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Point Patterns

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Point Patterns

10/11/00

Patterns (scattered, random, or clustered)

- Nearest-neighbor analysis - a technique developed by plant ecologists (Clark and Evans, 1954)
- measuring pattern in terms of the arrangement

point pattern

dran=1/2

A

= expected mean nearest neighbor

distance for a random arrangement

of points

dran

B

p=density of the points

=number of points divided by the area

=8/144=0.056

C

D

E

F

G

H

assume area is 144 km2

Random points

dran=1/2

= 1/2x0.237

= 2.11

which means that if the point pattern is arranged randomly

the mean nearest-neighbor distance will be 2.11 km

Dispersed Point Pattern- uniform, or regular

maximum possible distance separating them

dran=21/2/ 31/4

=1.07453/

for the previous case

dran = 4.534

d = d /n = 33/8 = 4.125

Nearest

Neighbor

B

A

D

F

C

D

F

G

point

A

B

C

D

E

F

G

H

n=8

d

5

5

4

3

4

3

3

6

d=33

Clustered pattern

- make a guess, what value will be for the dran?

Nearest-neighbor Index

- R = dobs/dran
- ranges from 0 to 2.15 (clustered to totally dispersed)
- Random R will be 1
- The present case R = 4.125/2.11 = 1.955 (very dispersed)

statistic test

c = (dobs - dran)/SEd

where SEd is the standard error of the mean nearest-neighbor distance =

0.26136 /

where n = number of points and p is the density of points per unit area

for the current case,

S = 0.26136/

=0.391

so, c=(4.125-2.11)/0.391 = 5.15

Significant or not?

- 1.645 - significance level of 0.05

Spatial autocorrelation

- Autocorrelation - the relationship between successive values of residuals along a regression line.
- Strong spatial autocorrelation means that adjacent values or ones which are near to each other are strongly related.
- Joint count statistics

joints counting

- binary applications - electoral geography, arable/non-arable farms, poverty/non-poverty and others
- Black/white joins counting

Exercise: Create a new project

- Projection - UTM, Zone 16
- Map units - meters
- Measurement - meters
- Create a polygon theme - with area around 200 m2 (fix your scale to 1:1000)
- copy files from GISLAB01 to your machine (today’s folder)

Procedure

- Add a new field (Area) to your polygon theme using Area_cacu.avx (an extension)
- generate a random point patterns using “randompt2.avx” (an extension)
- Calculate the R for the point pattern within the polygon using Nearest18 (a script)

Calculate the point pattern from your study county

- Make sure you have county boundary file ready
- Use the matched student profile as the point pattern
- Run “Nearest18” script
- Make sure you have your projection system set up.