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. d ran =1/2. A. = expected mean nearest neighbor

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Point Patterns

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Point patterns

Point Patterns

10/11/00


Patterns scattered random or clustered

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

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

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

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

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

Clustered pattern

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


Nearest neighbor index

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

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

Significant or not?

  • 1.645 - significance level of 0.05


Spatial autocorrelation

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

joints counting

  • binary applications - electoral geography, arable/non-arable farms, poverty/non-poverty and others

  • Black/white joins counting


Black white join

Black/white join


Exercise create a new project

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

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

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.


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