Spatial Analysis

1. Spatial Analysis Concepts and Challenges Briggs Henan University 2012

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

6. Process, Pattern and Analysis • Processesoperating 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. 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. 2.5% 2.5% -1.96 1.96 0 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) 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. 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 examinationSee handout!!! You need this course! Briggs Henan University 2012

19. A 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. 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. 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. 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. 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. Large scale >objects are large, small area covered 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 • Small scale >objects are small, large area covered Dallas 0 1 2 10 km polygon point Km Briggs Henan University 2012

29. 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. Non-uniformity of Space: things are not evenly distributed in space Bank robbery Banks • Bank robberies are clustered • But only because banks are clustered 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. Illiteracy in China Non-uniformity of Space and Choropleth Maps 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. 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! • Datafrom 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. 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. 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. 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. Distance is not simple! • Cartesian distance via Pythagorus • Use for projecteddata, 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 unprojecteddata, 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 1st order rook hexagon queen 2nd order Briggs Henan University 2012

44. Interaction Based on a Hierarchy Based on the Gravity Model How do you fly from Zhengzhou to Wuhan? 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 Shanghai Zhengzhou Wuhan Central Place Hierarchy Briggs Henan University 2012

45. Today, we discussed spatial analysisand 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. Texts O’Sullivan, David and David Unwin, 2010. Geographic Information Analysis. Hoboken, NJ: John Wiley, 2nd ed. Other Useful Books: Mitchell, Andy 2005. ESRI Guide to GIS Analysis Volume 2: Spatial Measurement & Statistics. Redlands, CA: ESRI Press. Allen, David W 2009. GIS Tutorial II: Spatial Analysis Workbook. Redlands, CA: ESRI Press. Wong, David W.S. and Jay Lee 2005. Statistical Analysis of Geographic Information. Hoboken, NJ: John Wiley, 2nd ed. Briggs Henan University 2012