1. Concepts and Challenges
Spatial Analysis
Concepts and Challenges
Briggs Henan University 2012

2. Briggs Henan University 2012
Topics
Description versus Analysis
The concepts of Process, Pattern and Analysis
Issues and challenges in spatial data analysis
Measuring space
Briggs Henan University 2012

3. Description and Analysis
Most GIS systems are used by governments and private companies to describe the real world
this helps the organization “do its job”
For example, manage sewer and water networks
Manage land resources
Most GIS systems are primarily designed for this purpose
They are used to develop spatial databases to describe the real world and help manage it.
Briggs Henan University 2012

4. Description and Analysis
Is the locations of the software industry different from the telecommucations industry?
Analysis
Tries to understand the processes which cause or create the patterns in the real world
Understanding processes:
Helps the organization do its job better
Make better decisions, for example
Helps us understand the phenomena itself
This is the role of science
Here, we are using “centrographic statistics” to help answer this question
Briggs Henan University 2012

5. Briggs Henan University 2012
Analysis: Do the locations of the software and telecommucations industries differ?
Description: Water and Sewer system
We will talk about analysis.
Briggs Henan University 2012

6. Process, Pattern and Analysis
Processes operating in space create patterns
Spatial Analysis is aimed at:
Identifying and describing the pattern
Identifying and understanding the process
Create
Patterns
Processes
(or cause)
Briggs Henan University 2012

7. Briggs Henan University 2012
Spatial Analysis is aimed at:
Identifying and describing the pattern
The pattern is clearly clustered
(points are in “groups”)
Identifying and understanding the process
Access to transportation.
Agglomeration economies* from sharing ideas, access to skilled labor, access to business services.
We will focus on spatial analysis
*cost savings from many firms locating in the same area
Briggs Henan University 2012

8. Process, Pattern and Analysis
Often, we cannot observe (or “see’) the process, so we have to infer (“guess at” ?) the process by observing the pattern No
Infer
Yes
Create
Patterns
Processes
(or “cause”)
Briggs Henan University 2012

9. Spatial Analysis: successive levels of sophistication
Four levels of Spatial Analysis:
--Each is more advanced (more difficult!)
Spatial data description:
Exploratory Spatial Data Analysis (ESDA)
Spatial statistical analysis and hypothesis testing
Spatial modeling and prediction
We will look at all 4 levels in this lecture series
More difficult,
but more useful!
(more powerful)
Briggs Henan University 2012

10. Spatial Analysis: successive levels of sophistication
Spatial data description:
Focus is on describing the world,
and representing it in a digital
format
--computer map
--computer database
Uses classic GIS capabilities
--buffering, map layer overlay
--spatial queries & measurement
Briggs Henan University 2012

11. Spatial Analysis: successive levels of sophistication
2. Exploratory Spatial Data Analysis (ESDA):
searching for patterns and possible explanations
GeoVisualization through data graphing and mapping
--Density Kernel Estimation
--Overlay transportation network
Briggs Henan University 2012

12. Spatial Analysis: successive levels of sophistication
2. Exploratory Spatial Data Analysis (ESDA):
searching for patterns and possible explanations
GeoVisualization through calculation and display of Centrographic statistics
--Calculation of Centrographic
Statistics
Briggs Henan University 2012

13. Spatial Analysis: successive levels of sophistication
3. Spatial statistical analysis and hypothesis testing
Are data “to be expected” or are they
“unexpected” relative to some statistical model,
usually of a random process (pure chance)
We will look at
statistical hypothesis testing for:
--point patterns
--also for polygon data
We can test if the spatial pattern for software & telecommmunications companies in Dallas is
clustered (a pattern) or “random” (no pattern)
-1.96
2.5%
1.96
Briggs Henan University 2012

14. Spatial Analysis: successive levels of sophistication
4. Spatial modeling: prediction
Construct models (of processes) to
predict spatial outcomes (patterns)
Notice how the density of points (number per square km) decreases as we move away from the highway.
We can construct regression
models to predict location patterns.
Density of points = f (distance from highway)
However, for spatial data, we need special:
Spatial regression models
Density of points
Distance from highway
Briggs Henan University 2012

15. The first example of Spatial Analysis
John Snow’s maps of cholera in 1850s London
Was it ESDA or hypothesis testing?
Did he discover the association between water and cholera after drawing the map: ESDA
Did he draw the map in order to prove the association: using a map for hypothesis testing
Briggs Henan University 2012

16. Maps are good—but more is needed!
A. Is this clustered?
B. Is this clustered?
We must test rigorously using spatial analysis methods.
Not just look and guess
Source: R & Y, p. 5
Briggs Henan University 2012

17. Briggs Henan University 2012
Why is this important? ?
We must measure and test
--not just look and guess!
Is it clustered?
Because that is science!
Because that is how earth management decisions must be made!
Briggs Henan University 2012

18. Why we need analysis --and not just visual examination See handout!!!
You need this course!
Briggs Henan University 2012

19. Briggs Henan University 2012
Clustered or random? B
Clustered or random?
(clustered = points are in “groups”)
= pattern exists
(random = points can be anywhere)
= no pattern
Source: Rogerson and Yamada, 2009
Briggs Henan University 2012

20. Issues/Challenges/Problems
in Spatial Analysis
Summarize these now.
Talk in greater detail about them throughout this lecture series.
Briggs Henan University 2012

21. Critical Issues in Spatial Analysis
Spatial autocorrelation
Data from locations near to each other are usually more similar than data from locations far away from each other
Modifiable areal unit problem (MAUP-zone )
Results may depend on the specific geographic unit used in the study
Province or county; county or city
Scale affects representation and results
Cities may be represented as points or polygons
Results depend on the scale at which the analysis is conducted: province or county
MAUP—scale effect
Ecological fallacy
Results obtained from aggregated data (e.g. provinces) cannot be assumed to apply to individual people
MAUP—individual effect
Non-uniformity of Space
Phenomena are not distributed evenly in space
Be careful how you interpret results!
Edge issues
Edges of the map, beyond which there is no data, can significantly affect results
Briggs Henan University 2012

22. Critical Issues in Spatial Analysis
Modifiable areal unit problem (MAUP)
Results may depend on the specific geographic unit used in the study
Province or county; county or city
MAUP—zone effect
Scale affects representation and results
Results depend on the scale at which the analysis is conducted
MAUP—scale effect
Ecological fallacy
Results obtained from aggregated data (e.g. provinces) cannot be assumed to apply to individual people
MAUP—individual effect
Non-uniformity of Space
Phenomena are not distributed evenly in space
Be careful how you interpret results!
Edge issues
Edges of the map, beyond which there is no data, can significantly affect results
Spatial autocorrelation –the biggest of all!
Data from locations near to each other are usually more similar than data from locations far away from each other
Briggs Henan University 2012

23. Briggs Henan University 2012
Modifiable areal unit problem (MAUP): 3 in 1!!!
Results may depend on the specific geographic unit used in the study
Dangerous to assume results for one set of units will also apply for another
Zonal effect: Similar size and number of units, but different boundaries
Zip codes versus census tracts
Postal zones versus city neighborhoods
Scale effect: increases size and decreases number of units
Counties versus provinces
Individual effect: ecological fallacy
results from geograhic units
may not apply to individual people
Briggs Henan University 2012

24. Modifiable areal unit problem (MAUP): zonal
Census Tracts versus Zip codes
Problem not as big—usually—as for scale differences
Census Tract
(used by US Census Bureau for data)
Zipcode Areas
(used by US Post Office)
Briggs Henan University 2012

25. Briggs Henan University 2012
Modifiable areal unit problem (MAUP): scale
Counties versus Provinces codes
Usually a bigger problem than for zonal
Will results be the same?
Do conclusions still apply?
Briggs Henan University 2012

26. Briggs Henan University 2012
Aggregation
combining smaller units into bigger units
affects results!
Note how:
variance (s2) decreases
Correlation coefficient (rXY) increases (‘cos of less variability)
Briggs Henan University 2012

27. Briggs Henan University 2012
Scale:
Results obtained at one scale do not necessarily apply at other scales
A pattern may be clustered at one scale but dispersed at another scale
Population clustered into cities
City populations are dispersed
Scale is always very important in spatial analysis!
Briggs Henan University 2012

28. Briggs Henan University 2012
Scale: Always Important
ratio of distance on a map, to the equivalent distance on the earth's surface.
Scale must be shown on every map
Use scale bar because that is correct when map is enlarged or reduced
Affects how objects are represented on a map and how data is stored in a data base
Important for research design and data collection
Cities may be points or polygons
Large scale >objects are large, small area covered Km 1 2
Small scale >objects are small, large area covered
Dallas
polygon
10 km
point
Briggs Henan University 2012

29. Briggs Henan University 2012
Ecological fallacy
Results from aggregated data (e.g. provinces) cannot be applied to individual people
A special case of the MAUP problem
Encountered in spatial and non-spatial analysis
Usually because a variable was left out (omitted variable)
crime rate
income
Cannot assume low income people commit crimes.
Perhaps low income provinces do not have money to pay for police.
--”Yuans on policing” is omitted variable
If low income provinces have high crime rate.
Briggs Henan University 2012

30. Briggs Henan University 2012
Non-uniformity of Space: things are not evenly distributed in space
Bank robberies are clustered
But only because banks are clustered
Bank robbery
Banks
Bank Robberies
Bonnie and Clyde were two very famous bank robbers in Texas in the 1930s
They were asked “Why do you rob banks?”
They replied “Because that is where the money is!
What a stupid question!”
(the expected answer was, perhaps, “because we needed money for food”)
Briggs Henan University 2012

31. Non-uniformity of Space and Choropleth Maps
Illiteracy in China
Henan does not have high illiteracy!
Henan has high illiteracy!
Briggs Henan University 2012

32. Non-uniformity of Space and Choropleth Maps
Always normalize data if drawing a choropleth map
By total population
By geographic area
Do not map “counts” unless population and/or geographic area are the same size for all observation units
Failing to “normalize” is a very common mistakes made by non-professional GIS people
You are professionals
Do not make that mistake!
Briggs Henan University 2012

33. Briggs Henan University 2012
Edge or Boundary Effect
Every study region has a boundary (unless you study the entire world!)
You do not have data for outside your study region
However, the outside data can affect the inside data if there is spatial autocorrelation
Consequently, edges of the map, beyond which there is no data, can significantly effect results
Solutions:
Core study region
periphery or guard area
Use the toroid concept
--bends the left edge to meet the right and the top to meet the bottom
--uses all the data
--assumes that there is no systematic spatial trend in data
Use Core/Periphery
--analyze only the core
--use edge only for “neighborhood”
calculations
--reduces amount of data available
Briggs Henan University 2012

34. Spatial Autocorrelation
Spatial organization is usually important
The results from a traditional regression analysis ignore how the observation units are organized spatially!
Data from location near to each other are usually more similar than data from locations far away
Must be considered in your analysis
Also causes serious problems with traditional statistical hypotheses testing
Spatial statistical models are essential
Briggs Henan University 2012

35. What is the most common mistake in GIS analysis?
Much more basic than any discussed above.
Briggs Henan University 2012

36. Briggs Henan University 2012
Single most common error in GIS Analysis
--intending a one to one join of attribute data to spatial table
--getting a one to many join of attribute data to spatial table
51 states
Hawaii
Spatial
After joining attribute to spatial data
54 observations
Briggs Henan University 2012

37. Briggs Henan University 2012
Errors with the attribute data will occur if Hong Kong or Guangdong are not correctly drawn in the shapefile (spatial data)
If there are islands, the province must drawn as a multi-part feature in the shapefile (the spatial data)
--then there is only one row in the attribute table
If each island is drawn as a separate feature, there will be multiple rows in the attribute table
Briggs Henan University 2012

38. Briggs Henan University 2012
Measuring Space
Not easy!
Briggs Henan University 2012

39. Spatial is special: 3 primary concepts
Distance
Adjacency
or neighborhood
Interaction
Briggs Henan University 2012

40. Fundamental Spatial Concepts
Distance
The magnitude of spatial separation
Euclidean (straight line) distance often only an approximation
Adjacency or neighborhood
Nominal or binary (0,1) equivalent of distance
Levels of adjacency exist: 1st, 2nd, 3rd nearest neighbor, etc..
Interaction
The strength of the relationship between entities
An inverse function of distance
Briggs Henan University 2012

41. Briggs Henan University 2012
Distance is not simple!
Cartesian distance via Pythagorus
Use for projected data, at local scale
Spherical distance via spherical coordinates
Cos d = (sin a sin b) + (cos a cos b cos P)
where: d = arc distance
a = Latitude of A
b = Latitude of B
P = degrees of long. A to B
Use for unprojected data, or at world scale
possible distance metrics:
Euclidean straight line/airline
city block/manhattan metric
distance through network
time/friction through network
Briggs Henan University 2012

42. Spatial neighbors based on adjacency
Hexagons
Square raster
Irregular
Rook: Sharing a boundary
Queen:
Sharing a boundary or a point
Briggs Henan University 2012

43. 1st and 2nd order adjacency
rook
hexagon
queen
2nd
order
Briggs Henan University 2012

44. Briggs Henan University 2012
Interaction
Based on a Hierarchy
How do you fly from Zhengzhou to Wuhan?
Based on the Gravity Model
Gravity Model: Interaction between i and j is a function of:
Pi --the population (size) at i
Pj --the population (size) at j
dij --the distance from i to j
Wuhan
Zhengzhou
Shanghai
Central Place Hierarchy
Briggs Henan University 2012

45. Next time: Spatial data and why it is special!
Today, we discussed spatial analysis and some of its problems and challenges However, to do spatial analysis you must have spatial data
Next time:
Spatial data and why it is special!
Briggs Henan University 2012

46. Briggs Henan University 2012
Texts
O’Sullivan, David and David Unwin, Geographic Information Analysis. Hoboken, NJ: John Wiley, 2nd ed.
Other Useful Books:
Mitchell, Andy ESRI Guide to GIS Analysis Volume 2: Spatial Measurement & Statistics. Redlands, CA: ESRI Press.
Allen, David W GIS Tutorial II: Spatial Analysis Workbook. Redlands, CA: ESRI Press.
Wong, David W.S. and Jay Lee Statistical Analysis of Geographic Information. Hoboken, NJ: John Wiley, 2nd ed.
Briggs Henan University 2012