Spatial Clustering

Yogi Vidyattama

Main methodology

• Local Moran Index of Spatial Autocorrelation

where:Zi = deviation of point i to the mean

Wij = the spatial weights matrix

m2 = total variance ( )

• Weight matrix– The nature of spatial relationship: contiguity

N

Zm i i

2

2

j

jiji

i ZWm

ZI

2

3

Methodology

• Weight matrices – Describes the nature of the spatial relationships

• Rook-Contiguity based

– As opposed to• Queen-Contiguity based

• Distance based

What it has been used for

• Concentration area of disadvantage– Joblessness– Overcrowded housing– Less developed region– Ethnic group: Ancestry, Language

• Why?– Spill over effect– Intertemporal effect– Public service/ infrastructure distribution

• Further analysis necessary– Changes over time – Different behaviour/attitude– Impact on regression

¯0 25 5012.5 Kilometers

Legend

Dual Carriageway

Principal Road

Not significant (48)

High-High (9)

Low-Low (7)

Low-High (0)

High-Low (0)

Sydney Fairfield

Bankstown

Warringah (A)

Parramatta

Strathfield (A)

Pittwater (A)

Gosford (C)

Moran's I = 0.5185

-3

-2

-1

0

1

2

3

-3 -2 -1 0 1 2 3

Standard Deviation of %CJH 2001

Sta

nd

ard

De

via

tio

n o

f n

eig

hb

ou

r's

%C

JH

20

01

Parramatta (C) - South

Sydney (C) - West

Warringah (A)

Bankstown-South

Strathfield (A)

Fairfield (C) - East

Fairfield (C) - West

Parramatta (C) - North-West

Gosford (C) - West

Children in Jobless household

¯0 25 5012.5 Kilometers

Legend

Dual Carriageway

Principal Road

Not significant (46)

High-High (9)

Low-Low (7)

Low-High (2)

High-Low (0)

Sydney Fairfield

Bankstown

Warringah (A)

Parramatta

Strathfield (A)

Pittwater (A)

Gosford (C)

Moran's I = 0.5244

-3

-2

-1

0

1

2

3

-3 -2 -1 0 1 2 3

Standard Deviation of %CJH 2006

Sta

nd

ard

Dev

iatio

n o

f nei

gh

bo

ur'

s %

CJH

200

6

Parramatta (C) - South

Sydney (C) - West

Warringah (A)

Fairfield (C) - East

Fairfield (C) - West

Parramatta (C) - North-West

Strathfield (A)

Bankstown-South

Gosford (C) - West

Children in Jobless household

¯0 10 205 Kilometers

Legend

Dual Carriageway

Principal Road

Not significant (50)

High-High (13)

Low-Low (14)

Low-High (2)

High-Low (0)

Hobsons Bay (C) - Williamstown

Hume (C) - Broadmeadows

Whittlesea (C) - South

Melbourne (C)

Nillumbik (S) - South

Darebin (C) - Northcote

Moran's I = 0.3822

-4

-3

-2

-1

0

1

2

3

4

-4 -3 -2 -1 0 1 2 3 4

Standard Deviation of % CJH 2001

Sta

nd

ard

De

via

tio

n o

f n

eig

hb

or'

s %

CJ

H 2

00

1

Hobsons Bay (C) - Williamstown

Darebin (C) - Northcote

Melbourne (C) - Inner

Hume (C) - Broadmeadows

Whittlesea (C) - South-West

Nillumbik (S) - South

Whittlesea (C) - South-East

Melbourne (C) - Remainder

Children in Jobless household

¯0 10 205 Kilometers

Legend

Dual Carriageway

Principal Road

Not significant (53)

High-High (8)

Low-Low (15)

Low-High (3)

High-Low (0)

Hobsons Bay (C) - Williamstown

Hume (C) - Broadmeadows

Whittlesea (C) - South

Melbourne (C)

Nillumbik (S) - South

Darebin (C) - Northcote

Moran's I = 0.3646

-4

-3

-2

-1

0

1

2

3

4

-4 -3 -2 -1 0 1 2 3 4

Standard Deviation of % CJH 2006

Sta

nd

ard

Dev

iati

on

of

nei

gh

bo

ur'

s %

CJH

200

6

Moonee Valley (C) - West Hobsons Bay (C) - Williamstown Darebin (C) - Northcote

Melbourne (C) - Inner

Hume (C) - Broadmeadows

Whittlesea (C) - South-

Nillumbik (S) - South

Whittlesea (C) - South-East

Melbourne (C) - Remainde

Children in Jobless household

EthnicitySYDNEY

Cluster 2006 2011Ancestry - not significant 28.38 30.35 - high-high 62.03 66.42 - low-low 8.55 8.89 - low-high 25.16 21.79 - high-low 33.51 37.36Language - not significant 27.42 30.35 - high-high 64.44 66.42 - low-low 6.66 8.89 - low-high 25.93 21.79 - high-low 33.42 37.36English - not significant 15.48 15.16 - high-high 27.24 26.35 - low-low 6.61 5.82 - low-high 12.21 10.41 - high-low 19.85 17.28

EthnicityMELBOURNE

Cluster 2006 2011Ancestry - not significant 24.95 27.33 - high-high 51.39 56.39 - low-low 8.04 9.06 - low-high 18.45 12.95 - high-low 28.04 33.32Language - not significant 25.88 28.08 - high-high 55.09 58.13 - low-low 6.82 7.99 - low-high 19.72 16.84 - high-low 28.66 33.59English - not significant 16.17 15.65 - high-high 28.21 26.48 - low-low 6.99 6.90 - low-high 10.97 10.52 - high-low 20.10 18.60

Cluster of HDI 1999

Cluster of HDI 2008

Moran’s “Arrow” plot of HDI 1999-2008

• Disease– Contagion, connected topography

• Crime– Vulnerable target, location of criminal

• Natural disaster and its impact– Flood, fire, earthquake

Other used

Software

• OpenGeoDa 09.09.12• AURIN PORTAL

• Choose or import your dataset

• Spatialise your dataset

• Create your weight matrix

Step in AURIN portal

• Calculate the Local Moran’s I statistics

• Visualise the result

Step in AURIN portal (2)

• Percentage is mainly used but comparing the result to the result in number is often important

Analyse in AURIN portal