tuesday

e.g. Bailey and Gatrell Interactive spatial data analysis Harlow, UK: Longman Scientific and Technical (1995):
A. Point patterns
B. Spatial continuous data (fields of interval/ratio variables)
C. Area data
spatially intensive or spatially extensive
the cartographic problem
D. Spatial interaction data
how to model spatial interaction?
<origin object, destination object, attributes>

By six classes

queries and reasoning
measurements
transformations
descriptive summaries
optimization
hypothesis testing

2. QUERIES AND REASONING

Interacting with views

catalog view
icons
properties
metadata
map view
location
object identity
table view
histogram, pie chart
scatterplot
linked views
exploratory spatial data analysis

SQL

SELECT... FROM... WHERE...

Spatial reasoning

e.g. route-finding directions

www.mapquest.com
map view
direction list view

Driving directions from 909 West Campus Lane to 1401 De La Vina St

Go that way (pointing) and turn right at the fence. When the road curves to the right head straight, under the big coral tree. Turn left at the first stop sign, pass the daycare center on the right, and turn right at the stop sign at the end. At the light head straight through, and follow Storke through two more lights (the second one is Hollister). At the third light turn right to take the ramp onto 101 South (it's actually heading east at this point). In about eight miles take the Mission Street exit, and turn left at the bottom of the ramp. Go through three lights, watch out for the sharp dip in the road at Bath, and turn right on De La Vina. 1401 is at the corner of Sola, one block after the light at Micheltorena.

3. MEASUREMENTS

The original motivation for GIS

the Canada Geographic Information System of 1965
measurement of area
planimetry
dot counting
overlay of layers to obtain joint areas

Distance metrics

Pythagorean
great circle
Manhattan

Bias in the length of a polyline

relative to a true line
because of slopes

Area of a polygon

Shape

Elbridge Gerry and the salamander
12th District of N Carolina 1992

In 1992, following the release of population data from the 1990 Census, new boundaries were proposed for the voting districts of North Carolina. For the first time race was used as an explicit criterion, and districts were drawn that as far as possible grouped minorities (notably African Americans) into districts in which they were in the majority. The intent was to avoid the historic tendency for minorities to be thinly spread in all districts, and thus to be unable to return their own representative to Congress. African Americans were in a majority in the new 12th District, but in order to achieve this the district had to be drawn in a highly contorted shape.

The new district, and the criteria used in the redistricting, were appealed to the U.S. Supreme Court. Writing for the 5-4 majority, and striking down the new districting scheme, Chief Justice William Rehnquist wrote that "A generalized assertion of past discrimination in a particular industry or region is not adequate because it provides no guidance for a legislative body to determine the precise scope of the injury it seeks to remedy. Accordingly, an effort to alleviate the effects of societal discrimination is not a compelling interest."

perimeter for a given area
shape = perimeter / (3.54 sqrt area)
1 for a circle (most compact)
>1 otherwise

4. TRANSFORMATIONS

Buffering

dilation
erosion
all territory within a defined distance of an object
generalization to variable rates of spread/travel

Points in polygons

Polygon overlay

the discrete object case
the field case

Spatial interpolation

estimation of the value of a field variable at a location where it has not been measured
at all locations
contouring
inverse distance weighting
Kriging

Density estimation

estimation of the density of discrete objects
replacing each object by a suitably weighted kernel function
result depends on the radius of the kernel

5. DESCRIPTIVE SUMMARIES

Statistics that summarize a distribution

and satisfy the test for whether a method of analysis is spatial
reducing a potentially complex system to a few numbers
that are relevant to a question or application

By analogy to one dimension:

measures of central tendency
measures of dispersion
skewness, kurtosis

Two-dimensional versions of the mean and their variational properties

centroid
minimizing distance squared
the balance point
means of coordinates
median
minimizing distance
bivariate median
minimizing Manhattan distance

Applications of centers

summarizing change through time
westward march of the US population centroid
land use in London, Ontario
site selection
the Mendeleev Centrographic Laboratory

Dispersion

mean distance from center

Measures of spatial dependence

the First Law of Geography
all things are related but nearby things are more related than distant things
endemic in geographic information
Type II errors
Geary and Moran statistics
variograms

Measures of fragmentation

FRAGSTATS

Measures of fractional dimension

Measures of clustering

the K function

6. OPTIMIZATION

Design to achieve specific objectives

points
lines
areas

Location of central point-like facilities

to serve dispersed demand
location-allocation methods
central facilities location
retailing
agency offices
emergency facilities
recreation facilities

Location of linear facilities

delivery routes

power lines, highways, transmission corridors

Location of areas

political districting

7. HYPOTHESIS TESTING

Application of inferential methods

based on traditional statistical methods
null hypothesis
test statistic
known distribution under the null hypothesis
alpha level
Type I and Type II errors

Inference

from a sample to a population
sample is drawn randomly and independently
geographic objects as samples
the entire population is often analyzed
inference about what population?

The independence assumption

and the First Law of Geography

Randomization tests