crime concentration index

Using Crime Concentration
Indices in Crime Analysis
VCAN Spring Symposium
2010
Isaac T. Van Patten

Web site for presentation
www.radford.edu/~ivanpatt/crimemaps

The map is not the territory.
-Alfred Korzybski
…an abstraction derived from something, or a reaction to it,
is not the thing itself…

City of Roanoke, Virginia: “The Star City of the South”
CONTEXT

Our Fair City

Roanoke, Virginia
• Located in southwest Virginia at the southern
end of the Shenandoah Valley
• Roanoke City Population = 93,048 (2007)
• Roanoke MSA = 295,700
– City plus surrounding counties
• Major health-care consortium is the biggest
employer
• Former headquarters for the N&W Railroad

±
0 1 2 4 Miles

Measuring Crime
for Thematic Mapping
• Typically thematic crime maps aggregate
crime to some areal unit (polygon)
• Crimes can be measured in several ways, we’ll
examine three:
– Crime counts
– Crime Rates
– Crime Concentration Indices
• Each has strengths and weaknesses

Crime Count Example
LAX
Inglewood-Lennox
±
Homicides
0 1.25 2.5 5 Miles

Step 1: Aggregate the crimes to the areal unit
R-click on the layer and
choose Joins and Relates

Display as Graduated Colors
±
Homicides
0 1.25 2.5 5 Miles

The Results
• Looks pretty good
– The darker polygons seem to have the most crimes
in them
– All polygons with a crime are shaded
– Natural Breaks (the default) seems to work okay
• But consider this…

Selection: 184 Tracts
Area in Sq Miles
Min 0.09 Max 2.92
Mean 0.48
SD 0.38
±
0 1.25 2.5 5 Miles

The MAUP
• The Modifiable Areal Unit Problem
– Occurs when areal units of aggregation are created
through an arbitrary (non-spatial) process such as
census enumeration polygons
– Does not represent anything in physical geography
– Can create problems in the statistical analysis of
spatially arrayed data

Illustration
Dark & Bram, 2007

A final issue
• Because larger polygons are more likely to
capture more points, you can’t really compare
one polygon to another
– This comparison is implied in thematic mapping
and can be misleading when the metric is unknown

Crime rates standardize crime counts and allow for direct
comparison between dissimilarly sized units
A PARTIAL SOLUTION

Crime Rates
• Crime rates standardize crime counts to some
common denominator such as population
• When studying crimes-against-persons this
reflects the number of crimes compared to
the population “at risk”
• By standardizing the count, we can compare
disparate areal units with one another

Crime
rate
Crime Rates
Count of crimes
Population
100,000
• Count the crimes in the areal unit and divide
by the population
• Multiply by a constant (in this case 100K)
• Crimes per hundred-thousand people

To calculate in ArcGIS
• R-click on the layer with the aggregated data
• Open the Attribute Table
• Click on the Options tab at the bottom-right
• Choose Add Field
– You’re going the populate this new field with your
computed crime rates

In ArcGIS, create a new Field
• Select a Numeric field of
type Double
• Precision: 12
• Scale: 8

The Field Calculator
• With the new attribute field added R-click in
the tab at the top with the Field Name
• Next choose the Field Calculator

Using the Field Calculator
• This will calculate an
Attribute Field with a
Homicide Rate per
100,000 people
• Make sure the
denominator term has
no zero-value units

The Results
The census tract with
the highest homicide
rate is just south of
LAX. Others have
faded in emphasis.
±
0 1.25 2.5 5 Miles

This is the LAX Tank Farm
& support services area.
Population = 1; Homicides=1.
But look…

An alternative to counts and rates for thematic mapping
CRIME CONCENTRATION
INDEX

The Location Quotient
• Location quotients were developed in regional
planning to compare economic activity in a
local area with a larger study region
– For example, one county compared to a whole
region of the state
• It is a measure that describes the activity at a
local level relative to the larger region that
contains the local area of interest

The Location Quotient
LQ
Localeconomic activity
Regional
economic activity
• Generates a ratio of activity so that unity is the same
level of activity (local equivalent to region)
• Values less than 1 indicate less local activity
• Values greater than 1 indicate more local activity
• Always compared to the larger region

Unemployment Example
LQ
UE
12 local
105 regional
unemployed
unemployed
100 local pop.
1000 regional pop.
LQ
UE
0.12
0.105
1.143
• The LQ of 1.143 indicates there is 0.143 more
unemployment in the locality compared to the
region
• …or, there is 14.3% more unemployment in
the locality

Crime Concentration Index
• A direct adaptation of the location quotient to
measuring crime concentration in a locality
compared to a larger area
CCI
Crime
in a
Crime
neighborhood
in the
city

Crime Concentration Index
• Both the numerator and the denominator are
a standardized ratio measuring crime
• The numerator gives the concentration in the
neighborhood
• The denominator gives the concentration citywide
• The CCI is a ratio of these ratios

Two Unique Advantages
• The denominator term for each of the ratios
can be anything meaningful to the analyst
– Square miles
– Total crime, violent crime, or property crime
– Linear miles
– Population
• Unlike crime rates, CCIs do not require censusbased
information and can be applied to
custom polygons

The original reference
Brantingham, P.L. & Brantingham, P.J. (1998)
Mapping crime for analytic purposes:
Location quotients, counts, and rates. In D.
Weisburd & T. McEwen (Eds.) Crime mapping
& crime prevention (pp 263-288). Monsey, NY:
Criminal Justice Press.

Availableonline at:
http://www.popcenter.org/library/crimeprevention/volume_08/09-Brantingham.pdf

Robbery in Roanoke: Concentration by Area
A BASIC CCI ANALYSIS

Using Census Block Groups & Robberies
STEP 1: DISPLAY THE MAP
LAYERS

Use a spatial join to create a Count field in the Attribute Table for each
Block Group
STEP 2: USE A SPATIAL JOIN

Changing the Field Name
• The Join operation creates a Field called
Count_
• It is easy to lose track of what “Count_” is, so I
rename it by Adding a New Field from the
Options tab on the Attribute Table
• Then use the Field Calculator to write the
values
• Clean up by deleting the Count_ field

Populate the new field…

Then delete “Count_” field

Add a new field for the CCI
• We’ll next add a new field for the CCI to the
Attribute Table
• Add a Numeric field of Type: Double;
Precision: 12; and Scale: 8
• This is the field where we’ll write our CCI
values to:

With the new field added…
• …we’ll next use the CCI formula to populate
the values in the Attribute Table
• In this case we are interested in which
neighborhoods (using Block Groups as an
analog) will have the relative highest
concentrations of robberies per square mile
– If there is no field for square miles it will need to be
added first

The Formula:
CCI
Robbery
C
C
BG
BG
A
BG
A
BG
C BG :
A BG :
C BG :
A BG :
Robbery count per block group
Area of the block group
Sum of all the robberies for the city
Sum of the total city area

The Field Calculator

The Sorted CCIs

Select by Attributes: All CCIs > 1

Interpretation
• The two highest concentration neighborhoods
have just over 900% more robberies than
would be expected given the distribution of
robberies in the city
– (10.72-1=9.72 or 972% greater concentration)
• 42.7% of the neighborhoods have a higher
than expected concentration of robberies
– 35 out of 82 neighborhoods

±
0 1 2 4 Miles
Robbery Concentration
CCI Value
0.000000 - 0.446111
0.446112 - 1.000000
1.000001 - 3.349550
3.349551 - 5.989783
5.989784 - 10.718559

±
0 1 2 4 Miles
Robbery Concentration
CCI Value
Very Low
Low
Moderate
High
Very High

A application with a different denominator
COMMERCIAL ROBBERY
ANALYSIS

The Problem
• The Commander of the north patrol districts
wants an analysis of commercial robberies
compared to robberies as a whole
– Just interested in the situation in his area of
responsibility – not the whole city
– Wants the analysis done by the patrol districts in his
Area of Operation

14
2
6
8
12
4
10
5
0
7
11
1
9
13
±
3
0 1 2 4 Miles

The Process
• First, develop a layer of just the north patrol
districts
• Also, create layer of just commercial robberies
in the north patrol districts
• Using spatial joins, create a layer with robbery
counts (total and commercial)
• Calculate the CCI for commercial robberies
compared to all robberies

The Concentration Index
CCI
(Comm. Robberies in Dist.
(Sum Comm. Robberies
All Robberies in Dist.)
Sum All Robberies)
• The CCI developes the ratio of commercial
robberies in a patrol district to all the
robberies in that district…
• …and then compares that ratio to the ratio of
all commercial robberies to all robberies in all
the north patrol districts

The Field Calculator

The Results
• Four districts have a greater concentration of
commercial robberies
– Ranging from 18.6% greater to 66.3% greater
• Three districts have lower concentrations
– Ranging from 14% less to 48% less

1.663018
1.465418
1.297896
0.519309
1.186008
0.859856
0.655128
±
Commercial Robberies
0 1 2 4 Miles

Using CCIs to Facilitate Crime Prevention Initiatives
REAL NEIGHBORHOODS

Neighborhood Organizations
• Like most cities, Roanoke has 41 officially
recognized neighborhood organizations
• Some are formal crime watch groups
• Some are commerce/business focused
• Some are neighborhood alliances
• All are concerned with crime in their area of
greatest interest – the neighborhood

±
0 1 2 4 Miles

Generating the Neighborhood
CCI
• For this project, we’re going to generate a CCI
for each neighborhood organization/area
relative to the city as a whole
• First step is to join the Robberies to the
Neighborhood layer
• Next is to calculate the CCI
• Then display the map

The Neighborhoods with Robbery Counts

The CCI Formula
CCI
( Robbery AreaSQMi)
(907
42.89)
• The denominator term is for the city (all
robberies/city area)
• …but if you wanted to compare just the
neighborhood organizations to one another,
change the denominator

The Field Calculator

The Results
Only 10 out of the 41
areas (24.4%) have
a robbery concentration
greater than would be
expected given the
city-wide robbery
distribution.
Five had no robberies
at all (12.2%).

±
0 1 2 4 Miles

Drilling down for a micro-spatial analysis
LOOKING AT A LOCALIZED
PROBLEM

±
0 1 2 4 Miles

Getting started
• Using the “Go to XY” tool, mark the
intersection of interest
• Covert the graphic element to a feature
• Buffer the feature – I’m using 660 feet (an
eighth of a mile)
• The buffer ring will be our polygon feature
• Calculate the area (I used Hawth’s Tools)

Shenandoah & Westwood
TROUTLAND
ROSEMEAD
WILMONT
WESTWOOD
CROWMORR
36TH
ROLLING HILL
SHENANDOAH
BEECH
LUCKETT
BARBERRY
SIGNAL HILL
MULBERRY
JUNIPER
BEECH
NORWAY
NORWAY

Finish it up
• Do a spatial join (or in this case just count the
robberies)
• Calculate the CCI:
CCI
(6 0.049)
(907 42.89)
CCI
122.449
21.147
5.79

Interpretation
• Based on this analysis, the intersection of
Shenandoah and Westwood has 4.8 times
(5.79-1 4.8) as many robberies as would be
expected given the distribution of robberies in
Roanoke

An application to a linear analysis along street segments
PROBLEM STREETS

The Problem
• The commander of the north districts has
identified a residential street segment that
seems to have too many robberies
• The questions is, are there more robberies
along this segment than would be expected
given the linear distribution of robbery in
Roanoke?

PALM
MELROSE
FOREST PARK
OLIVE
LAFAYETTE
STAUNTON
MARYLAND
CRESCENT
HANOVER
25TH
HANOVER
31ST
ORANGE
30TH
29TH
24TH
23RD
SALEM
SALEM
ESSEX
30TH
KEATS
GLENGARY
MILTON
NAHO
SHENANDOAH
DELTA
CENTRE
24TH
24TH
CENTRE
LOUDON
22ND
±
BAKER
BAKER
27TH
JOHNSON
25TH
0 0.05 0.1 0.2 Miles
BAKER

Salem Tpke between 24 th & 30th
• First, identify the street segment(s) of interest
– It may be necessary to form a single segment with
the Dissolve tool
• Do a spatial join, joining the robberies (points)
to the street segment (lines)
– Select the “closest to it” option
• Compute the linear CCI

The Results
CCI
(Robberies close to segment Segment length)
(All Robberies Total network length)
CCI
(22 0.47 miles)
(907 610 miles)
31.4

The Results
CCI
(Robberies close to segment Segment length)
(All Robberies Total network length)
CCI
(22 0.47 miles )
(907 610 miles)
31.4
• This indicates there are 30 times more
robberies along this segment than would be
expected

The Results
• But, to be realistic, most of the 610 miles of
road network don’t have any robberies
• This CCI tends to make it seem there is a more
serious problem along this segment than
might be the actual case
• There is an alternative: create a polygon
buffer and use the concentration per unit of
area

PALM
MELROSE
FOREST PARK
OLIVE
LAFAYETTE
STAUNTON
MARYLAND
CRESCENT
HANOVER
25TH
HANOVER
31ST
ORANGE
30TH
29TH
24TH
23RD
SALEM
SALEM
ESSEX
30TH
KEATS
GLENGARY
MILTON
NAHO
SHENANDOAH
DELTA
CENTRE
24TH
24TH
CENTRE
LOUDON
22ND
±
BAKER
BAKER
27TH
JOHNSON
25TH
0 0.05 0.1 0.2 Miles
BAKER

The Alternative
• Using a 755-foot buffer, the same 22 robberies
are captured
• The area of the buffer calculated
• A new CCI is computed based on the
concentration per unit of area in the buffer
• CCI=(22/0.198845)/(907/42.89)=5.23
• This suggests that there are a little more than
4 times as many robberies in this area

To summarize
• The CCI is a good addition to the analyst’s
toolbox
• It is flexible and adaptable to the problem at
hand
• Applies well to tactical, strategic, and
administrative analysis tasks
• Overcomes some of the problems with
traditional crime measures