfect SSH; q: degree of SSHmax q(Y | #)
Xq(Y | #X) If X determines Y, their spatial distribution tend to be consistent
q [0, 1]: 100q% of variance of Y is explained by the strata of Xmax q(Y | #X)
X1,2 q(Y | X1 X2) Interaction between X1 and X2 impacting Y
Thanks !
www.geodetector.cn