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Point Pattern Analysis

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Point Pattern Analysis

Chapter 4

Geographic Information Analysis

By David O’ Sullivan and David J. Unwin

- Simplest Possible Spatial Data
-A point pattern is a set of events in a study region

-Each event is symbolized by a point object

-Data are the locations of a set of point objects

- Applications
-Hot-spot analysis (crime, disease)

-Vegetation, archaeological studies

- Requirements for a set of events to constitute a point pattern
-Pattern should be mapped on a plane

-Study area determined objectively

-Pattern is a census of the entities of interest

-One-to-one correspondence between objects and

events

-Event locations are proper

Point Density

-First-order effect: Variation

of intensity of a process

across space

-Number of events per unit

area

-Absolute location

Point Separation

-Second-order effect:

Interaction between

locations based on distance

between them

-Relative location

- Describing a point pattern

- Descriptive statistics to provide summary descriptions of point patterns
-Mean center

-Standard Distance

- First-order effect
- Sensitive to the definition of the study area

- Quadrant count methods
-Record number of events of a pattern in a set of

cells of a fixed size

-Census vs. Random

- Kernel-density estimation
-Pattern has a density at any location in the study

region

-Good for hot-spot analysis, checking first-order

stationary process, and linking point objects to

other geographic data

Naive method

- Second-order effect
- Nearest-neighbor distance
-The distance from an event to the nearest event in

the point pattern

- Mean nearest-neighbor distance
-Summarizes all the nearest-neighbor distances by a

single mean value

-Throws away much of the information about the

pattern

- G function
-Simplest

-Examines the cumulative frequency distribution of

the nearest-neighbor distances

-The value of G for any distance tells you what

fraction of all the nearest-neighbor distances in the

pattern are less than that distance

- F function
-Point locations are selected at random in the study

region and minimum distance from point location to

event is determined

-The F function is the cumulative frequency

distribution

-Advantage over G function: Increased sample size

for smoother curve

- K function
-Based on all distances between events

-Provides the most information about the pattern

- Problem with all distance functions are edge effects
- Solution is to implement a guard zone

- Null hypothesis
-A particular spatial process produced the observed

pattern (IRP/CSR)

- Sample
-A set of spatial data from the set of all possible

realizations of the hypothesized process

- Testing
-Using a test to illustrate how probable an observed

value of a pattern is relative to the distribution of values

in a sampling distribution

- Quadrant counts
-Probability distribution for a quadrant count

description of a point pattern is given by a Poisson

distribution

-Null hypothesis: (IRP/CSR)

-Test statistic: Intensity (λ)

-Tests: Variance/mean ratio, Chi-square

- Nearest-neighbor distances
-R statistic

- G and F functions
-Plot observed pattern and IRP/CSR pattern

- K function
-Difficult to see small differences between expected

and observed patterns when plotted

-Develop another function L(d) that should equal

zero if K(d) is IRP/CSR

-Use computer simulations to generate IRP/CSR

(Monte Carlo procedure)

- Peter Gould
-Geographical data sets are not samples

-Geographical data are not random

-Geographical data are not independent random

-n is always large so results are almost always

statistically significant

-A null hypothesis of IRP/CSR being rejected means

any other process is the alternative hypothesis

- David Harvey
-Altering parameter estimates by changing study

region size often can alter conclusions