spatial and spatio-temporal analysis in small area

Concepts in spatial data exploration

1. Spatial Data
What is special about Spatial Data?
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2. What is needed for spatial analysis?
1.Locationinformation—a map
2.An attributedataset: e.g
population, rainfall
3.Linksbetween the locations
and the attributes
4.Spatial proximity information
–Knowledge about relative
spatial location
–Topological information
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Topology --knowledge about relative spatial positioning
Topography --the form of the land surface, in particular, its elevation

3. Berry’s geographic matrix
location
Attributes or variables
Variable 1Variable 2…Variable P
areal unit 1
areal unit 2
.
.
.
areal unit n
location
Attributes or variables
PopulationIncome…Variable P
areal unit 1
areal unit 2
.
.
.
areal unit n
location
Attributes or Variables
PopulationIncome …Variable P
Henan
Shanxi
.
.
.
areal unit n
time
geographic
associations
geographic
distribution geographic
fact
Berry, B.J.L 1964 Approaches to regional analysis: A synthesis . Annals of the Association of American Geographers, 54,
pp. 2-11
2010
1990
2000
3
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5. Typesof Spatial Data
•Continuous (surface) data
•Polygon (lattice) data
•Point data
•Network data
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6. Spatial data type 1: Continuous
(Surface Data)
•Spatially continuous data
–attributes existeverywhere
•There are an infinitenumber
locations
–But, attributes are usually only
measuredat a fewlocations
•There is a sampleof point
measurements
•e.g. precipitation, elevation
–A surfaceis used to represent
continuous data
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7. Spatial data type 2: Polygon Data
•polygons completely
covering the area*
–Attributes exist and are
measured at each location
–Area can be:
•irregular (e.g. US state or
China province boundaries)
•regular (e.g. remote sensing
images in raster format)
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*Polygons completely covering an area are
called a lattice

8. Spatial data type 3: Point data
•Point pattern
–The locationsare the focus
–In many cases, there is no attribute involved
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9. Spatial data type 4: Network data
•Attributes may measure
–the networkitself (the roads)
–Objectson the network (cars)
•We often treat network
objects as point data, which
can cause serious errors
–Crimes occur at addresses on
networks, but we often treat
them as points
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See: Yamada and Thill Local Indicators of network-constrained clusters in
spatial point patterns. Geographical Analysis 39 (3) 2007 p. 268-292

10. Which will we study?
Point data
(point pattern analysis: clustering and dispersion)
Polygon data*
(polygon analysis: spatial autocorrelation and spatial regression)
Continuous data*
(Surface analysis: interpolation, trend surface analysis and kriging)
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3Surface analysis: nterpolation, trend surface analysis and kriging)
*in the fall semester

11. Convertingfrom one type of data
to another.
--very common in spatial analysis
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12. Converting point to continuous data:
interpolation#
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13. Interpolation
•Finding attribute values at locations where
there is no data, using locations with known
data values
•Usually based on
–Valueat known location
–Distancefrom known location
•Methods used
–Inverse distance weighting
–Kriging
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Simple linear
interpolation
Unknown
Known

14. Converting point data to polygons
using Thiessen polygons #
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15. Thiessen or Proximity Polgons
(also called Dirichlet or Voronoi Polygons)
•Polygons created from a point
layer
•Each point has a polygon (and
each polygon has one point)
•any location within the polygon
is closer to the enclosed point
than to any other point
•space is divided as ‘evenly’ as
possible between the polygons
A
Thiessen or Proximity
Polygons
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16. How to create Thiessen Polygons
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1. Connect point
to its nearest
(closest) neighbor
2. Draw
perpendicular
line at midpoint
3. Repeat for
other points
4. Thiessen
polygons

17. Converting polygon to point data using
Centroids
•Centroid—the balancing point for a polygon
•used to apply point pattern analysis to polygon data
•More about this later
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18. Using a polygon to represent a set of
points: Convex Hull
•the smallest convex polygon able to
contain a set of points
–no concave angles pointing inward
•A rubber band wrapped around a set of
points
•“reverse” of the centroid
•Convex hull often used to create the
boundaryof a study area
–a “buffer” zone often added
–Used in point pattern analysis to solve the
boundary problem.
•Called a “guard zone”
No!
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19. Modelsfor Spatial Data:
Raster and Vector
two alternative methods for
representingspatial data
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20. 0123456789
0 RT
1 R T
2 H R
3 R
4 RR
5 R
6 R TT H
7 R TT
8 R
9 R Real World
Vector Representation
Raster Representation
Concept of Vector and Raster
line
polygon
point
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house
river
trees

21. Comparing Raster and Vector Models
Raster Model
•area is covered by grid with (usually) equal-size, square cells
•attributesare recorded by giving each cell a single value based
on the majority feature (attribute) in the cell, such as land use
type or soil type
•Imagedata is a special case of raster data in which the “attribute”
is a reflectance value from the geomagnetic spectrum
–cells in image data often called pixels(picture elements)
Vector Model
The fundamental concept of vectorGIS is that all geographic
features in the real work can be represented either as:
•points or dots (nodes): trees, poles, fire plugs, airports, cities
•lines (arcs): streams, streets, sewers,
•areas (polygons): land parcels, cities, counties, forest, rock type
Because representation depends on shape, ArcGIS refers to files containing
vector data as shapefiles
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22. Raster model
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corn
wheat
fruit
clover
fruit
0123456789
0
1
2
3
4
5
6
7
8
9
1111144555
1111144555
1111144555
1111144555
1111144555
2222222333
2222222333
2222222333
2244222333
2244222333
Land use (or soil type)
186
21
Each cell (pixel)
has a value
between 0 and 255
(8 bits)
Image

23. Vector Model
•point(node): 0-dimensions
–single x,y coordinate pair
–zero area
–tree, oil well, location for label
•line(arc): 1-dimension
–two connected x,y coordinates
–road, stream
–A networkis simply 2 or more
connected lines
•polygon: 2-dimensions
–four or more ordered and
connected x,y coordinates
–first and last x,y pairs are the
same
–encloses an area
–county, lake
1
2
78
.
x=7
Point: 7,2
y=2
Line: 7,2 8,1
Polygon: 7,2 8,1 7,1 7,2
1
2
7 8
1
2
1
1
2
7 8
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24. Using raster and vector models to
represent surfaces
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25. Representing Surfaces
with raster and vector models –3 ways
•Contour lines
–Lines of equal surface value
–Good for maps but not computers!
•Digital elevation model (raster)
–raster cells record surface value
•TIN (vector)
–Triangulated Irregular Network (TIN)
–triangle vertices (corners) record surface
value
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26. Contour (isolines) Lines
for surface representation
Advantages
•Easy to understand (for most people!)
–Circle = hill top (or basin)
–Downhill > = ridge
–Uphill <= valley
–Closer lines = steeper slope
Disadvantages
•Not good for computer representation
•Lines difficult to store in computer
Contour lines of constant elevation
--also called isolines (iso = equal)

27. Raster
for surface representation
Each cell in the raster records the height (elevation) of the surface
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Raster cells
(Contain
elevation
values)
Surface
Raster cells with
elevation value
Contour lines

28. •a set of non-overlapping
triangles formed from
irregularly spaced points
•preferably, points are located at
“significant” locations,
–bottom of valleys, tops of ridges
•Each corner of the triangle
(vertex) has:
–x, y horizontal coordinates
–zvertical coordinate measuring
elevation.
Triangulated Irregular Network (TIN):
Vector surface representationPoint #X Y Z
1 10 30 160
2 25 30 150
3 30 25 140
4 15 20 130
etc
valley
ridge
vertex
1 2
4 3
5

29. Draft: How to Create a TIN
surface:
from points to surfaces
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Thiessen3.jpg Thiessen4.jpg
Links together all spatial concepts: point, line, polygon, surface

30. Using raster and vector models to
represent polygons
(and points and lines)
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31. Representing Polygons
(and points and lines)
with raster and vector models
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•Raster model notgood
–not accurate
•Also a big challenge for the vectormodel
–but much more accurate
–the solution to this challenge resulted in the
modern GIS system
0123456789
0
1
2
3
4
5
6
7
8
9
1111144555
1111144555
1111144555
1111144555
1111144555
2222222333
2222222333
2222222333
2244222333
2244222333X

32. Using Raster model for points,
lines and polygons
--not good!
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Polygon boundary
not accurate
Line not
accurate
Point located at cell center
--even if its not
Point “lost” if two
points in one cell
For points
For lines and polygons

33. Using vector model to represent
points, lines and polygons:
Node/Arc/Polygon Topology
The relationships between allspatial elements (points, lines, and polygons) defined
by four concepts:
•Node-ARCrelationship:
–specifies which points(nodes) are connected to form arcs (lines)
•Arc-Arcrelationship
–specifies which arcsare connected to form networks
•Polygon-Arcrelationship
–defines polygons (areas) by specifying
which arcsform their boundary
•From-Torelationship on all arcs
–Every arc has a direction froma node toa node
–This allows
•This establishes left side and right side of an arc (e.g. street)
•Also polygon on the left and polygon on the right for
every side of the polygon
Left
Right
from
to
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from to
New!

34. Node Table
Node IDEastingNorthing
1126.5578.1
2218.6581.9
3224.2470.4
4129.1471.9 Node Feature Attribute Table
Node IDControlCrosswalkADA?
1light yes yes
2stop no no
3yield no no
4none yes no Arc Table
Arc IDFrom NTo NL PolyR Poly
I 4 1 A34
II 1 2 A34
III 2 3A35A34
IV 3 4 A34 Polygon Feature AttributeTable
Polygon IDOwner Address
A34 J. Smith500 Birch
A35 R. White200 Main Polygon Table
Polygon IDArc List
A34 I, II, III, IV
A35 III, VI, VII, XI Arc Feature Attribute Table
Arc IDLengthConditionLanesName
I 106good 4
II 92poor 4Birch
III 111fair 2
IV 95fair 2Cherry Birch
Cherry
I
II
III
IV
1
4
3
Node/Arc/ Polygon and Attribute Data
Example of computer implementation
Spatial Data
Attribute Data
A35
Smith
Estate
A34
2
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35. This is how a vector GIS system works!
This data structure was invented by Scott Morehouse at the
Harvard Laboratory for Computer Graphics in the 1960s.
Another graduate student named Jack Dangermond hired
Scott Morehouse, moved to Redlands, CA, started a new
company called ESRI Inc., and created the first commercial
GIS system, ArcInfo, in 1971
Modern GIS was born!
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36. Other ways to represent polygons
with vector model
2. Whole polygon structure
3. Points and Polygons structure
•Used in earlier GIS systems before
node/arc/polygonsystem invented
•Still used today for some, more simple,
spatial data (e.g. shapefiles)
•Discuss these if we have time!
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37. Vector Data Structures:
Whole Polygon
Whole Polygon (boundary structure): list coordinatesof points in
order as you ‘walk around’ the outside boundary of the polygon.
–all data stored in one file
–coordinates/borders for adjacent polygons stored twice;
•may not be same, resulting in slivers (gaps), or overlap
–all lines are ‘double’ (except for those on the outside periphery)
–no topological information about polygons
•which are adjacent and have a common boundary?
–used by the first computer mapping program, SYMAP, in late
1960s
–used by SAS/GRAPH and many later business mapping programs
–Still used by shapefiles.
Topology --knowledge about relative spatial positioning
--knowledge about shared geometry
Topography --the form of the land surface, in particular, its elevation
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38. Whole Polygon:
illustration
A 3 4
A 4 4
A 4 2
A 3 2
A 3 4
B 4 4
B 5 4
B 5 2
B 4 2
B 4 4
C 3 2
C 4 2
C 4 0
E
AB
C
D
1 2 3 4 5
0
1
2
3
4
5
C 3 0
C 3 2
D 4 2
D 5 2
D 5 0
D 4 0
D 4 2
E 1 5
E 5 5
E 5 4
E 3 4
E 3 0
E 1 0
E 1 5
Data File
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39. Vector Data Structures:
Points & Polygons
Points and Polygons: list ID numbers of points in order
as you ‘walk around’ the outside boundary
•asecond file lists all points and their coordinates.
–solves the duplicate coordinate/double border problem
–still no topological information
•Do not know which polygons have a common border
–first used by CALFORM, the second generation mapping
package, from the Laboratory for Computer Graphics and
Spatial Analysis at Harvard in early ‘70s
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40. Points and Polygons:
Illustration 1 3 4
2 4 4
3 4 2
4 3 2
5 5 4
6 5 2
7 5 0
8 4 0
9 3 0
10 1 0
11 1 5
12 5 5
E
AB
CD
1 2 3 4 5
0
1
2
3
4
5 A 1, 2, 3, 4, 1
B 2, 5, 6, 3, 2
C 4, 3, 8, 9, 4
D 3, 6, 7, 8, 3
E 11, 12, 5, 1, 9,
10, 11
Points File
1
2
3
4
5
6
78910
11
12
Polygons File
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41. Hopefully, you now have a better
understanding of
what is special about spatial data!
Monday, we will begin talking about
Spatial Statistics
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42. Briggs Henan University 2012
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43. Some Thoughts
•It is hard to find a general spatial statistics
paper. In the following slides, I recommend
a workshop, a professor, two websites, and
one book, which are related with spatial
statistics.

44. A Good Workshop
Short Course: Introduction to Spatial Data Analysis at UIUC,
Luc Anselin
•The course is organized into six broad topics
(http://www.csiss.org/events/workshops/2002/data2002/outline.pdf):
1.Concepts: what makes spatial data analysis different, some basic GIS concepts,
understanding of the paradigms in spatial data analysis
2.Geovisualization: the visualization and exploration of spatial data, dynamically linked
windows, outlier analysis, smoothing of maps for rates.
3.Point pattern analysis: assessing whether a pattern of locations (points) is clustered, spatial
point processes, nearest neighbor statistics, second order statistics, bivariate and space-
time point patterns.
4.Spatial autocorrelation analysis: descriptive statistics for spatial autocorrelation,
constructing spatial weights, visualizing spatial autocorrelation, local indicators of spatial
association, multivariate spatial correlation
5.Geostatistics: the geostatistical perspective, variograms, kriging
6.Spatial regression: specifying spatial econometric models, spatial externalities, estimation
methods, specification tests
Wei: please read the course outline, it includes many good paper references

45. An Interesting Professor
•http://sal.uiuc.edu/users/anselin/
•Research Projects
–Geovisualization and Spatial Analysis of Cancer Data (NCI)
–The sensitivity of concentration-response functions to the
explicit modeling of space-time dependence (NSF/EPA)
–Center for Spatially Integrated Social Science (NSF)
–A web-based spatial analytic toolkit for the study of
homicide data (NCOVR)

46. A Good Website
•the Center for Spatially Integrated Social Science (CSISS) main
site, especially its learning materials, syllabi and search engines,
http://www.csiss.org/
–Summer Workshops 2002 Video Clips -Spatial Pattern Analysis in a
GIS Environment http://www.csiss.org/streaming_video/2002/spa.html
•The Nature of Spatial Pattern Analysis, Art Getis
•Problems Associated with Spatial Pattern Analysis, Art Getis
•An Introduction to GIS, Mike Goodchild
•GIS Functionality, Mike Goodchild
•Current Technologies in GIS, Mike Goodchild
•Spatial Patterns of Birth Data, John R. Weeks
•Spatial Patterns of Fertility in Egypt, John R. Weeks
Wei:I checked several clips, the quality is good.

47. Another Good Website
Spatial Statistics Software
http://www.spatial-statistics.com/
•The company website collects useful information on
–Spatial autoregressions (SAR)
–Conditional spatial autoregressions (CAR)
–Mixed regressive spatially autoregressive (MRSA)
–Exact log-determinant computations
–Nearest neighbors
–Contiguity/contiguous observations
–Spatial temporal routines
–Multivariate dependence
–Matrix exponential spatial specifications
–Doubly stochastic weight matrices
–Spatial autoregressive local estimation
–Log-determinant approximations

48. A Good Book
•It is a popular textbook used by undergraduate or first year graduate students.
•Review
"It has been difficult to find a good introductory statistics text that can be used with a class
consisting of both physical and social science students. This textbook meets that demand by
incorporating a good number of examples from both aspects of the discipline and including
thorough discussions of introductory spatial statistics....Should prove useful as both a classroom
textbook and a basic statistical reference." -David R. Legates,
University of Oklahoma
"Burt and Barber have extended and modernized a text that has long served geography students
as a methodological foundation....This text will find its place in upper-level undergraduate
courses and first-year graduate study for those with limited statistics backgrounds." -Randall W.
Jackson,
Ohio State University
"The text is very well organized and contains a wealth of excellent examples and diagrams.
Chapters on time-series and computer-intensive methods are particularly valuable."
-Scott Robeson, Indiana University
http://www.amazon.com/Elementary-Statistics-Geographers-James-
Burt/dp/0898629993