1. Stefan Falke stefan@me.wustl.edu
An Overview of Spatial Data Analysis
Stefan Falke

2. Pop vs Soda vs Coke

3. Pop vs Soda vs Coke by County

4. 2000 Presidential Election Results
Bush
States: 30
votes: 50,456,169
Gore
States: 21
votes: 50,996,116

5. 2000 Presidential Election Results by County
Bush
Gore

6. Environmental Pattern and Trend Analysis
When analyzing environmental data we examine:
Spatial Patterns
Temporal Trends
We are particularly interested in changes in these patterns and trends and relationships with other patterns and trends
The analysis also strives to determine why we see these patterns and trends – what are the casual factors and what are their impacts.

7. Spatial and Temporal Data Analysis
Turns raw data into useful information
by adding greater informative content and value
Wisdom
Knowledge /
Evidence
Data
Information

8. What is Spatial Data Analysis?
Spatial analysis is the quantitative and qualitative study of phenomena that are located in space.
Environmental spatial data analysis describes characteristics and behavior of the environment
Explores patterns, trends, and relationships in environmental data
Seeks to explain these patterns, trends, and relationships
Differs from general data analysis and statistics in that:
Spatial data are dependent on location and related by location (they do not adhere to the independence assumption made in regular data analysis)
Have properties that require special analysis methods
Why is spatial analysis such a big deal?
about 85% of environmental data is spatial

9. What is GIS?
Traditional definition is that GIS is a set of computer tools for accessing, processing, visualizing, analyzing, interpreting, and presenting spatial data.
‘GIS’ is Geographical Information System OR IS IT
Geographical Information Science?
GISystems: Emphasis on technology and tools
GIScience: Fundamental issues raised by the use of GIS, such as
Spatial analysis
Map projections
Accuracy
Scientific visualization
Implementation and application of GIS covers a wide spectrum:
Simple maps
Overlaying multiple map “layers”
Conducting proximity or cluster analysis based on distance
Comparing data sets (simple spatial statistics)
Complex statistical analysis

10. Nature
Vol 427
22 January 2004

11. Special Spatial Nomenclature
Geographic – Limited to phenomena and problems relating to Earth’s surface and near-surface
Spatial – Any space, including geographic, but not restricted to geographic coordinate space, e.g. medical imaging
Geospatial – A recent term to represent the subset of spatial applied specifically to the Earth’s surface. (synonymous with geographic)

13. Tobler’s First Law of Geography
“Everything is related to everything else, but near things are more related than distant things.”
Tobler, 1970
This general assumption is what subjects spatial data subject to special statistical laws

14. Types of Spatial Analysis
There are literally thousands of techniques
Bailey and Gatrell, 1995 offer four spatial data analysis classes:
Point Data Analysis
Do the locations of point data and the relationship among the points represent a ‘significant’ pattern
Continuous Data Analysis
What are the spatial pattern and characteristics over a region given a set of samples
Area Data Analysis
Analysis of data that have been aggregated over a spatial zone, e.g. county

15. The John Snow Map
A classic example of the use of location to draw inferences
1854 cholera outbreak in London
Point data map indicated some spatial clustering
Overlaying a map of water pump locations showed many cases were concentrated around a single pump

16. Continuous Data Analysis
Temperature data is well suited for converting from point to continuous data
- It has high spatial density
- Ambient temperature is relatively spatially homogenous (no sharp gradients)

17. County Level Aggregated Data
Also known as a chloropleth plot

18. Scale
The most appropriate analysis method to use depends on the spatial and temporal scales of the problem.
The spatial variability of temperature at a ‘local’ scale is not necessarily significant when conducting an analysis over at the ‘regional’ or ‘global’ scale.

19. Scale Dependent Measurements
How long is Maine’s coastline?
length=340 km
length=355 km
length=415 km
From Longley et al., 2001

20. What’s in a map, anyway? Theme: Static map
Maps of entities whose location is known and constant (relatively)
Roads, borders, locations of buildings
These types of layers are often referred to as “thematic” layers
Are usually used to provide context to other spatial data
Statistical: Realization of one of the many possible patterns that may have been generated by a process
Given a set of conditions, a given spatial pattern is just one instance among a distribution of possible patterns
The question is: Is the observed realization significantly different than what would be expected by chance?

21. Deterministic versus Stochastic Processes
Deterministic processes have one realization: the value at a given location is always the same, regardless of the number of times the process is occurs
Stochastic processes have multiple realizations that are not precisely predicted and involve a random component.
For our purposes, random refers to the method used to generate a pattern not the resulting pattern itself.

22. Examples of Deterministic & Stochastic Processes
random variable

23. Random Spatial Processes
A random process does not mean that all events are independent of one another, as is the case with flipping a coin or rolling dice.
Rather, spatial random processes are random with dependence (or rules).
Consider a “conditionally” random display of 4 coins:
Flip the first 3 coins and display by their flipped side (head or tails)
The 4th coin will not be flipped
The 4th coin is displayed as follows:
If the 2nd and 3rd flipped coins are heads, the 4th is the same as the first
Otherwise, the 4th is opposite of the first.

24. Basic Statistical Concepts
Variance:
Mean:
Median: The value in the distribution at which 50% of the data points lie both above and below
Covariance:
Frequency/Probability Distributions
Normal or Gaussian
Poisson
mean=variance
mean=median

25. Distribution Summary Statistics
The features of a distribution can be summarized using:
Measures of Location
Mean
Median
Quantiles
Measures of Spread
Standard Deviation = Square Root of Variance
Measures of Shape
Coefficient of skewness – a measure of symmetry
Kurtosis – a measure of the likelihood of outliers

26. Complete Spatial Randomness
Take as an example a randomly generated point data set
where
1) the chance of a given x,y point existing is equal to the chance any other point existing (uniform probability distribution)
2) the existence of a x,y point is independent of the existence of any other point
These two conditions constitute an independent random process (IRP) or complete spatial randomness (CSR)

27. Exploratory Spatial Data Analysis (ESDA)
Aim is to identify data properties for purposes of pattern detection
Based on the use of graphical and visual methods and the use of numerical techniques that are statistically robust i.e. not much affected by extreme or atypical data values.
ArcGIS Geostatistical Analyst extension
contains a set of ESDA tools:
Histogram (Frequency Distribution)
Voronoi Map
QQPlot
Trend Analysis

28. Exploratory Analysis Example

29. Summary Statistics

30. Quantile Plots
Graphs the quantiles of a dataset against the quantiles of a normal distribution

31. Vornoi Plot
Voronoi plots assign or calculate values to a point’s polygon.
Including:
value itself
mean of neighboring polygons
most frequent value among neighboring polygons
unique value among neighbors
variation among neighbors

32. Spatial Smoothing/Averaging

33. Data Types Two general views to organizing spatial data:
Entities or objects
Point measurements, rivers, structures
Have attributes or features attached to them
Point, vector or area format
Values exist at discrete locations
Fields
Continuous data such as temperature gradient fields and satellite imagery
Values exist over an area
Raster format (grids)

34. Data Types
Entities and fields can be transformed to the other type

35. Raster and Vector Data Models
Real World
600 1 2 3 4 5 6 7 8 9 10 1 B G
Trees
500 2 B G G 3 B
400 4 B G G
Trees
Y-AXIS 5 B G G
300 6 B
G G BK
House 7 B
200 8 B B
River 9 B
100 10 B
100
200
300
400
500
600
X-AXIS
Raster Representation
Vector Representation
adapted from Lembo, 2003

36. Landcover Raster Grid (16-20) (11-15) (6-10) (1-5) 2 17 16 15 14 11 1312 10 8 7 6 5 4 3
Legend
Mixed conifer
Douglas fir
Oak savannah
Grassland

37. What is GIS?
Traditional definition is that GIS is a set of computer tools for accessing, processing, visualizing, analyzing, interpreting, and presenting spatial data.
‘GIS’ is Geographical Information System OR IS IT
Geographical Information Science?
GISystems: Emphasis on technology and tools
GIScience: Fundamental issues raised by the use of GIS, such as
Spatial analysis
Map projections
Accuracy
Scientific visualization
Implementation and application of GIS covers a wide spectrum:
Simple maps
Overlaying multiple map “layers”
Conducting proximity or cluster analysis based on distance
Comparing data sets (simple spatial statistics)
Complex statistical analysis

38. GIS Functionality Filtering Aggregation Integration
Retrieves a subset of a dataset
Examples
Query (search)
Aggregation
Combines attributes or features within data sources (layers)
Reclassify, dissolve
Integration
Combine two or more data sources (layers)
Example
Polygon overlay, table joining

39. Spatial Queries (Filter)
Identifying features based on spatial criteria
Criteria include variations on:
adjacency, containment, arrangement, and connectivity
Adjacency
Which states are adjacent to the State of Missouri?
Containment
Which states “contain” the Mississippi River and its tributaries?

40. Reclassification (Aggregation)
An assignment of a class or value based on the attributes or geography of an object

41. Reclassification & Dissolve

42. Variable Distance Buffering

43. Polygon Overlay (Integration)
Topology describes the relationships between elements of a map.
A topological data structure defines the elements of the map in a way that makes it possible to know which line segments are connected to each other and to know what polygon is adjacent to each side of a line segment.

44. Polygon Overlay Examples
“Cookie-cutter” method

45. © Paul Bolstad, GIS Fundamentals
Coordinate Systems
A geographical coordinate system uses a three-dimensional spherical surface to define locations on the earth.
Divides space into orderly structure of locations.
Two types: Cartesian and angular (spherical)
© Paul Bolstad, GIS Fundamentals

46. Parallels and Meridians
Meridians are great circles of constant longitude
Example is the prime meridian
Parallels are circles of constant latitude
Example is the equator
latitude (φ): angular distance from equator
longitude (λ): angular distance from standard meridian
St. Louis 38° 39' N 90° 38' W
New York 40° 47' N 73° 58' W
Los Angeles 34° 3' N 118° 14' W
Rome 41° 48' N  12° 36' E
Sydney 33° 52' S  151° 12' E

47. Earth’s Expanding Waistline
From the Chronicle of Higher Education Jan 17, 2003

48. Datum
While a spheroid approximates the shape of the earth, a datum defines the position of the ellipsoid relative to the center of the Earth
The datum provides a frame of reference for measuring locations on the surface of the Earth
A datum is chosen to align a spheroid to closely fit the Earth’s surface in a particular area

49. Map Projections and Distortions
Three general types of projections:
Equal area – the ratio of areas on the earth and on the map are constant. Shape, angle, and scale are distorted.
Conformal – the shape of any small surface of the map is preserved in its original form. If meridians and parallel lines are at 90-degree angles, then angles are also preserved.
Equidistant - preserve distances between certain points. Scale is not maintained correctly, however, typically one or more lines has its scale maintained.

50. Comparing Projections

51. Summary Statistics of a Point Pattern
Mean center average of the x and y coordinates (geographic mean) X
Standard Distance average distance of points from center (provides measure of dispersion) X
Summary Circle
Centered at mean center with a radius of the standard distance X

52. US Population Density

53. Geographic Center of US Population
The center of the US population is calculated as the average latitude and longitudes weighted by the population at a uniformly spaced set of points

54. Quadrant Count
A quadrant count is conducted by superimposing a regular grid over data, counting the number of events in each grid cell and divide the count by its cell area to get intensity.
40 grid cells
Variance:
Mean cell count
A s2 to µ ratio greater than 1 indicates clustering

55. Spatial Autocorrelation
Defines the correlation between values of the same variable at different spatial locations
Positive Spatial Autocorrelation
Like values tend to cluster in space
Negative Spatial Autocorrelation
Neighbors are dissimilar
Zero Spatial Autocorrelation
No correlation

56. spatial estimation method continuous surface of estimates (map)
From points to fields
The factor that determines how much influence a data point is assigned during the calculation of the estimate
spatial estimation method
ci is the estimated value at location i
n is the number of data points
cj is the value at data point j
wij is the weight assigned to data point j
continuous surface of estimates (map)
point
monitoring data
The weighting factor is usually the distinguishing feature of interpolation methods.
Biggest challenge: How to determine the weights?

57. Inverse Distance Interpolation
k is the power-law of distance weighting
Constrained to the minimum and maximum values in point data set

58. Spatial Smoothing/Averaging

59. Landcover Raster Grid (16-20) (11-15) (6-10) (1-5) 2 17 16 15 14 11 1312 10 8 7 6 5 4 3
Legend
Mixed conifer
Douglas fir
Oak savannah
Grassland

60. Raster Analysis (Continuous Data)2 7
Moving Windows
minimum
maximum 2 3 5 2 3 6 3 5 7
range
mean 5 4

61. Slope
Slope is the change is elevation (rise) with a change in horizontal position (run).
The steepest decent between a cell and its neighbors is known as the gradient.
Slope is often reported in degrees (0° is flat, 90° is vertical) but is also expressed as a percent

62. Hands-on Exercise: Mapping Census Data
Database manipulation (table joins)
Reprojecting maps
Calculating derived values (population density, change population over time)
Visualization

63. ArcGIS Main Components
ArcCatalog
ArcToolbox
ArcMap

65. Data Quality
It is impossible to make a perfect representation of the world, so uncertainty about it is inevitable
Uncertainty is found in data and in its processing and analysis
The outputs from spatial data analysis and GIS are only as good as the inputs and associated assumptions.

66. Logical Consistency Representation of data that does not make sense
Road in the water
Contours that cross or end
Features on steep slopes

67. Modifiable areal unit problem
Multiple ways to aggregate data into zones and thereby yielding different results.

68. Anscombe’s Quartet
These four data sets look identical from a statistical perspective.

69. Anscombe’s Quartet
They don’t look anything alike from a graphical perspective!!