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Briggs Henan University 2010 1

Spatial Analysis

Concept and Challenges

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Description and AnalysisDescription

Most GIS systems are used by governments and private companies todescribe the real world

this help the organizationcarry out its work For example, manage sewer

and water networks

Spatial databases are

important for this Most GIS systems are primarily designed for this purpose

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Description and AnalysisAnalysis

Tries to understand the processes which cause or create the patterns in the realworld

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

Is the locations of the software industry different from the telecommucations industry?

Here, we are using centrographicstatistics to help answer this question

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Description: Water and Sewer system

Analysis: Do the locations of thesoftware and telecommucationsindustries differ?


We will talk about analysis.

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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

CreateProcesses Patterns

(or cause)

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Spatial Analysis is aimed at: Identifying and describing the

patternThe pattern is clearly

clustered

Identifying andunderstanding the process

Access to transportation.

Agglomeration economies* from sharing ideas, access to skilled labor, access tobusiness services.

Briggs Henan University 2010 6We will focus on spatial analysis*cost savings from many firmslocating in the same area

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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

CreateProcesses Patterns

(or cause )

Infer

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Spatial Analysis: successive levels of sophistication

Four levels of Spatial Analysis:--Each is more advanced (more difficult!)

1. Spatial data description:2. Exploratory Spatial Data Analysis (ESDA)3. Spatial statistical analysis and hypothesis testing4. Spatial modeling and predictionWe will look at all 4 levels in this lecture series

More difficult,but more useful!(more powerful)

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1. Spatial data description: classic GIS capabilities Spatial queries & measurement, buffering, map layer overlay

The ArcMap project is anexample of this!

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2. Exploratory Spatial Data Analysis (ESDA): searching for patterns and possible explanations GeoVisualization through data graphing and mapping

--DensityKernelEstimation

--Overlaytransportationnetwork

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2. Exploratory Spatial Data Analysis (ESDA): searching for patterns and possible explanations GeoVisualization through data graphing and mapping Calculation of Centrographic statistics

--Calculation of CentrographicStatistics

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3. Spatial statistical analysis and hypothesistesting Are data to be expected or are they

unexpected relative to some statistical model,usually of a random process (pure chance)

We will look atstatistical hypothesis testing for:--point patterns--spatial autocorrelation

We can test if the spatial pattern for software &telecommmunications companies in Dallas isclustered, or random (no pattern)

0-1.96

2.5%

1.96

2.5%

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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 regressionmodels to predict location patterns.


Density of points = f (distance from highway)

However, for spatial data, we need special:Spatial auto-regressive models

Distance from highway

D e n s i t y of

p oi n

t s

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The first example of Spatial Analysis John Snows maps of cholera in 1850s London

Was it ESDA or hypothesis testing?

Did he discover the association between water andcholera 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 2010 14

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Issues/Challenges/Problemsin Spatial Analysis

Summarize these now.

Talk in greater detail about themthroughout this lecture series.

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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)

Results may depend on the specific geographic unit used in the study Province or county; county or city

Ecological fallacy Results obtained from aggregated data (e.g. provinces) cannot be assumed to apply

to individual people

Scale affects representation and results Cities may be represented as points or polygons Results depend on the scale at which the analysis is conducted

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

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Modifiable areal unit problem (MAUP) Results may depend on the specific geographic unit used in the study Dangerous to assume results at one level will be the same at another level

Provinces versus counties also a scale issue Problem is biggest here

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Census Tract(used by US Census Bureau for data)

Zipcode Areas

(used by US Post Office)

Modifiable areal unit problem (MAUP) Census Tracts versus Zip codes Not a scale issue Problem not as big--usually

19Briggs Henan University 2010

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Aggregation Different ways of

aggregating the data

Note how: variance (s 2)

decreases Correlation

coefficient (r XY)increases ( cos of less variability)

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Ecological fallacyResults from aggregated data (e.g. provinces) cannot be appliedto individual peopleA special case of the MAUP problemEncountered in spatial and non-spatial analysisUsually because a variable was left out (omitted variable)

If low income provinces havehigh crime rate.

Cannot assume low income peoplecommit crimes.Perhaps low income provinces donot have money to pay for police.

income c r

i m e r a

t e

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Scale: 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 mapand how data is stored in the data base Important for research design and data collection Cities may be points or polygons


Large scale >objects arelarge, small area covered

Small scale >objects aresmall, large area covered

Km

0 1 2

point polygon

Dallas

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Scale: always a very important issue in spatial analysis

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

MAUP may be considered to be a scale issue (but not always)


Populationclusterd intocities

City populationsare dispersed

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Bank robberies are clustered But only because banks are clustered


Bank robbery

Banks

Bonnie and Clyde were two very famous bank robbers in Texas in the 1930sThey 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)

Bank Robberies

Non-uniformity of Space: things are not evenly distributed in space

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Illiteracy in ChinaNon-uniformity of Spaceand Choropleth Maps

Henan has highilliteracy!

Henan does not havehigh illiteracy!

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Non-uniformity of Space andChoropleth Maps

Always normalize data if drawing a choropleth map By total population By geographic area

Do not map counts unless population and/or geographicarea are the same size for all observation units

Failing to normalize is a very common mistakes made bynon-professional GIS people You are professionals Do not make that mistake!


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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 spatialautocorrelation Consequently, edges of the map, beyond which there is no data, can

significantly effect results

Use the toroid concept -- bends the left edge to meet the rightand the top to meet the bottom--uses all the data--assumes that there is no systematic

spatial trend in data

Solutions:

Core studyregion

Use Core/Periphery--analyze only the core--use edge only for neighborhood calculations--reduces amount of data available

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periphery or guard area

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What is the most common

mistake in GIS analysis?


Much more basic than anydiscussed above.

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NAME FIPS CODE POP2000 Alabama 01 AL 4,447,100 Alaska 02 AK 626,932..Georgia 13 GA 8,186,453Hawaii 15 HI 1,211,537Idaho 16 ID 1,293,953..Wisconsin 55 WI 5,363,675Wyoming 56 WY 493,782

51 states Total 282,421,906

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

Spatial

FID SHAPE NAME FIPS CODE POP20000 Polygon Alabama 01 AL 4,447,1001 Polygon Alaska 02 AK 626,932

..11 Polygon Georgia 13 GA 8,186,45312 Polygon Hawaii-Hawai 15 HI 1,211,537

13 Polygon Hawaii-Maui 15 HI 1,211,53714 Polygon Hawaii-Oahu 15 HI 1,211,53715 Polygon Hawaii-Kauai 15 HI 1,211,53716 Polygon Idaho 16 ID 1,293,953

..53 Polygon Wisconsin 55 WI 5,363,67554 Polygon Wyoming 56 WY 493,782

Total 286,056,517

After joiningattribute tospatial data

Hawaii

54 observations

51 states

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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 tableIf each island is drawn as a separate feature, there will bemultiple rows in the attribute table

Errors with the

attribute data willoccur if Hong Kong or Guangdong are notcorrectly drawn in theshapefile (spatial data)

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Measuring Space Not easy!


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Spatial is special: 3 primary concepts

Distance

Adjacencyor neighborhood

Interaction

Briggs Henan University 2010

A

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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: 1 st, 2 nd, 3 rd nearest neighbor, etc.. Interaction

The strength of the relationship between entities An inverse function of distance

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Distance is not simple!


Cartesian distance via Pythagorus

Use for projected data Spherical distance via spherical coordinates

Cos d = (sin a sin b) + (cos a cos b cos P)

where: d = arc distancea = Latitude of Ab = Latitude of BP = degrees of long. A to B

Use for unprojected data

possible distance metrics: Euclidean straight line/airline city block/manhattan metric distance through network time/friction through network

22 )()( ji jiij Y Y X X d

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1st and 2nd order adjacency

hexagonrook queen

1st

order

2nd

order

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Interaction

ijd

j

i

ij

e

PP I

Gravity Model: Interaction

between i and j is a function of:Pi --the population (size) at iP j --the population (size) at jdij --the distance from i to j

Based on the Gravity Model Based on a Hierarchy

How do you fly fromZhengzhou to Wuhan?

WuhanZhengzhouShanghai

Central Place Hierarchy

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Today, we discussed spatial analysis and some of its problems andchallenges

However, to do spatial analysis youmust have spatial data

Next time:Spatial data and why it is special!


T

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Texts

OSullivan, 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.

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