Sharp tools make good work

--The Analects of Confucius 



Software for testing spatial stratified heterogeneity (SSH) and making spatial attribution



1.       Introduction

2.       How to Use This Software

3.       Output of Geodetector

4.       Download of Geodetector Software and Example Datasets

5.       Citations

6.       Bibliography of Geodetector

7.       Developers and Contact Information



1.      Introduction

Spatial stratified heterogeneity (SSH) refers to the phenomena that within strata are more similar than between strata, such as well known landuse types and climate zones and that yet to be known, is ubiquitous in spatial data. As a set of information, SSH has been a window for humans to understand the nature and society since Aristotle time. In another aspect, SSH may cause confounding in modelling and bias of a sample, which can be solved if SSH is identified then modeling in strata.

Geographical detector is a novel tool to identify SSH and to attribute spatial patterns: (1) measure and find SSH of a variable Y; (2) test the association between two variables Y and X, according to the coupling between their spatial distributions, without assumption of linearity; and (3) investigate general interaction between two explanatory variables X1 and X2 to a dependent variable Y, without any assigned interaction such as product in econometrics. All of the tasks are implementable by the geographical detector q-statistic (Fig. 1):


Image 1

Fig. 1. Principle of Geodetector


where N and  stand for the number of units and the variance of Y in study area, respectively;  the population Y is composed of L strata (h = 1, 2, …, L), Nh and  stand for the number of units and the variance of Y in stratum h, respectively. The strata of Y (red polygons in Fig.1) are a partition of Y, either by itself (h(Y) in Fig. 1) or by an explanatory variable X which is a categorical variable (h(X) in Fig. 1). X should be stratified if it is a numerical variable, the number of strata L might be 2-10 or more, according to prior knowledge or a classification algorithm. [(N-L)q]/[(L-1)(1-q)] ~ F(L-1, N-L, g), where g is a non central parameter (Wang et al 2016).

In Geodetector, the terms “spatial stratified heterogeneity (SSH)”, “stratification”, “classification” and “partition” are equivalent.

Interpretation of q value (please refer to Fig.1). The value of q  [0, 1].

If Y is stratified by itself h(Y), then q = 0 indicates that Y is not SSH; q = 1 indicates that Y is SSH perfectly; the value of q indicates that the degree of SSH of Y is q.

If Y is stratified by an explanatory variable h(X), then q = 0 indicates that there is no association between Y and X; q = 1 indicates that Y is completely determined by X; the value of q-statistic indicates that X explains 100q% of Y. Please notice that the q-statistic measures the association between X and Y, both linearly and nonlinearly.

Besides identification of SSH and attribution, Geodetector q statistic helps to avoid confounding in global models, overfitting in local models, and sampling bias in data collection. (1) SSH in population causes confounding in global models, appeared as insignificant statistical results; (2) Local models sometimes result in overfitting or their parameters are too many to be interpretable; (3) A sample would be biased to population if the latter is SSH and not all strata are sampled. All the three problems can be avoided if SSH is identified (by Geodetector q statistic) so simple models or stratified sampling is applied to each of the strata, separately. Please note that the “spatial” in SSH can be either geospatial or the spatial in mathematics such as time, attributes.

Functions of Geodetector. Geographical detector consists of four functions:

(1)    The risk detector indicates potential risk areas Y(X);

(2)    The factor detector q-statistic measures the SSH of a variable Y, or the determinant power of a covariate X of Y;

(3)    The ecological detector identifies the impact differences between two risk factors X1 ~ X2;

(4)    The interaction detector reveals whether the risk factors X1 and X2 (and more X) have an interactive influence on a disease Y. (Fig.2)



Fig.2. Interaction between X1 and X2 upon Y


2.      How to Use This Software

The GeoDetector software was developed using Excel and R, respectively. The tools are free of charge, freely downloadable, and easy to use, and were designed without any GIS plug-in components and with “one click” execution. Users can run the following demo, then simply replace the demo data in the software using your own data, click Run and you get results ! We henceforth describe Excel Geodetector software. R users can download the R Geodetector software in the following section “Download of Geodetector Software and Example Datasets”.


As a demo, neural-tube birth defects (NTD) Y and suspected risk factors or their proxies Xs in villages are provided, including data for the health effect layers “NTD prevalence” and environmental factor layers, “elevation”, “soil type”, and “watershed”. Their field names are defined as Y and X1, X2, X3 respectively.

Step 1. Download the software and input your data in Excel

(1) Download the Excel Geodetector software (In the following section “Software and Examples Data Download”), one click to download any one of the three Examples, unzip the downloaded file, you will find an Excel file (this is Geodetector software with an Example dataset!) and double click the Excel file, Fig. 3 and Fig. 5 appear. Fig. 3 gives the format of the input data for the GeoDetector: each row denotes a sample unit (e.g. a village); the 1st column record the disease prevalence (Y); the 2nd and following columns denote partitions of Y or factors X, the latter were partitioned according to the similarity within strata.

(2) Input your data into the Excel Geodetector software in the format of Fig. 3. Then go to Step 2.


说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: image004

Fig. 3. Input data in Excel and the execution interface

(Note: Y is numerical; X MUST be categorical, e.g. landuse types. If X is numerical it should be transformed to be categorical, e.g. GDP per capita is stratified into 5 strata)


(3) If your data is in GIS format, as Fig. 4, please transform the GIS data into Excel data as Fig. 3.


Fig. 4. Data in GIS format


Step 2. Run GeoDetector software

Only one operation interface was designed (Fig. 5). The function of the “Read Data” button is to load data; thus, when the button is clicked, all variables are listed in the “variables” list box. Then, disease and partition of Y or environmental factor variables are selected into their corresponding list boxes Y and X on the right of the interface. Finally, GeoDetector is executed by clicking the “Run” button.


说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: UI

Fig. 5. User interface for GeoDetector


3.      Output of Geodetector

GeoDetector outputs results from the risk detector, factor detector, ecological detector, and interaction detector in four Excel spreadsheets (Fig. 6).


说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: image014

Fig. 6. Interface for GeoDetector results


In the “Risk detector” sheet (Fig. 7), result information for each environmental risk factor is presented in two tables. The first table gives the average disease incidence in each stratum of a risk factor, the name of which is written at the top left of the table. The second table gives the statistically significant difference in the average disease incidence between two strata; if there is a significant difference, the corresponding value is “Y”, else it is “N”.



Fig. 7. Results of risk detector


The Fig. 8 shows the output format of the q values for each environmental risk factor, as given in the “Factor detector” sheet. The table header gives the names of the environmental risk factors, while the associated q values (q1, q2, …, qn) and their corresponding p values are presented in the row below.




Fig. 8. Results of factor detector


In the “Ecological detector” sheet (Fig. 9), results of the statistically significant differences between two environmental risk factors are presented. If Y(X1) (risk factor names in row) was significantly bigger than Y(X2) (risk factor names in column), the associated value is “Y”, while “N” expresses the opposite meaning.


Fig. 9. Results of ecological detector


The format of the results for the interaction detector is shown in Fig. 10.Interaction relationships” below the table represent the interaction relationship for the two factors. The relationship is defined in a coordinate axis. It has 5 intervals, including “(-min(q(x), q(y)))”,“(min(q(x), q(y)), max(q(x), q(y)))”, “(max(q(x), q(y)), q(x) + q(y))”,“q(x) + q(y)”,“( q(x) + q(y),+∞)”, and the interaction relationship is determined by the location of q(xÇy) in the 5 intervals (see Table 1).



Fig. 10. Results of interaction detector


Table 1 Redefined interaction relationships

Graphical representation




q(X1ÇX2) < Min(q(X1), q(X2))


Weaken, nonlinear

Min(q(X1),q(X 2))<q(X1Ç X2)<Max(q(X1)), q(X2))


Weaken, uni-


q(X1Ç X2) > Max(q(X1), q(X2))


Enhance, bi-


q(X1Ç X2) = q(X1)+ q(X2)




q(X1Ç X2) > q(X1)+ q(X2)


Enhance, nonlinear


说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: image029


4.      Download of Geodetector Software and Example Datasets

The software was developed using Excel 2007 and R, respectively. It is completely free. You can click any one of the following links to download the Geodetector software. The first three are Geodetector software in Excel: (1) click one and unzip the file, an Excel file appears; (2) click the Excel file to start the Geodetector, you may exercise the demo data; then (3) input your own data to get your own results.

1: GeoDetector Software in Excel, enclosed an Example of a Disease Dataset

2: GeoDetector Software in Excel, enclosed an Example of a Toy Dataset

3: GeoDetector Software in Excel, enclosed an Example of a NDVI Dataset

4: GeoDetector Software in R


5.  Citations. The Geodetector can be cited as:

[1] Wang JF, Li XH, Christakos G, Liao YL, Zhang T, Gu X & Zheng XY. 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.

[2] Wang JF, Zhang TL, Fu BJ. 2016. A measure of spatial stratified heterogeneity. Ecological Indicators 67(2016): 250-256.



6.  Geodetector Bibliography

[1] Wang JF, Li XH, Christakos G, Liao YL, Zhang T, Gu X & Zheng XY. 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.

[2] Luo W, Jasiewicz J, Stepinski T, Wang JF, Xu CD, Cang XZ. 2016. Spatial association between dissection density and environmental factors over the entire conterminous United States. Geophysical Research Letters 43(2): 692-700.

[3] 刘彦随,     . 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.

   Liu YS, Yang R.2012.Spatial characteristics and formation mechanism of the county urbanization in China. Acta Geographica Sinica 67(8): 1011-1020.

[4] 王劲峰,徐成东. 2017. 地理探测器:原理与展望. 地理学报 72(1): 116-134.

   Wang JF, Xu CD. 2017. Geodetector:Principle and prospective. Acta Geographica Sinica 72(1): 116-134

[5] Lecture ppt in 181203: Geodetector & its Applications in Natural and Social Sciences


1.         Wang JF, Li XH, Christakos G, Liao YL, Zhang T, Gu X & Zheng XY. 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.

2.         Liao YL,Wang JF, Wu JL, Driskell L, Wang WY, Zhang T, Gu X, Zheng XY. 2010. Spatial analysis of neural tube defects in a rural coal mining area. International Journal of Environmental Health Research 20(6): 439-450.


3.         Hu Y, Wang JF, Li XH, Ren D, Zhu J. 2011. Geographical detector-based risk assessment of the under-five mortality in the 2008 Wenchuan earthquake, China. PLoS ONE 6(6): e21427.

4.         Zou B, Wilson JG, Zhan FB, Zeng YN, Wu KJ. 2011. Spatial-temporal variations in regional ambient sulfur dioxide concentration and source-contribution analysis: A dispersion modeling approach. Spatial-temporal variations in regional ambient sulfur dioxide concentration and source-contribution analysis: A dispersion modeling approach. Atmospheric Environment 45: 4977-4985.


5.         Gajos M. 2012. Geoinformation technologies in biomedicine and health care: review of scientific journals. E. Piętka and J. Kawa (Eds.): ITIB 2012, LNCS 7339: 510–524.

6.         Li LF, Wang JF, Wu J. 2012. A spatial model to predict the incidence of neural tube defects. BMC Public Health 12: 951.

7.         Wang JF, Hu Y. 2012. Environmental health risk detection with GeogDetector. Environmental Modelling & Software 33: 114-115.

8.         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.

Liu YS, Yang R.2012.Spatial characteristics and formation mechanism of the county urbanization in China. Acta Geographica Sinica 67(8): 1011-1020.


9.         Cao F, Ge Y, Wang JF. 2013. Optimal discretization for geographical detectors-based risk assessment. GIScience & Remote Sensing 50(1): 78-92.

10.     Li XW, Xie YF, Wang JF, Christakos G, Si JL, Zhao HN, Ding YQ, Li J. 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.

11.     Lee WC. 2013. Assessing causal mechanistic interactions: a peril ratio index of synergy based on multiplicativity. PLoS ONE 8(6): e67424. doi:10.1371/journal.pone.0067424.

12.     Raghavan RK, Brenner KM, Harrington Jr JA, Higgins JJ, Harkin KR. 2013. Spatial scale effects in environmental risk-factor modelling for diseases. Geospatial Health 7(2): 169-182.

13.     Wang JF, Wang Y, Zhang J, Christakos G, Sun JL, Liu X, Lu L, Fu XQ, Shi YQ, Li XM. 2013. Spatiotemporal transmission and determinants of typhoid and paratyphoid fever in Hongta District, China. PLoS Neglected Tropical Diseases 7(3): e2112.

14.     Wang JF, Xu CD, Tong SL, Chen HY, Yang WZ. 2013. Spatial dynamic patterns of hand-foot-mouth disease in the People’s Republic of China. Geospatial Health 7(2): 381-390.


15.     Bai HX, Ge Y, Wang JF, Li DY, Liao YL, Zheng XY. 2014. A method for extracting rules from spatial data based on rough fuzzy sets. Knowledge-Based Systems 57: 28-40.

16.     Hu Y, Gao J, Chi M, Luo C, Lynn H, Sun LQ, Tao B, Wang DC, Zhang ZJ, Jiang QW. 2014. Spatio-temporal patterns of schistosomiasis Japonica in lake and marshland areas in China: the effect of snail habitats. American Journal of Tropical Medicine and Hygiene 91(3): 547–554.

17.     Hu Z, Tang GA, Lu GN. 2014. A new geographical language: a perspective of GIS. Journal of Geographical Sciences 24(3): 560-576.

18.     Huang JX, Wang JF, Bo YC, Xu CD, Hu MG. 2014. Identification of health risks of Hand, Foot and Mouth Disease in China using the Geographical Detector Technique. International Journal of Environmental Research and Public Health 11: 3407-3423.

19.     Luo W. 2014. Impact cratering as a major factor controlling valley dissection density on MARS - a geographical detector approach. 45th Lunar and Planetary Science Conference. 2580.pdf.

20.     Qian Q, Zhao J, Fang LQ, Zhou H, Zhang WJ, Wei L, Yang H, Yin WW, Cao WC, Li Q. 2014. Mapping risk of plague in Qinghai-Tibetan Plateau, China. BMC Infectious Diseases 14: 382.

21.     Ren Y, Deng LY, Zuo SD, et al. 2014. Geographical modeling of spatial interaction between human activity and forest connectivity in an urban landscape of southeast China. Landscape Ecology 29(10): 1741-1758.

22.     Wu JL, Zhang CS, Pei LJ, Chen G, Zheng XY. 2014. Association between risk of birth defects occurring level and arsenic concentrations in soils of Lvliang, Shanxi province of China. Environmental Pollution 191: 1-7.

23.     Xu EQ, Zhang HQ. 2014. Characterization and interaction of driving factors in karst rocky desertification: a case study from Changshun, China. Solid Earth 5: 1329-1340.

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Ding Y, Cai JM, Ren ZP, Yang ZS. 2014. Spatial disparities of economic growth rate of China’s National-level ETDZs and their determinants based on geographical detector analysis. Progress in Geography 33(5): 657-666.

26.         丹,舒晓波,尧    波,曹安庆. 2014. 江西省县域人均粮食占有量的时空格局演变. 地域研究与开发 33(4): 157-162.

Hu D, Shu XB, Yao B, Cao QA. 2014. The evolvement of spatial-temporal pattern of per capita grain possession in counties of Jiangxi Province. Areal Research And Development 33(4): 157-162.

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Tong LG, Xu XL, Fu Y, Wei FH. 2014. Impact of environmental factors on snail distribution using geographical detector model. Progress in Geography 33(5): 625-635.

30.     魏凤娟,李江风,刘艳中. 2014. 湖北县域土地整治新增耕地的时空特征及其影响因素分析. 农业工程学报 30(14): 267-275.

Wei FJ, Li JF, Liu YZ.2014. Spatial-temporal characteristics and impact factors of newly increased farmland by land consolidation in Hubei province at county level. Transactions of the Chinese Society of Agricultural Engineering 30(14): 267-276.

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32.     俞佳根,叶世康. 2014. 空间视角下中国对外直接投资与产业结构升级水平研究. 商业经济研究 34: 127-128.

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34.     Hu Y, Bergquist R, Lynn H, Gao FH, Wang QZ, Zhang SQ, Li R, Sun LQ, Xia CC, Xiong CL, Zhang ZJ, Jiang QW. 2015. Sandwich mapping of schistosomiasis risk in Anhui Province, China. Geospatial Health 10: 324.

35.     Hu Y, Li R, Bergquist R, Lynn H, Gao FH, Wang QZ, Zhang AQ, Sun LQ, Zhang ZJ, Jiang QW. 2015. Spatio-temporal transmission and environmental determinants of schistosomiasis Japonica in Anhui Province, China. PLoS Neglected Tropical Diseases 9(2): e0003470. doi:10.1371/journal.pntd.0003470.

36.     Lee WC. 2015. Testing for sufficient-cause gene-environment interactions under the assumptions of independence and Hardy-Weinberg equilibrium. American Journal of Epidemiology 182(1): 9–16.

37.     Shen J, Zhang N, Gexi geduren, He B, Liu CY, Li Y, Zhang HY, Chen XY, Lin H. 2015. Construction of a GeogDetector-based model system to indicate the potential occurrence of grasshoppers in Inner Mongolia steppe habitats. Bulletin of Entomological Research 105: 335-346.

38.     Yang R, Liu YS, Long HL, Qiao LY. 2015. Spatio-temporal characteristics of rural settlements and land use in the Bohai Rim of China. Journal of Geographical Sciences 25(5): 559-572.

39.     Zhu H, Liu JM, Chen C, Lin J, Tao H. 2015. A spatial-temporal analysis of urban recreational business districts: A case study in Beijing, China. Journal of Geographical Sciences 25(12): 1521-1536.

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Xu QR, Zheng XQ.2015. Analysis of influencing mechanism of urban growth using geographical detector. Acta Geodaetica at Cartographica Sinica 44(S0): 96-101.

44.        , 刘彦随, 龙花楼, 陈呈奕. 2015. 基于格网的农村居民点用地时空特征及空间指向性的地理要素识别——以环渤海地区为例. 地理研究 34(6): 1077-1087.

Yang R, Liu YS, Long HL, Chen CY. 2015. Spatial-temporal characteristics of rural residential land use change and spatial directivity identification based on grid in the Bohai Rim in China. Geographical Research 34(6): 1077-1087.

45.         佳,刘吉平. 2015. 基于地理探测器的东北地区气温变化影响因素定量分析. 湖北农业科学 54(19): 4682-4687.

Yu J, Liu JP.2015. Quantitative Analysis with Geographical Detector on the influence factor of temperature variation in Northeast China. Hubei Agricultural Sciences 54(19): 4682-4687.

46.     湛东升, 张文忠, 余建辉,   , 党云晓. 2015. 基于地理探测器的北京市居民宜居满意度影响机理. 地理科学进展 34(8): 966-975.

Zhan DS, Zhang WZ, Yu JH, Meng B, Dang XY.2015. Analysis of influencing mechanism of residents’ livability satisfaction in Beijing using geographical detector. Progress in Geography 34(8): 966-975.

47.         , 任志远. 2015. 基于Whittaker滤波的陕西省植被物候特征. 中国沙漠 45(4): 901-906.

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48.         , 刘家明,    ,   ,   . 2015. 北京城市休闲商务区的时空分布特征与成因. 地理学报 70(8): 1215-1228.

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50.     Du Z, Xu X, Zhang H, Wu Z, Liu Y. 2016. Geographical detector-based identification of the impact of major determinants on aeolian desertification risk. PLoS ONE 11(3): e0151331.

51.     Fan LX, Wu EQ, Liu J, Qu XC, Ning BA, Liu Y. 2016. Distribution Characteristics of Spermophilus dauricus in Manchuria City in China in 2015 through “3S” Technology. Biomedical Environmental Sciences 29(8): 603-608.

52.     Fei XF, Wu JP, Liu QM, Ren YJ, Lou ZH. 2015. Spatiotemporal analysis and risk assessment of typhoid cancer in Hangzhou, China. Stochastic Environmental Research and Risk Analysis 30: 2155–2168.

53.     Fei XF, Wu JP, Liu QM, Ren YJ, Lou ZH. 2015. Spatiotemporal analysis and risk assessment of thyroid cancer in Hangzhou, China. Stochastic Environmental Research and Risk Assessment 30: 2155–2168.

54.     Ju HR, Zhang ZX, Zuo LJ, Wang JF, Zhang SR, Wang X, Zhao XL. 2016. Driving forces and their interactions of built-up land expansion based on the geographical detector – a case study of Beijing, China. International Journal of Geographical Information Science 30(11): 2188–2207.

55.     Liang P, Yang XP. 2016. Landscape spatial patterns in the Maowusu (Mu Us) Sandy Land, northern China and their impact factors. Catena 145: 321-333.

56.     Liao YL, Zhang Y, He L, Wang JF, Liu X, Zhang NX, Xu B. 2016. Temporal and spatial analysis of neural tube defects and detection of geographical factors in Shanxi Province, China. PLoS ONE 11(4): e0150332. doi:10.1371/journal.pone.0150332.

57.     Lou CR, Liu HY, Li YF, Li YL. 2016. Socioeconomic drivers of PM2.5 in the accumulation phase of air pollution episodes in the Yangtze river delta of China. International Journal of Environmental Research and Public Health 13: 928.

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