Sharp tools make good work
--The Analects of
Confucius
Geodetector
Software for measure and
attribution of stratified heterogeneity (SH)
Contents
1. Introduction
2. Tutorial
3. Output
5. Citations
6. Bibliography
7. FAQs
1.
Introduction
Stratified
heterogeneity (SH)
refers to the phenomena that the within strata are more similar than the
between strata. Examples are landuse types and
climate zones in spatial data, seasons and years in time series, incomes in
strata, etc. SH is ubiquitous in universe and has been a window for humans to
conceptualize the nature and to understand its underlaid principles since
Aristotle time. In another aspect, SH of a population is the sources of sample
bias and statistical confounding.
Geographical
detector is a novel tool to measure and
attribution of SH (Fig. 1):
(1) to measure and find SH of a variable Y;
(2) to test the coupling between two variables Y and X, according to
their spatial distributions, without assumption of linearity of the
association; and (3) to investigate
interaction between two explanatory variables X1 and X2
to a response variable Y, without any
specific form such as assumed product in econometrics (Fig. 2).
Each of the tasks can be accomplished by the geographical
detector q-statistic:
Fig. 1.
Principle of Geodetector
(The
bottom map, the color indicates the values of a population Y. The top map, the population Y
is stratified into strata {h}; the
terms “stratification” and “partition” are equivalent, can be either
classification or zonation. Between the two maps is the equation q(Y|{h}), in which the numerator is the
summation of the within strata variance and the denominator is the pooled
variance.)
where N and s2
stand for the number of units and the variance of Y in a study area, respectively; the population Y is composed of L strata (h = 1, 2, …, L). The strata of Y (red polygons in Fig.1)
are a partition of Y, either by
itself h(Y) or by an explanatory variable X which is a categorical h(X). 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).
The strata of Y (red polygons in Fig.1)
are a partition of Y, either by Y itself or by an explanatory variable X. X
is a categorical variable or 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. The terms “stratified heterogeneity (SH)”, “stratification”,
“classification” and “partition” are equivalent. SH can be either spatial (spatial
stratified heterogeneity, SSH) or aspatial such as
time and some attributes.
Interpretation of q value
(Fig.1).
The
value of q is strictly within [0, 1].
(1)
If Y is stratified by Y itself,
then q = 0 indicates that Y is absent of SH; q = 1 indicates that Y is
SH perfectly; 100q% measures the
degree of SH of Y.
(2)
If Y is stratified by an explanatory variable X, then q = 0 indicates
that there is no coupling between Y
and X; q = 1 indicates that Y is
completely determined by X; X explains 100q% of Y. Please notice
that the q-statistic measures the
association between X and Y, both linearly and nonlinearly.
Geodetector
q statistic helps understand spatial
confounding, sample bias and overfitting.
(1)
Confounding arises if applying a
global model to SH population, appeared as insignificant or misleading
statistical results. The problem can be simply avoided if SH is identified (by Geodetector q
statistic) then modelling in the strata, separately.
(2)
A
sample would be biased if a population is SH and the sample do not cover all
strata. The problem can be solved if SH is identified (by Geodetector
q statistic) then apply stratified
sampling or bias remedy models such as Heckman regression and Bshade method.
(3)
Local
models aim to overcome heterogeneity but often suffer overfitting and too many
parameters to interpret. The problems can be avoided if modelling in strata or
stratifying the parameters of a local model then interpreting the parameters in
the strata.
Functions of Geodetector:
(1) The
risk detector maps response variable in strata: Y(X);
(2) The
factor detector q-statistic measures
the degree of SH of a variable Y; and
the determinant power of an explanatory variable X of Y;
(3)
The ecological detector
identifies the difference of the impacts between two explanatory variables X1 ~ X2;
(4)
The interaction detector
reveals whether the risk factors X1
and X2 (and more X) have an interactive influence on a response variable Y (Fig.2).
Fig.
2.
Interaction between explanatory variables X1
and X2 impacting on a response variable Y: q(Y|X1
X2).
2.
Tutorial
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 is the format of the input data
for the Geodetector: each row denotes a sample unit
(e.g. a village); the 1st column record the response variable 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.
Fig. 3.
Input data in Excel and the execution interface
(Note:
Y is numerical; X MUST
be categorical, e.g. landuse types, seasons. 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.
Fig. 5.
User interface for Geodetector
3.
Output
Geodetector
outputs results from the risk detector, factor detector, ecological detector,
and interaction detector in four Excel spreadsheets (Fig. 6).
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 |
Description |
Interaction |
|
|
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) |
Independent |
|
|
q(X1Ç X2) > q(X1)+ q(X2) |
Enhance, nonlinear |
Legend
4.
Download, with 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
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.
[3] http://www.geodetector.cn/
6. Geodetector
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